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% Title
|
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{\sf %Sans Serif
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%\bf% Serif
|
||||
Expression Invariant Face Recognition with a 3DMM}
|
||||
% Authors
|
||||
{\sf %Sans Serif
|
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% Serif
|
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\vspace{1em}\{Brian.Amberg, Reinhard.Knothe, Thomas.Vetter\}@unibas.ch
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}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\headerbox{Contribution}{name=contribution,column=0,row=0}{
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
{}We introduce a method for expression invariant face recognition. A
|
||||
generative 3D Morphable Model (3DMM) is used to separate identity and
|
||||
expression components. The expression removal results in increased
|
||||
recognition performance, even on difficult datasets, without a decrease in
|
||||
performance on expression-less datasets.
|
||||
|
||||
It is applicable to any kind of input data, and was evaluated here on
|
||||
textureless range scans.
|
||||
\vspace{0.3em}
|
||||
}
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\headerbox{Model}{name=model,column=0,below=contribution}{
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
The Model was learnt from 275 subjects. We used one neutral expression scan
|
||||
per identity and 150 expression scans of a subset of the subjects.
|
||||
|
||||
The identity model is a linear model build from the neutral scans.
|
||||
\begin{align}
|
||||
\VEC f&=\VEC\mu + \MAT M_n\VEC\alpha_n\qquad.
|
||||
\end{align}
|
||||
For each of the 150 expression scans, we calculated an expression vector as
|
||||
the difference between the expression scan and the corresponding neutral
|
||||
scan of that subject. This data is already mode-centered, if we regard the
|
||||
neutral expression as the natural mode of expression data. From these offset
|
||||
vectors an additional expression matrix $\MAT M_e$ was calculated, such that the complete linear Model is
|
||||
\begin{align}
|
||||
\VEC f&=\VEC\mu + \MAT M_n\VEC\alpha_n + \MAT M_e\VEC\alpha_e
|
||||
\end{align}
|
||||
The assumption here is, that the face and expression space are linearly
|
||||
independent, such that each face is represented by a unique set of
|
||||
coefficients.
|
||||
\vspace{0.3em}
|
||||
}
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\headerbox{Fitting}{name=fitting,column=0,below=model}{
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
A Robust Nonrigid ICP method was used to fit the model to the data.
|
||||
Robustness was achieved by iteratively reweighting the correspondences and
|
||||
using hard compatability test for the closest points.
|
||||
|
||||
Fitting was initialized by a simple nose detector and proceeded fully
|
||||
automatic.
|
||||
\vspace{0.3em}
|
||||
}
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\headerbox{Distance Measure}{name=measure,column=0,below=fitting}{
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
The Mahalanobis angle between the identity coefficients $\VEC{\alpha_{n}}$
|
||||
was used for classification.
|
||||
\vspace{0.3em}
|
||||
}
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\headerbox{Expression Neutralization}{name=results neutralization,column=1,row=0}{
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
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|
||||
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|
||||
\path
|
||||
(0,0) node{\includegraphics[width=0.42\linewidth]{D1077}}
|
||||
(1,0) node{\includegraphics[width=0.47\linewidth]{D1077_fit_expression}}
|
||||
(2,0) node{\includegraphics[width=0.47\linewidth]{D1077_fit}}
|
||||
|
||||
(0,1) node{\includegraphics[width=0.42\linewidth]{D1360}}
|
||||
(1,1) node{\includegraphics[width=0.47\linewidth]{D1360_fit_expression}}
|
||||
(2,1) node{\includegraphics[width=0.47\linewidth]{D1360_fit}}
|
||||
|
||||
(0,1.6) node {\smaller a) Target}
|
||||
(1,1.6) node {\smaller b) Fit}
|
||||
(2,1.6) node {\smaller c) Normalized};
|
||||
\end{tikzpicture}
|
||||
\vspace{0.5em}
|
||||
|
||||
Expression normalisation for two scans of the same individual.
|
||||
The robust fitting gives a good estimate (b) of the true face surface given
|
||||
the noisy measurement (a). It fills in holes and removes artifacts using
|
||||
prior knowledge from the face model. The pose and expression normalized faces
|
||||
(c) are used for face recognition.
|
||||
\vspace{0.5em}
|
||||
}
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\headerbox{Funding}{name=funding,column=1,span=2,above=bottom}{
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\smaller
|
||||
\hspace{1em}This work was supported in part by Microsoft Research through the European PhD Scholarship Programme.
|
||||
}
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\headerbox{Results}{name=results,column=1,span=2,below=results neutralization,above=funding}{
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\begin{multicols}{2}
|
||||
The method was evaluated on the GavabDB expression dataset which
|
||||
contains 427 Scans, with 3 neutral scans and 4 expression scans per ID.
|
||||
To test the impact of expression invariance on neutral data we used the
|
||||
UND Dataset from the Face Recognition Great Vendor Test, which contains
|
||||
953 neutral scans with one to eight scans per subject.
|
||||
\end{multicols}\vspace{-1em}
|
||||
\mbox{\hspace{0.3\linewidth}\rule{0.4\linewidth}{1pt}\hspace{0.3\linewidth}}\\
|
||||
\begin{tabular}{cc}
|
||||
\hspace{-0.5em}\scalebox{0.735}{\input{shrec_mncg}} &
|
||||
\hspace{0.5em}\scalebox{0.735}{\input{und_mncg}}
|
||||
\end{tabular}\\
|
||||
% \begin{multicols}{2}
|
||||
{Expression neutralization improves results on the expression dataset
|
||||
without decreasing the accuracy on the neutral testset. Plotted is the
|
||||
ratio of correct answers to the number of possible correct answers.
|
||||
%Note the different scales for the two graphs.
|
||||
%Our approach has a high accuracy on the neutral (UND) dataset.
|
||||
}
|
||||
% \end{multicols}\vspace{-1em}
|
||||
\\\mbox{\hspace{0.3\linewidth}\rule{0.4\linewidth}{1pt}\hspace{0.3\linewidth}}\\
|
||||
\begin{tabular}{cc}
|
||||
\hspace{-0.5em}\scalebox{0.735}{\input{shrec_pr}} &
|
||||
\hspace{0.5em}\scalebox{0.735}{\input{und_pr}}
|
||||
\end{tabular}\\
|
||||
% \begin{multicols}{2}
|
||||
{Plotted are precision and recall for different retrieval depths. The lower
|
||||
precision of the UND database is due to the fact that some queries have no
|
||||
correct answers.}
|
||||
% \end{multicols}\vspace{-1em}
|
||||
\\\mbox{\hspace{0.3\linewidth}\rule{0.4\linewidth}{1pt}\hspace{0.3\linewidth}}\\
|
||||
\begin{tabular}{cc}
|
||||
\hspace{-0.5em}\scalebox{0.735}{\input{shrec_far_frr}} &
|
||||
\hspace{0.5em}\scalebox{0.735}{\input{und_far_frr}}
|
||||
\end{tabular}\\
|
||||
% \begin{multicols}{2}
|
||||
{Impostor detection is reliable, as the minimum distance to a match
|
||||
is smaller than the minimum distance to a nonmatch. }
|
||||
% \end{multicols}
|
||||
\\
|
||||
\vspace{0.5em}
|
||||
}
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\headerbox{Robustness}{name=robustness,column=2,row=0,above=results,span=1}{
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\begin{tikzpicture}[x=0.3333\linewidth,y=-0.42\linewidth]
|
||||
\path [use as bounding box] (-0.5,-0.5) rectangle(2.5,1.7);
|
||||
\path
|
||||
(0,0) node{\includegraphics[width=0.42\linewidth]{D1160}}
|
||||
(1,0) node{\includegraphics[width=0.42\linewidth]{D1425}}
|
||||
(2,0) node{\includegraphics[width=0.42\linewidth]{D1205}}
|
||||
|
||||
(0,1) node{\includegraphics[width=0.28\linewidth]{D1160_fit_expression}}
|
||||
(1,1) node{\includegraphics[width=0.28\linewidth]{D1425_fit_expression}}
|
||||
(2,1) node{\includegraphics[width=0.28\linewidth]{D1205_fit_expression}}
|
||||
|
||||
(1,0.5) node {\smaller a) Target}
|
||||
(1,1.6) node {\smaller b) Robust Reconstruction};
|
||||
\end{tikzpicture}
|
||||
\vspace{0.5em}
|
||||
|
||||
The reconstruction (b) is robust against scans (a) with artifacts, noise, and
|
||||
holes.
|
||||
|
||||
This is achieved by a robust iteratively reweighted ICP algorithm and outlier
|
||||
rejection based on angle comparisions between corresponding points.
|
||||
}
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\headerbox{References}{name=references,column=0,above=bottom}{
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\smaller
|
||||
\vspace{-0.4em}
|
||||
\bibliographystyle{ieee}
|
||||
\renewcommand{\section}[2]{\vskip 0.05em}
|
||||
\begin{thebibliography}{1}\itemsep=-0.01em
|
||||
\setlength{\baselineskip}{0.4em}
|
||||
\bibitem{amberg07:nonrigid}
|
||||
B.~Amberg, S.~Romdhani, T. Vetter.
|
||||
\newblock {O}ptimal {S}tep {N}onrigid {ICP} {A}lgorithms for {S}urface {R}egistration
|
||||
\newblock In {\em Computer Vision and Pattern Recognition 2007}
|
||||
\bibitem{amberg08:recognition}
|
||||
B.~Amberg, R.~Knothe, T. Vetter.
|
||||
\newblock Expression Invariant Face Recognition with a 3D Morphable Model
|
||||
\newblock In {\em Automated Face and Gesture Recognition 2008}
|
||||
\end{thebibliography}
|
||||
}
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\headerbox{Open Questions}{name=questions,column=0,span=1,below=measure,above=references}{
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
While the expression and identity space are linearly independent, there is
|
||||
some expression left in the identity model. This is because a ``neutral''
|
||||
face is interpreted differently by the subjects.
|
||||
|
||||
We investigate learning ``pure'' separated models from our the available ``impure'' data.
|
||||
}
|
||||
|
||||
\end{poster}
|
||||
|
||||
\end{document}
|
||||
@@ -1,5 +0,0 @@
|
||||
\relax
|
||||
\bibstyle{ieee}
|
||||
\bibcite{amberg07:nonrigid}{1}
|
||||
\bibcite{amberg08:recognition}{2}
|
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|
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{\sf %Sans Serif
|
||||
%\bf% Serif
|
||||
Expression Invariant Face Recognition using a 3D Morphable Model}
|
||||
% Authors
|
||||
{\sf %Sans Serif
|
||||
% Serif
|
||||
Brian Amberg\hspace{3em}
|
||||
brian.amberg@unibas.ch\hspace{3em}
|
||||
University of Basel, Switzerland
|
||||
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|
||||
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||||
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\headerbox{Contribution}{name=contribution,column=0,row=0}{
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
{}We introduce a method for expression invariant face recognition. A
|
||||
generative 3D Morphable Model (3DMM) is used to separate identity and
|
||||
expression components. The expression removal results in greatly increased
|
||||
recognition performance, even on difficult datasets, without a decrease in
|
||||
performance on expression-less datasets.
|
||||
|
||||
It is applicable to any kind of input data, and was evaluated here on
|
||||
textureless range scans.
|
||||
}
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\headerbox{Model}{name=model,column=0,below=contribution}{
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
The Model was learnt from 175 subjects. We used one neutral expression scan
|
||||
per identity and 50 expression scans of a subset of the subjects.
|
||||
|
||||
The identity model is a linear model build from the neutral scans.
|
||||
\begin{align}
|
||||
\VEC f&=\VEC\mu + \MAT M_n\VEC\alpha_n\qquad.
|
||||
\end{align}
|
||||
For each of the 50 expression scans, we calculated an expression vector as
|
||||
the difference between the expression scan and the corresponding neutral
|
||||
scan of that subject. This data is already mode-centered, if we regard the
|
||||
neutral expression as the natural mode of expression data. From these offset
|
||||
vectors an additional expression matrix $\MAT M_e$ was calculated, such that the complete linear Model is
|
||||
\begin{align}
|
||||
\VEC f&=\VEC\mu + \MAT M_n\VEC\alpha_n + \MAT M_e\VEC\alpha_e
|
||||
\end{align}
|
||||
The assumption here is, that the face and expression space are linearly
|
||||
independent, such that each face is represented by a unique set of
|
||||
coefficients.
|
||||
}
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\headerbox{Fitting}{name=fitting,column=0,below=model}{
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
A Robust Nonrigid ICP method was used to fit the model to the data.
|
||||
Robustness was achieved by iteratively reweighting the correspondences and
|
||||
using hard compatability test for the closest points.
|
||||
|
||||
Fitting was initialized by a simple nose detector and proceeded fully
|
||||
automatic.
|
||||
}
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\headerbox{Distance Measure}{name=measure,column=0,below=fitting,above=bottom}{
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
The Mahalanobis angle between the identity coefficients $\VEC{\alpha_{n}}$
|
||||
was used for classification.
|
||||
}
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\headerbox{Expression Neutralization}{name=results neutralization,column=1,row=0}{
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\begin{tabular}{@{}c@{ }c@{ }c@{ }c@{}@{ }@{ }c@{ }c@{ }c@{ }c@{ }}
|
||||
\includegraphics[height=0.42\linewidth]{16_1_tgt}&
|
||||
\includegraphics[height=0.42\linewidth]{16_1_expression}&
|
||||
\includegraphics[height=0.42\linewidth]{16_1_neutral}\\[-0.8em]
|
||||
\smaller a) Target & \smaller b) Fit & \smaller c) Normalized\\[0.8em]
|
||||
\includegraphics[height=0.42\linewidth]{16_6_tgt}&
|
||||
\includegraphics[height=0.42\linewidth]{16_6_expression}&
|
||||
\includegraphics[height=0.42\linewidth]{16_6_neutral}\\[-0.8em]
|
||||
\smaller a) Target & \smaller b) Fit & \smaller c) Normalized
|
||||
\end{tabular}
|
||||
Expression normalisation for two scans of the same individual.
|
||||
The robust fitting gives a good estimate (b) of the true face surface given
|
||||
the noisy measurement (a). It fills in holes and removes artifacts using
|
||||
prior knowledge from the face model. The pose and expression normalized faces
|
||||
(c) are used for face recognition.
|
||||
}
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\headerbox{Robustness}{name=robustness,column=1,below=results neutralization,span=1,above=bottom}{
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\begin{tabular}{@{}c@{ }c@{ }c@{ }c@{}}
|
||||
\includegraphics[height=0.42\linewidth]{56_4_tgt}&
|
||||
\includegraphics[height=0.42\linewidth]{23_2_tgt}&
|
||||
\includegraphics[height=0.42\linewidth]{5_6_tgt}\\[-0.8em]
|
||||
& \smaller a) Targets & \\[0.8em]
|
||||
\includegraphics[height=0.42\linewidth]{56_4_expression}&
|
||||
\includegraphics[height=0.42\linewidth]{23_2_expression}&
|
||||
\includegraphics[height=0.42\linewidth]{5_6_expression}\\[-0.8em]
|
||||
& \smaller b) Fits &
|
||||
\end{tabular}
|
||||
The reconstruction (b) is robust against scans (a) with artifacts, noise, and
|
||||
holes.
|
||||
}
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\headerbox{Results}{name=results,column=2,span=2,row=0}{
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\begin{multicols}{2}
|
||||
The method was evaluated on the GavabDB expression dataset which
|
||||
contains 427 Scans, with 3 neutral scans and 4 expression scans per ID.
|
||||
To test the impact of expression invariance on neutral data we used the
|
||||
UND Dataset from the Face Recognition Great Vendor Test, which contains
|
||||
953 neutral scans with one to eight scans per subject.
|
||||
\end{multicols}\vspace{-1em}
|
||||
\mbox{\hspace{0.3\linewidth}\rule{0.4\linewidth}{1pt}\hspace{0.3\linewidth}}\\
|
||||
\begin{tabular}{cc}
|
||||
\hspace{0.5em}\scalebox{0.74}{\input{shrec_MNCG}} &
|
||||
\hspace{0.5em}\scalebox{0.74}{\input{und_MNCG}}
|
||||
\end{tabular}\\
|
||||
% \begin{multicols}{2}
|
||||
{Expression neutralization improves results on the expression dataset
|
||||
without decreasing the accuracy on the neutral testset. Plotted is the
|
||||
ratio of correct answers to the number of possible correct answers.
|
||||
%Note the different scales for the two graphs.
|
||||
%Our approach has a high accuracy on the neutral (UND) dataset.
|
||||
}
|
||||
% \end{multicols}\vspace{-1em}
|
||||
\\\mbox{\hspace{0.3\linewidth}\rule{0.4\linewidth}{1pt}\hspace{0.3\linewidth}}\\
|
||||
\begin{tabular}{cc}
|
||||
\hspace{0.5em}\scalebox{0.74}{\input{shrec_PR}} &
|
||||
\hspace{0.5em}\scalebox{0.74}{\input{und_PR}}
|
||||
\end{tabular}\\
|
||||
% \begin{multicols}{2}
|
||||
{Plotted are precision and recall for different retrieval depths. The lower
|
||||
precision of the UND database is due to the fact that some queries have no
|
||||
correct answers.}
|
||||
% \end{multicols}\vspace{-1em}
|
||||
\\\mbox{\hspace{0.3\linewidth}\rule{0.4\linewidth}{1pt}\hspace{0.3\linewidth}}\\
|
||||
\begin{tabular}{cc}
|
||||
\hspace{0.5em}\scalebox{0.74}{\input{shrec_FARFRR}} &
|
||||
\hspace{0.5em}\scalebox{0.74}{\input{und_FARFRR}}
|
||||
\end{tabular}\\
|
||||
% \begin{multicols}{2}
|
||||
{Impostor detection is reliable, as the minimum distance to a match
|
||||
is smaller than the minimum distance to a nonmatch. }
|
||||
% \end{multicols}
|
||||
\\
|
||||
}%
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\headerbox{Open Questions}{name=questions,column=2,span=1,above=bottom,below=results}{
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
While the expression and identity space are linearly independent, there is
|
||||
some expression left in the identity model. This is because a ``neutral''
|
||||
face is interpreted differently by the subjects. We investigate the
|
||||
possibilty to build an identity/expression separated model without using
|
||||
the data labelling, based on a measure of independence.
|
||||
}%
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\headerbox{Funding}{name=funding,column=3,span=1,above=bottom}{
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\smaller
|
||||
This work was supported in part by Microsoft Research through the European PhD Scholarship Programme.
|
||||
}%
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\headerbox{References}{name=references,column=3,above=funding,below=results}{
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\smaller
|
||||
\vspace{-0.4em}
|
||||
\bibliographystyle{ieee}
|
||||
\renewcommand{\section}[2]{\vskip 0.05em}
|
||||
\begin{thebibliography}{1}\itemsep=-0.01em
|
||||
\setlength{\baselineskip}{0.4em}
|
||||
\bibitem{amberg07:nonrigid}
|
||||
B.~Amberg, S.~Romdhani, T. Vetter.
|
||||
\newblock {O}ptimal {S}tep {N}onrigid {ICP} {A}lgorithms for {S}urface {R}egistration
|
||||
\newblock In {\em CVPR 2007}
|
||||
\bibitem{amberg08:recognition}
|
||||
B.~Amberg, R.~Knothe, T. Vetter.
|
||||
\newblock Expression Invariant Face Recognition with a 3D Morphable Model
|
||||
\newblock In {\em AFGR 2008}
|
||||
\end{thebibliography}
|
||||
}%
|
||||
\end{poster}%
|
||||
%
|
||||
\end{document}
|
||||
@@ -1,121 +0,0 @@
|
||||
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Package color not loaded in conjunction with
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|
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|
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|
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|
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|
||||
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|
||||
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|
||||
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|
||||
Package graphicx or graphics not loaded%
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
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|
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|
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% no textcolor at all
|
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|
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|
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|
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|
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|
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|
||||
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|
||||
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|
||||
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|
||||
\expandafter\def\csname LT5\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT6\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT7\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT8\endcsname{\color{black}}%
|
||||
\fi
|
||||
\fi
|
||||
\setlength{\unitlength}{0.0500bp}%
|
||||
\begin{picture}(6242.40,2016.00)%
|
||||
\gplgaddtomacro\gplbacktext{%
|
||||
\csname LTb\endcsname%
|
||||
\put(129,216){\makebox(0,0)[r]{\strut{} 0}}%
|
||||
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|
||||
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|
||||
\csname LTb\endcsname%
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||||
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|
||||
\csname LTb\endcsname%
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||||
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|
||||
\csname LTb\endcsname%
|
||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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|
||||
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|
||||
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|
||||
\put(3185,-100){\makebox(0,0){\strut{}Recall}}%
|
||||
\put(3185,1746){\makebox(0,0){\strut{}}}%
|
||||
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|
||||
\gplgaddtomacro\gplfronttext{%
|
||||
\csname LTb\endcsname%
|
||||
\put(2505,909){\makebox(0,0)[r]{\strut{}Mahalanobis Distance}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(2505,729){\makebox(0,0)[r]{\strut{}Mahalanobis Angle}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(2505,549){\makebox(0,0)[r]{\strut{}Vertex Distance}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(2505,369){\makebox(0,0)[r]{\strut{}Geodesic}}%
|
||||
}%
|
||||
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|
||||
\put(0,0){\includegraphics{precision_recall}}%
|
||||
\gplfronttext
|
||||
\end{picture}%
|
||||
\endgroup
|
||||
@@ -1,162 +0,0 @@
|
||||
|
||||
#Curve 0 of 1, 158 points
|
||||
#x y type
|
||||
0 9.56614 i
|
||||
1 4.65213 i
|
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|
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|
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20 4.40897 i
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|
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|
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||||
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|
||||
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|
||||
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|
||||
40 4.37076 i
|
||||
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|
||||
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|
||||
43 4.36247 i
|
||||
44 4.58017 i
|
||||
45 4.62716 i
|
||||
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|
||||
47 4.46866 i
|
||||
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|
||||
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|
||||
50 4.4299 i
|
||||
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|
||||
52 4.34516 i
|
||||
53 4.42074 i
|
||||
54 4.54043 i
|
||||
55 4.52633 i
|
||||
56 4.50612 i
|
||||
57 4.55656 i
|
||||
58 4.37762 i
|
||||
59 4.49876 i
|
||||
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|
||||
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|
||||
62 4.75925 i
|
||||
63 4.72314 i
|
||||
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|
||||
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|
||||
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|
||||
67 4.58217 i
|
||||
68 4.694 i
|
||||
69 4.43123 i
|
||||
70 4.45953 i
|
||||
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|
||||
72 4.65747 i
|
||||
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|
||||
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|
||||
75 4.74689 i
|
||||
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|
||||
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|
||||
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|
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|
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|
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|
||||
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|
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|
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|
||||
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|
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|
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|
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|
||||
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|
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|
||||
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||||
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|
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|
||||
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|
||||
157 0.496333 i
|
||||
|
||||
@@ -1,344 +0,0 @@
|
||||
\documentclass{vgtc} % final (conference style)
|
||||
\usepackage{amsmath}
|
||||
\usepackage{relsize}
|
||||
%\documentclass[review]{vgtc} % review
|
||||
%\documentclass[widereview]{vgtc} % wide-spaced review
|
||||
%\documentclass[preprint]{vgtc} % preprint
|
||||
%\documentclass[electronic]{vgtc} % electronic version
|
||||
\newif\ifGPblacktext
|
||||
\GPblacktexttrue
|
||||
|
||||
%% Uncomment one of the lines above depending on where your paper is
|
||||
%% in the conference process. ``review'' and ``widereview'' are for review
|
||||
%% submission, ``preprint'' is for pre-publication, and the final version
|
||||
%% doesn't use a specific qualifier. Further, ``electronic'' includes
|
||||
%% hyperreferences for more convenient online viewing.
|
||||
|
||||
%% Please use one of the ``review'' options in combination with the
|
||||
%% assigned online id (see below) ONLY if your paper uses a double blind
|
||||
%% review process. Some conferences, like IEEE Vis and InfoVis, have NOT
|
||||
%% in the past.
|
||||
|
||||
%% Figures should be in CMYK or Grey scale format, otherwise, colour
|
||||
%% shifting may occur during the printing process.
|
||||
|
||||
%% These three lines bring in essential packages: ``mathptmx'' for Type 1
|
||||
%% typefaces, ``graphicx'' for inclusion of EPS figures. and ``times''
|
||||
%% for proper handling of the times font family.
|
||||
|
||||
\usepackage{bm}
|
||||
\usepackage{mathptmx}
|
||||
\usepackage{graphicx}
|
||||
\usepackage{times}
|
||||
|
||||
|
||||
\newcommand*{\SET}[1] {\ensuremath{\mathcal{#1}}}
|
||||
\newcommand*{\MAT}[1] {\ensuremath{\mathbf{#1}}}
|
||||
\newcommand*{\VEC}[1] {\ensuremath{\bm{#1}}}
|
||||
\newcommand*{\CONST}[1]{\ensuremath{\mathit{#1}}}
|
||||
\newcommand*{\norm}[1]{\mathopen\| #1 \mathclose\|}% use instead of $\|x\|$
|
||||
\newcommand*{\abs}[1]{\mathopen| #1 \mathclose|}% use instead of $\|x\|$
|
||||
\newcommand*{\absLR}[1]{\left| #1 \right|}% use instead of $\|x\|$
|
||||
\newcommand*{\normLR}[1]{\left\| #1 \right\|}% use instead of $\|x\|$
|
||||
|
||||
%% We encourage the use of mathptmx for consistent usage of times font
|
||||
%% throughout the proceedings. However, if you encounter conflicts
|
||||
%% with other math-related packages, you may want to disable it.
|
||||
|
||||
%% If you are submitting a paper to a conference for review with a double
|
||||
%% blind reviewing process, please replace the value ``0'' below with your
|
||||
%% OnlineID. Otherwise, you may safely leave it at ``0''.
|
||||
\onlineid{0}
|
||||
|
||||
%% declare the category of your paper, only shown in review mode
|
||||
\vgtccategory{Research}
|
||||
|
||||
%% allow for this line if you want the electronic option to work properly
|
||||
\vgtcinsertpkg
|
||||
|
||||
%% In preprint mode you may define your own headline.
|
||||
%\preprinttext{To appear in an IEEE VGTC sponsored conference.}
|
||||
|
||||
%% Paper title.
|
||||
|
||||
\title{SHREC'08 Entry: Shape Based Face Recognition with a Morphable Model}
|
||||
|
||||
%% This is how authors are specified in the conference style
|
||||
|
||||
%% Author and Affiliation (single author).
|
||||
%%\author{Roy G. Biv\thanks{e-mail: roy.g.biv@aol.com}}
|
||||
%%\affiliation{\scriptsize Allied Widgets Research}
|
||||
|
||||
%% Author and Affiliation (multiple authors with single affiliations).
|
||||
%%\author{Roy G. Biv\thanks{e-mail: roy.g.biv@aol.com} %
|
||||
%%\and Ed Grimley\thanks{e-mail:ed.grimley@aol.com} %
|
||||
%%\and Martha Stewart\thanks{e-mail:martha.stewart@marthastewart.com}}
|
||||
%%\affiliation{\scriptsize Martha Stewart Enterprises \\ Microsoft Research}
|
||||
|
||||
%% Author and Affiliation (multiple authors with multiple affiliations)
|
||||
\author{Brian Amberg\thanks{e-mail: \{brian.amberg, reinhard.knothe, thomas.vetter\}@unibas.ch} %
|
||||
\and Reinhard Knothe$^*$%
|
||||
\and Thomas Vetter$^*$}%
|
||||
|
||||
%% Abstract section.
|
||||
\abstract{
|
||||
We present a method for face recognition by fitting a 3D Morphable Model to
|
||||
shape data. Fitting is done with a a robust nonrigid ICP algorithm. For
|
||||
recognition, it is possible to use either the fitted model parameters, or the
|
||||
correspondences induced by the model. We compare different similarity measures,
|
||||
and show that a 3D Morphable Model allows very robust retrieval results.
|
||||
} % end of abstract
|
||||
|
||||
%% ACM Computing Classification System (CCS).
|
||||
%% See <http://www.acm.org/class/1998/> for details.
|
||||
%% The ``\CCScat'' command takes four arguments.
|
||||
|
||||
\CCScatlist{
|
||||
\CCScat{I.4.8}{Image Processing and Computer Vision}{Scene Analysis}{Object Recognition, Surface Fitting, Range Data}
|
||||
%\CCScat{I.4.7}{Image Processing and Computer Vision}{Feature Measurement}{Size and Shape, Feature representation}
|
||||
I.4.7: Feature Measurement---Size and Shape, Feature representation
|
||||
% \CCScat{I.4.9}{Image Processing and Computer Vision}{Applications}{}
|
||||
I.4.9: Applications
|
||||
% \CCScat{I.4.10}{Image Processing and Computer Vision}{Image Representation}{Statistical}
|
||||
\CCScat{I.5.1}{Pattern Recognition}{Models}{Statistical}
|
||||
% \CCScat{I.5.1}{}{Applications}{Computer Vision}
|
||||
}
|
||||
|
||||
%% Copyright space is enabled by default as required by guidelines.
|
||||
%% It is disabled by the 'review' option or via the following command:
|
||||
% \nocopyrightspace
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
%%%%%%%%%%%%%%%%%%%%%% START OF THE PAPER %%%%%%%%%%%%%%%%%%%%%%
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
|
||||
\begin{document}
|
||||
|
||||
%% The ``\maketitle'' command must be the first command after the
|
||||
%% ``\begin{document}'' command. It prepares and prints the title block.
|
||||
|
||||
%% the only exception to this rule is the \firstsection command
|
||||
\firstsection{Introduction}
|
||||
|
||||
\maketitle
|
||||
|
||||
We tackle the task of textureless 3D face recognition. The system is fully
|
||||
automatic and can handle the typical artifacts of 3D scanners, namely outliers
|
||||
and missing regions. Face recognition in this setting is a difficult task, and
|
||||
difficult tasks need strong prior knowledge. To introduce the prior knowledge
|
||||
we use a 3D Morphable Model (3DMM)~\cite{blanz:model}, which is a generative
|
||||
statistical model of 3D faces. 3DMM have been applied successfully for face
|
||||
recognition on different modalities. The most challenging setting is
|
||||
recognition from single images under varying light and illumination. This was
|
||||
adressed by~\cite{blanz03:face_rec,romdhani:recognition}. There a 3DMM with
|
||||
shape, texture and illumination model was fit to probe and gallery images. As
|
||||
the model separates shape and albedo parameters from pose and lighting, it
|
||||
enables pose and lighting invariant recognition. In~\cite{amberg07:stereo} a
|
||||
similar approach was used to fit a pure shape model to stereo images, also
|
||||
enabling recognition by correlating the shape parameters. We use the same
|
||||
approach for shape based face recognition. We fit a 3DMM build from 170
|
||||
subjects with neutral expressions to the \hbox{gavabDB}~\cite{gavabdb} database, and
|
||||
compare different distance measures which can be derived from the model fit.
|
||||
|
||||
An alternative to fitting a generative model is to align the probe to each
|
||||
example in the database using e.g.\ ICP~\cite{bowyer05:icp_recognition}. But
|
||||
comparing the probe directly to every gallery image has the disadvantage of
|
||||
scaling linearly with the number of entries in the gallery, while for a model
|
||||
based approach only a single fit to the probe is necessary, and the comparision
|
||||
to the database can then be performed by a distance measure in the lower
|
||||
dimensional space of registered faces.
|
||||
|
||||
Another interesting model-less approach~\cite{bronstein05:face_rec} compares
|
||||
surface by the distribution of geodesics, which stays constant for nonrigidly
|
||||
deforming (but not stretching or tearing) objects. This approach is difficult
|
||||
to apply in this setting though, as the scanning produces holes, disconnected
|
||||
regions and strong noise, which can best be handled by a method which uses
|
||||
specific information about the object class.
|
||||
|
||||
\section{Fitting}
|
||||
\begin{figure}
|
||||
\vspace{-0.5em}
|
||||
\begin{tabular}{@{ }c@{ }c@{ }c@{ }c@{}}
|
||||
\includegraphics[height=0.35\linewidth]{tgt}&
|
||||
\includegraphics[height=0.35\linewidth]{src}&
|
||||
\includegraphics[height=0.35\linewidth]{step}&
|
||||
\includegraphics[height=0.35\linewidth]{extrapolated}\\[-0.8em]
|
||||
\smaller a) Target & \smaller b) Fit & \smaller (a) + (b) & \smaller c) Deformed
|
||||
\end{tabular}
|
||||
\vspace{-1em}
|
||||
\caption{The robust fitting gives a good estimate (b) of the true face surface given
|
||||
the noisy measurement (a). It fills in holes and removes artifacts using prior
|
||||
knowledge from the face model. The fitted shape plus the exact
|
||||
correspondences found can be used to extrapolate the image by a robust
|
||||
poisson deformation (c).}
|
||||
\label{fig:fitting}
|
||||
\end{figure}
|
||||
The fitting algorithm used in this paper is a variant of the nonrigid ICP work
|
||||
in~\cite{amberg07:nicp}. It is a robust iterated fitting algorithm. Like other
|
||||
ICP methods, it is a local optimization method, which does not guarantee
|
||||
convergence to the global mimimum, but is dependent on the initialization. It
|
||||
consists of the following steps
|
||||
\begin{itemize}
|
||||
\item Iterate over a sequence of regularization values $\theta_1>\dots>\theta_N$:
|
||||
\begin{itemize}
|
||||
\item Repeat until convergence:
|
||||
\begin{enumerate}
|
||||
\item Find candidate correspondences by searching for the closest compatible
|
||||
point for each model vertex.
|
||||
\item Weight the correspondences by their distance using a robust estimator.
|
||||
\item Fit the 3DMM to these correspondences using a
|
||||
regularization strength of $\theta_i$\label{step_fit}.
|
||||
\item Continue with the lower $\theta_{i+1}$ if the median change in vertex
|
||||
position is smaller than a threshold.
|
||||
\end{enumerate}
|
||||
\end{itemize}
|
||||
\end{itemize}
|
||||
The search for the closest compatible point takes only points into account which
|
||||
have conforming normals.
|
||||
%The search is sped up by organizing the target scan in a space partitioning tree made up of spheres.
|
||||
%The robust weighting function used in this paper is
|
||||
%\emph{TODO: Check, what I have really done. I kind of hacked it.}
|
||||
%\begin{align}
|
||||
% w(r) = \left\{\begin{array}{ll} 1+\frac{m_1-r}{m_1}l_0 & \text{if }r<m_1\\\frac{1}{m_2(r-m_1)+1} &\text{otherwise}\end{array}\right.
|
||||
%\end{align}
|
||||
%where $m_1$ was set to $3$mm and $m_2$ to $20$mm. This leads to a robust
|
||||
%estimation, which discards outliers.
|
||||
Note, that it is necessary to balance robustness and regularization, as the
|
||||
right balance depends on the noise characteristic of the data. Suitable values
|
||||
were determined manually for a single scan and kept constant for all
|
||||
experiments. In step~\ref{step_fit} the 3DMM is fit to 3D-3D point
|
||||
correspondences. This is done with a gauss-newton least squares optimization,
|
||||
using an analytic Jacobian and first-order Hessian.
|
||||
|
||||
As the database is pose normalized, we initialize the registration such that
|
||||
the tip of the nose and pose coincides. This initialization is good enough to
|
||||
fit the complete database fully automatic. For non pose-normalized databases,
|
||||
we would either need three landmarks, or -- to keep the algorithm fully
|
||||
automatic -- repeated random initialization.
|
||||
|
||||
\section{Retrieval}
|
||||
We evaluated four different distance measures, see Figure~\ref{fig:precision} for an overview over their precision recall characteristics.
|
||||
|
||||
\subsection{Model Based Measures}
|
||||
We begin with measures which are acting in the parameter space of the model.
|
||||
These have the advantage of being extremely cheap to calculate, once the model
|
||||
has been fit.
|
||||
\begin{figure}
|
||||
\hspace{2.5em}\scalebox{0.68}{\input{precision_recall}}
|
||||
\vspace{-0.7em}
|
||||
\caption{Measures in Mahalanobis Space outperform vertex based measures.}
|
||||
\label{fig:precision}
|
||||
\end{figure}
|
||||
\begin{figure}
|
||||
\vspace{-1.0em}
|
||||
\hspace{2.5em}\scalebox{0.68}{\input{impostor}}
|
||||
\vspace{0.1em}
|
||||
\caption{Impostor detection is reliable, as the minimum distance to a match is smaller than the minimum distance to a nonmatch.}
|
||||
\label{fig:impostor}
|
||||
\end{figure}
|
||||
|
||||
\subsubsection{Mahalanobis distance of shape coefficients}
|
||||
%\paragraph{Mahalanobis distance of shape coefficients}
|
||||
The first method calculates the distance between two vectors of shape
|
||||
coefficients $\VEC \alpha_1$ and $\VEC\alpha_2$ expressed in Mahalanobis space
|
||||
as
|
||||
\begin{align}
|
||||
s_1(\VEC\alpha_1, \VEC\alpha_2) &= \norm{\VEC\alpha_1 - \VEC\alpha_2}\qquad.
|
||||
\end{align}
|
||||
|
||||
\subsubsection{Angular distance of shape coefficients}
|
||||
In face space, caricatures lie along the rays from the origin.
|
||||
Mapping all caricatured versions of a face onto a canonical face gives a method
|
||||
which has proven to have very high recognition rates~\cite{blanz03:face_rec}.
|
||||
To do this we use the angle between the shape coefficients in Mahalanobis space
|
||||
as the distance measure:
|
||||
\begin{align}
|
||||
s_2(\VEC\alpha_1, \VEC\alpha_2) &= \arccos\left(\frac{\VEC\alpha_1^T\VEC\alpha_2}{\norm{\VEC\alpha_1}\norm{\VEC\alpha_2}}\right)\qquad.
|
||||
\end{align}
|
||||
For the angular measure shown in Figure~\ref{fig:impostor} the distribution of
|
||||
distances towards the first match and the first nonmatch in the database. This
|
||||
shows, that by choosing a suitable threshold it is possible to perform face
|
||||
recognition with impostors, where we decide if the identity is in the database
|
||||
or not.
|
||||
|
||||
These two measures give similar results, but the caricature invariance of the
|
||||
angular distance improves recall a bit. This tells us, that in face space, the
|
||||
direction alone codes the identity.
|
||||
|
||||
\subsection{Shape Based Measures}
|
||||
The second type of measures acts in vertex space. If we want to compare
|
||||
two model instances, it does not make much sense to measure in vertex space
|
||||
instead of parameter space, as there is a one to one mapping between the spaces
|
||||
and the parameter space is of much lower dimensionality. But in our case we do
|
||||
have additional information which can not be expressed by the model.
|
||||
After fitting, some residual will remain, which is caused by three reasons. 1)
|
||||
The individuals used to train the model were not from the gallery, and we can
|
||||
not span the complete face space with 170 training examples. 2) The probe
|
||||
images have expressions, while the database was build using neutral expressions.
|
||||
3) The aquisition process introduces noise. Therefore, we add more
|
||||
flexibility to the model by allowing smooth nonrigid deformations of the final
|
||||
fit to minimize the remaining residual. This is achieved by robustly fitting a
|
||||
poisson deformation with soft boundary and zero right hand side, where the
|
||||
boundary is given by the correspondences found by the fitting algorithm, and
|
||||
the deformed shape is the fitted head. Results can be seen in
|
||||
Figure~\ref{fig:fitting}. With these correspondence established we can use
|
||||
different distance measures.
|
||||
|
||||
\subsubsection{Distance}
|
||||
Denote the $N$ vertices of the registered scan $i$ as $\VEC v^i_1,\dots,\VEC
|
||||
v^i_N$. We use the distance after removing the rigid transformation, measuring
|
||||
only in a mask defined on the model, which includes the parts which are visible
|
||||
in most of the scans. We compute
|
||||
\begin{align}
|
||||
s_3(\MAT v^1, \MAT v^2) &= \min_{\MAT R,\VEC t} \sum_i \norm{\MAT R\VEC v^1_i + \VEC t - \VEC v^2_i}\qquad.
|
||||
\end{align}
|
||||
where $\MAT R,\VEC t$ describe a similarity transform.
|
||||
%
|
||||
While this measure is straight forward, the recognition results are
|
||||
unsatisfying. The scaling of face space which is learned from the example faces
|
||||
results in an improved clustering of scans, which enables better classification
|
||||
than comparisions in the original vertex space.
|
||||
|
||||
\subsubsection{Geodesics}
|
||||
Inspired by~\cite{bronstein05:face_rec} we tried a geodesic based measure,
|
||||
which should be invariant against expression changes. We classify by comparing
|
||||
the distances of a selected set of vertices, which were assumed not to change
|
||||
under expressions. Denote the selected vertex pairs by $\SET P$. Note that
|
||||
this is different from~\cite{bronstein05:face_rec}, as we have already brought
|
||||
the meshes into correspondence during fitting. The measure is then
|
||||
\begin{align}
|
||||
s_4(\MAT v^1, \MAT v^2) &= \sum_{(i,j)\in \SET P} \absLR{ \norm{v^1_i - v^1_j} - \norm{v^2_i - v^2_j}}
|
||||
\end{align}
|
||||
Experiments with different sets of distances showed that the best
|
||||
classification results were achieved by selecting all neighboring edges of the
|
||||
model in the face area. Still, exactly because this method introduces some
|
||||
invariance, it also reduces the precision in the retrieval experiments. Also,
|
||||
it does not incorporate the knowledge about face space, which was exploited in
|
||||
the first two methods.
|
||||
|
||||
\section{Conclusion}
|
||||
We have shown that 3D Morphable Models provide a valuable tool for face
|
||||
recognition with 98.8\% recognition rate on this database. The strong prior
|
||||
knowledge allows robust handling of noisy data. Four distance measures
|
||||
were compared, and it turns out that the angular distance in Mahalanobis space
|
||||
is the most accurate classifier. It was noticably better than measuring
|
||||
the difference between the registered scans. This is because the face space
|
||||
learned from our training examples is constructed such that the identities are
|
||||
better separated than in vertex space.
|
||||
|
||||
In the future we wish to make the system expression invariant, by using a
|
||||
model which separates expression and identity. As we do establish
|
||||
correspondence between the model and the scans, it is trivial to add image
|
||||
based classification for datasets where a calibrated photo is available, by
|
||||
comparing the rectified textures.
|
||||
|
||||
%% if specified like this the section will be ommitted in review mode
|
||||
\acknowledgements{The authors wish to thank P.\ Paysan for the data
|
||||
acquisition. This work was supported in part by a grant from Microsoft
|
||||
Research and the Swiss National Science Foundation (200021-103814 and NCCR COME project 5005-66380).}
|
||||
|
||||
\bibliographystyle{abbrv}
|
||||
%%use following if all content of bibtex file should be shown
|
||||
%\nocite{*}
|
||||
\bibliography{shrec_08}
|
||||
\end{document}
|
||||
@@ -1,482 +0,0 @@
|
||||
\documentclass[10pt,twocolumn,letterpaper]{article}
|
||||
|
||||
\usepackage{relsize}
|
||||
\usepackage{fg}
|
||||
\usepackage{times}
|
||||
\usepackage{epsfig}
|
||||
\usepackage{graphicx}
|
||||
\usepackage{amsmath}
|
||||
\usepackage{amssymb}
|
||||
\usepackage{bm}
|
||||
\usepackage{textcomp}
|
||||
\renewcommand*{\d}{\mathrm{d}}
|
||||
\newcommand*{\dd}{\partial}
|
||||
\newcommand*{\diffp}[2]{\ensuremath{\frac{\dd #1}{\dd #2}}}
|
||||
\newcommand*{\diffpp}[3]{\ensuremath{\frac{\dd^2 #1}{\dd #2 \dd #3}}}
|
||||
\newcommand*{\diffppp}[4]{\ensuremath{\frac{\dd^3 #1}{\dd #2 \dd #3 \dd #4}}}
|
||||
\newcommand*{\difff}[2]{\ensuremath{\frac{\d #1}{\d #2}}}
|
||||
\newcommand*{\diffff}[3]{\ensuremath{\frac{\d^2 #1}{\d #2 \d #3}}}
|
||||
\newcommand*{\difffp}[3]{\ensuremath{\frac{\dd\d #1}{\d #2 \dd #3}}}
|
||||
\newcommand*{\difffpp}[4]{\ensuremath{\frac{\dd^2\d #1}{\d #2 \dd #3 \dd #4}}}
|
||||
|
||||
\newcommand{\Matrix}[1]{\begin{bmatrix} #1 \end{bmatrix}}
|
||||
\newcommand{\Vector}[1]{\Matrix{#1}}
|
||||
\newcommand*{\SET}[1] {\ensuremath{\mathcal{#1}}}
|
||||
\newcommand*{\MAT}[1] {\ensuremath{\mathbf{#1}}}
|
||||
\newcommand*{\VEC}[1] {\ensuremath{\bm{#1}}}
|
||||
\newcommand*{\CONST}[1]{\ensuremath{\mathit{#1}}}
|
||||
\newcommand*{\norm}[1]{\mathopen\| #1 \mathclose\|}% use instead of $\|x\|$
|
||||
\newcommand*{\abs}[1]{\mathopen| #1 \mathclose|}% use instead of $\|x\|$
|
||||
\newcommand*{\absLR}[1]{\left| #1 \right|}% use instead of $\|x\|$
|
||||
\newcommand*{\normLR}[1]{\left\| #1 \right\|}% use instead of $\|x\|$
|
||||
% Include other packages here, before hyperref.
|
||||
|
||||
% If you comment hyperref and then uncomment it, you should delete
|
||||
% egpaper.aux before re-running latex. (Or just hit 'q' on the first latex
|
||||
% run, let it finish, and you should be clear).
|
||||
\usepackage[pagebackref=true,breaklinks=true,letterpaper=true,colorlinks,bookmarks=false]{hyperref}
|
||||
|
||||
|
||||
\fgfinalcopy % *** Uncomment this line for the final submission
|
||||
|
||||
\def\httilde{\mbox{\tt\raisebox{-.5ex}{\symbol{126}}}}
|
||||
|
||||
% Pages are numbered in submission mode, and unnumbered in camera-ready
|
||||
\iffgfinal\pagestyle{empty}\fi
|
||||
\begin{document}
|
||||
|
||||
%%%%%%%%% TITLE
|
||||
\title{Expression Invariant 3D Face Recognition with a Morphable Model}
|
||||
|
||||
\author{Brian Amberg\\
|
||||
{\tt\small brian.amberg@unibas.ch} \and
|
||||
Reinhard Knothe\\
|
||||
{\tt\small reinhard.knothe@unibas.ch} \and
|
||||
Thomas Vetter\\
|
||||
{\tt\small thomas.vetter@unibas.ch}
|
||||
}
|
||||
|
||||
\maketitle
|
||||
% \thispagestyle{empty}
|
||||
|
||||
%%%%%%%%% ABSTRACT
|
||||
\begin{abstract}
|
||||
We present an expression-invariant method for face recognition by fitting an
|
||||
identity/expression separated 3D Morphable Model to shape data. The
|
||||
expression model greatly improves recognition and retrieval rates in the
|
||||
uncooperative setting, while achieving recognition rates on par with the best
|
||||
recognition algorithms in the face recognition great vendor test. The
|
||||
fitting is performed with a robust nonrigid ICP algorithm. It is able to
|
||||
perform face recognition in a fully automated scenario and on noisy data.
|
||||
The system was evaluated on two datasets, one
|
||||
with a high noise level and strong expressions, and the standard UND range
|
||||
scan database, showing that while expression invariance increases recognition
|
||||
and retrieval performance for the expression dataset, it does not decrease
|
||||
performance on the neutral dataset. The high recognition rates are achieved
|
||||
even with a purely shape based method, without taking image data into
|
||||
account.
|
||||
\end{abstract}
|
||||
|
||||
%%%%%%%%% BODY TEXT
|
||||
\section{Introduction}
|
||||
We present a system which is using shape information from a 3D scanner to
|
||||
perform automated face recognition. The main novelty of the system is its
|
||||
invariance to expressions. The system is tested on two
|
||||
public datasets. It is fully automatic and can handle the typical artifacts of
|
||||
3D scanners, namely outliers and missing regions. Face recognition in this
|
||||
setting is a difficult task, and difficult tasks benefit from strong prior knowledge.
|
||||
To introduce the prior knowledge we use a 3D Morphable Model
|
||||
(3DMM)~\cite{blanz:model}, which is a generative statistical model of 3D faces.
|
||||
3DMMs have been applied successfully for face recognition on different
|
||||
modalities. The most challenging setting is recognition from single images
|
||||
under varying light and illumination. This was adressed
|
||||
by~\cite{blanz03:face_rec,romdhani:recognition}. There, a 3DMM with shape,
|
||||
texture and illumination model was fit to probe and gallery images. As the
|
||||
model separates shape and albedo parameters from pose and lighting, it enables
|
||||
pose and lighting-invariant recognition. We use the same idea for
|
||||
expression-invariant face recognition from 3D shape. We fit an identity/expression
|
||||
separating
|
||||
3DMM~\cite{blanz03:expression} to shape data and normalize the
|
||||
resulting face by removing the pose and expression components. See
|
||||
Figure~\ref{fig:fitting} for an example of expression normalization. The
|
||||
expression and pose normalized data allows then efficient and effective
|
||||
recognition. A 3D MM has been fitted to range data before~\cite{blanz07:range}
|
||||
and the results were even evaluated on part of the UND database. Our approach
|
||||
differs from this work in the fitting method employed, which is independent of
|
||||
the acquisition device, and in the use of an expression model to improve face
|
||||
recognition. Additionally, our method is fully automatic,
|
||||
while~\cite{blanz07:range} needed seven manually selected landmarks.
|
||||
|
||||
\begin{figure}
|
||||
\vspace{-0.5em}
|
||||
\begin{tabular}{@{ }c@{ }c@{ }c@{ }c@{}}
|
||||
\includegraphics[height=0.42\linewidth]{16_1_tgt}&
|
||||
\includegraphics[height=0.42\linewidth]{16_1_expression}&
|
||||
\includegraphics[height=0.42\linewidth]{16_1_neutral}\\[-0.8em]
|
||||
\smaller a) Target & \smaller b) Fit & \smaller c) Normalized\\[0.8em]
|
||||
\includegraphics[height=0.42\linewidth]{16_6_tgt}&
|
||||
\includegraphics[height=0.42\linewidth]{16_6_expression}&
|
||||
\includegraphics[height=0.42\linewidth]{16_6_neutral}\\[-0.8em]
|
||||
\smaller a) Target & \smaller b) Fit & \smaller c) Normalized
|
||||
\end{tabular}
|
||||
\vspace{0.5em}
|
||||
\caption{Expression normalisation for two scans of the same individual.
|
||||
The robust fitting gives a good estimate (b) of the true face surface given
|
||||
the noisy measurement (a). It fills in holes and removes artifacts using
|
||||
prior knowledge from the face model. The pose and expression normalized faces
|
||||
(c) are used for face recognition.
|
||||
}
|
||||
\label{fig:fitting}
|
||||
\end{figure}
|
||||
Expression-invariant recognition for shape data was also approached in
|
||||
\cite{xiaoguang06:face_matching}, where a person specific 3D Morphable
|
||||
Expression Model was learned for each subject in the gallery. In contrast, we
|
||||
are using a general 3DMM learned from an independent database of face shapes
|
||||
which can be applied without any relearning to a new scan. This makes the
|
||||
enrollment phase trivial and the recognition phase effectively constant in the
|
||||
size of the gallery while still being accurate. We have to fit just one
|
||||
model to the probe, which can then be compared efficiently to
|
||||
the enrolled subjects, by comparing their coefficients in the low dimensional
|
||||
face space. While the number of comparisions is still at most linear in the
|
||||
number of examples (and can be made sublinear with an indexing method) the time
|
||||
it takes to compare coefficients in face space is neglectible compared to
|
||||
fitting time.
|
||||
%
|
||||
Model-less approaches which align the probe to each example in the database
|
||||
using e.g.\ ICP~\cite{bowyer05:icp_recognition} suffer from the same problem
|
||||
as~\cite{xiaoguang06:face_matching}.
|
||||
Because the probe has to be aligned with each gallery scan these methods scale
|
||||
linearly in the gallery size, While our model based approach needs only a
|
||||
single fit to the probe.
|
||||
|
||||
Another interesting model-less approach~\cite{bronstein05:face_rec} compares
|
||||
surface by the distribution of geodesics, which stays constant for nonrigidly
|
||||
deforming (but not stretching or tearing) objects. This approach is difficult
|
||||
to apply in this setting though, as the scanning produces holes, disconnected
|
||||
regions and strong noise, which can best be handled by a method which uses
|
||||
specific information about the object class.
|
||||
|
||||
\section{Model}
|
||||
A PCA model~\cite{blanz:model} built from 175 subjects was used. It was build
|
||||
from one neutral expression face scan per identity and 50 expression scans of a
|
||||
subset of the subjects. The data was registered with a modification
|
||||
of~\cite{amberg07:nicp}.
|
||||
The identity model consists of a mean shape $\VEC\mu$ and a matrix of offset
|
||||
vectors $\MAT M_n$ such that a new face instance $\VEC f$ is generated from a
|
||||
vector of coefficients $\VEC\alpha_n$ as
|
||||
\begin{align}
|
||||
\VEC f&=\VEC\mu + \MAT M_n\VEC\alpha_n\qquad.
|
||||
\end{align}
|
||||
The model is constructed such that the $\alpha_i$ are independently normally
|
||||
distributed with zero mean and unit variance under the standard assumption of a
|
||||
Gaussian distribution of the data. This was done by performing PCA
|
||||
on the data matrix built from the mean free shape vectors.
|
||||
Additionally, for each of the 50 expression scans, we calculated an expression
|
||||
vector as the difference between the expression scan and the corresponding
|
||||
neutral scan of that subject.
|
||||
This data is already mode-centered, if we regard the neutral
|
||||
expression as the natural mode of expression data. On these offset vectors
|
||||
again PCA was applied to get an expression matrix $\MAT M_e$ and
|
||||
expression coefficients $\VEC\alpha_e$, such that the complete expression model is
|
||||
\begin{align}
|
||||
\VEC f&=\VEC\mu + \MAT M_n\VEC\alpha_n + \MAT M_e\VEC\alpha_e
|
||||
=\VEC\mu + \MAT M\VEC\alpha\qquad,\\
|
||||
\MAT M &= \Matrix{\MAT M_n &|& \MAT M_e} \qquad \VEC\alpha = \Matrix{\VEC\alpha_n \\ \VEC\alpha_e}\qquad.
|
||||
\end{align}
|
||||
The basic assumption of this paper is, that the face and expression space are
|
||||
linearly independent, such that each face is represented by a unique set of
|
||||
coefficients. While the resulting expression and identity matrices are not
|
||||
perfectly orthogonal, they do have little overlap, which together with the
|
||||
regularisation employed is sufficient for this application. We assume, that the
|
||||
overlap between the spaces is due to the fact that it is impossible to aquire
|
||||
perfectly consistent neutral expressions.
|
||||
|
||||
We use the registered scans and a mirrored version of each registered scan to
|
||||
increase the variability of the model. This allows us to calculate a model with
|
||||
more than 175 neutral coefficients.
|
||||
|
||||
\section{Fitting}
|
||||
The fitting algorithm used in this paper is a variant of the nonrigid ICP work
|
||||
in~\cite{amberg07:nicp}. The main difference, is that the deformation model is
|
||||
a statistical model and the optimisation in each step is an iterative method,
|
||||
which finds the minimum of a convex function. Additionally, as it is applied on
|
||||
noisy data (see Figure~\ref{fig:difficult}), we included a more elaborate robust weighting term. Like other
|
||||
ICP methods, it is a local optimization method, which does not guarantee
|
||||
convergence to the global mimimum, but is dependent on the initialization. It
|
||||
consists of the following steps
|
||||
\begin{itemize}
|
||||
\item Iterate over regularization values $\theta_1>\dots>\theta_N$:
|
||||
\begin{itemize}
|
||||
\item Repeat until convergence:
|
||||
\begin{enumerate}
|
||||
\item Find candidate correspondences by searching for the closest compatible
|
||||
point for each model vertex.
|
||||
\item Weight the correspondences by their distance using a robust estimator.
|
||||
\item Fit the 3DMM to these correspondences using a
|
||||
regularization strength of $\theta_i$\label{step_fit}.
|
||||
\item Continue with the lower $\theta_{i+1}$ if the median change in vertex
|
||||
position is smaller than a threshold.
|
||||
\end{enumerate}
|
||||
\end{itemize}
|
||||
\end{itemize}
|
||||
\begin{figure}
|
||||
\vspace{-1.0em}
|
||||
\begin{tabular}{@{ }c@{ }c@{ }c@{ }c@{}}
|
||||
\includegraphics[height=0.42\linewidth]{56_4_tgt}&
|
||||
\includegraphics[height=0.42\linewidth]{23_2_tgt}&
|
||||
\includegraphics[height=0.42\linewidth]{5_6_tgt}\\[-1.0em]
|
||||
& \smaller a) Targets & \\[0.2em]
|
||||
\includegraphics[height=0.42\linewidth]{56_4_expression}&
|
||||
\includegraphics[height=0.42\linewidth]{23_2_expression}&
|
||||
\includegraphics[height=0.42\linewidth]{5_6_expression}\\[-0.8em]
|
||||
& \smaller b) Fits &
|
||||
\end{tabular}
|
||||
\vspace{0.2em}
|
||||
\caption{The reconstruction (b) is robust against scans (a) with artifacts, noise, and holes.}
|
||||
\label{fig:difficult}
|
||||
\end{figure}
|
||||
The search for the closest compatible point takes only points into account which
|
||||
have conforming normals, are closer than a threshold, and are not on or close
|
||||
to the border of the scan. This has the effect of removing many outliers. The
|
||||
search is sped up by organizing the target scan in a space partitioning tree
|
||||
made up of spheres.
|
||||
The correspondences are then weighted with a robust function by their
|
||||
residual distance. The robust function is linear for distances smaller than
|
||||
$2$mm, behaves like $1/x$ between $2$mm and
|
||||
$20$mm, and is zero for a distance larger than $20$mm.
|
||||
Note, that it is necessary to balance robustness and regularization, as the
|
||||
right balance depends on the noise characteristic of the data. Suitable values
|
||||
were determined manually from a few scans of the GavabDB database and kept
|
||||
constant for all experiments as well on the GavaDB as on the UND database. In
|
||||
step~\ref{step_fit} the 3DMM is fit to 3D-3D point correspondences. This is
|
||||
done with a gauss-newton least squares optimization, using an analytic Jacobian
|
||||
and Gauss-Newton Hessian approximation. Denote the correspondence points by
|
||||
$\MAT u=\Matrix{\VEC u_1, \dots, \VEC u_n}$ and the rows of the model which
|
||||
correspond to the $i$th vertex by subscript $i$, then we can write the cost
|
||||
function mimized in this step as
|
||||
\begin{align}
|
||||
f(\MAT R, \VEC t, \VEC\alpha) &= \sum_i \normLR{\MAT R( \VEC\mu_i + \MAT M_i\VEC\alpha) + \VEC t - \VEC u_i}^2 + \lambda\normLR{\VEC\alpha}^2\qquad.\label{eqn:mincost}
|
||||
\end{align}
|
||||
%We make the norm dependent on the target normal by using an orthonormal
|
||||
%covariance matrix $\MAT C_i$ per vertex, which makes the cost of deviation
|
||||
%along the normal higher than deviations inside the target surface.
|
||||
%\begin{align}
|
||||
% \MAT C_i &= \Matrix{ \VEC n_i^T\\ \nu \VEC a_i^T\\\nu\VEC b_i^T} & \VEC n_i &\bot \VEC a_i \bot \VEC b_i \bot \VEC n_i
|
||||
%\end{align}
|
||||
%where $\VEC n_i$ is the normal of the target correspondence and $\nu$ is an
|
||||
%anisotropy parameter. If we do not use the anisotropic distance measure (i.e.
|
||||
%$\MAT C_i=\MAT I$), then the cost function Equation~\ref{eqn:mincost} can be
|
||||
%minimized more efficiently by changing it to
|
||||
This can be minimized more efficiently by changing the direction of the rigid transform to
|
||||
\begin{align}
|
||||
f(\MAT R, \VEC t, \VEC\alpha) &= \sum_i \normLR{ \VEC\mu_i + \MAT M_i\VEC\alpha + {\VEC t'} - {\MAT R'}\VEC u_i }^2 + \lambda\normLR{\VEC\alpha}^2\nonumber\\
|
||||
{\VEC t'} &= \MAT R^{-1}\VEC t\qquad {\MAT R'} = \MAT R^{-1}\qquad.
|
||||
\end{align}
|
||||
because then the Jacobian consists of a large constant part and three columns
|
||||
which depend on the iteration.
|
||||
\begin{align}
|
||||
F_i &= \VEC\mu_i + \MAT M_i\VEC\alpha + {\VEC t'} - {\MAT R'_{r_1,r_2,r_3}}\VEC u_i\\
|
||||
\diffp{F_i}{\VEC\alpha} &= \MAT M_i\qquad
|
||||
\diffp{F_i}{\VEC t'} = \MAT I_3\qquad
|
||||
\diffp{F_i}{r_i} = \diffp{\MAT R'_{r_1,r_2,r_3}}{r_i}\VEC u_i\\
|
||||
\MAT J &= \Matrix{\MAT J_c & | & \MAT J_d }\\
|
||||
\MAT J_c &= \Matrix{\MAT M & \VEC 1 \otimes \MAT I_3\\ \MAT I & \MAT 0}\\
|
||||
\MAT J_d &= \Matrix{(\MAT I \otimes \diffp{\MAT R'}{r_1})\MAT u^T & (\MAT I \otimes \diffp{\MAT R'}{r_2})\MAT u^T& (\MAT I \otimes \diffp{\MAT R'}{r_3})\MAT u^T\\\MAT 0 & \MAT 0 & \MAT 0}
|
||||
\end{align}
|
||||
Accordingly, the Hessian can be approximated as
|
||||
\begin{align}
|
||||
\MAT H &= \Matrix{
|
||||
\MAT J_c^T\MAT J_c & (\MAT J_c^T\MAT J_d)^T\\
|
||||
\MAT J_c^T\MAT J_d & \MAT J_d^T\MAT J_d
|
||||
}\qquad.
|
||||
\end{align}
|
||||
By precalculating the constant parts of the matrices we can remove most of the
|
||||
computation time, making step~\ref{step_fit} very fast.
|
||||
|
||||
We initialize the registration by locating the tip of the nose with a
|
||||
heuristic, which assumes that the head is upright and looking into the camera.
|
||||
This initialization is good enough to for a fully automatic
|
||||
fit, as the fitting behaves like rigid ICP in the beginning, and rigid ICP is
|
||||
known to have a large basin of convergence.
|
||||
|
||||
\section{Experiments}
|
||||
\begin{figure*}
|
||||
\begin{tabular}{cc}
|
||||
\scalebox{0.82}{\input{shrec_MNCG}} &
|
||||
\scalebox{0.82}{\input{und_MNCG}}
|
||||
\end{tabular}
|
||||
\caption{For the expression dataset the retrieval rate is improved by
|
||||
including the expression model, while for the neutral expression dataset the
|
||||
performance does not decrease. Plotted is the mean normalized cumulative
|
||||
gain, which is the number of retrieved correct answers divided by the number
|
||||
of possible correct answers. Note also the different scales of the MNCG
|
||||
curves for the two datasets. Our approach has a high accuracy on the
|
||||
neutral (UND) dataset.}
|
||||
\label{fig:mcg}
|
||||
\end{figure*}
|
||||
\begin{figure*}
|
||||
\begin{tabular}{cc}
|
||||
\scalebox{0.82}{\input{shrec_PR}} &
|
||||
\scalebox{0.82}{\input{und_PR}}
|
||||
\end{tabular}
|
||||
\caption{Use of the expression model improves retrieval performance.
|
||||
Plotted are precision and recall for different retrieval depths. The lower
|
||||
precision of the UND database is due to the fact that some queries have no
|
||||
correct answers. For the UND database we achieve total recall when querying
|
||||
nine answers, while the maximal number of scans per individual is eight,
|
||||
while for the GavabDB database the expression model gives a strong
|
||||
improvement in recall rate but full recall can not be achieved.}
|
||||
\label{fig:precision_expression}
|
||||
\end{figure*}
|
||||
|
||||
\begin{figure*}
|
||||
\begin{tabular}{cc}
|
||||
\scalebox{0.82}{\input{shrec_FARFRR}} &
|
||||
\scalebox{0.82}{\input{und_FARFRR}}
|
||||
\end{tabular}
|
||||
\caption{Impostor detection is reliable, as the minimum distance to a match
|
||||
is smaller than the minimum distance to a nonmatch. Note the vast increase in
|
||||
recognition performance with the expression model on the expression database,
|
||||
and the fact that the recognition rate is not decreasing on the neutral
|
||||
database, even though we added expression invariance. We can operate at $0$\%
|
||||
false acceptance rate with less than $4$\% false rejection rate, or less than
|
||||
$1$\%\ FAR with less than $1$\%\ FRR.}
|
||||
\label{fig:impostor}
|
||||
\end{figure*}
|
||||
We evaluated the system on two databases with and without
|
||||
the expression model. We used the GavabDB~\cite{gavabdb} database and the
|
||||
UND~\cite{bowyer05:2d3d_recognition} database. For both databases, only the shape information was
|
||||
used. The GavabDB database contains 427 scans, with seven scans per ID, three
|
||||
neutral and four expressions. The expressions in this dataset varies
|
||||
considerably, including sticking out the tongue and strong facial distortions.
|
||||
Additionally it has strong artifacts due to facial hair, motion and the bad
|
||||
scanner quality. This dataset is typical for a non-cooperative environment.
|
||||
The UND database was used in the face recognition grand challenge~\cite{frvt06} and consists
|
||||
of 953 scans, with one to eight scans per ID. It is of better quality and
|
||||
contains only slight expression variations. It represents a cooperative
|
||||
scenario.
|
||||
|
||||
The fitting was initialized by detecting the nose, and assuming that the face is
|
||||
upright and looking along the $z$-axis. To detect the nose we
|
||||
first removed the spike artifacts typical of range scanners by repeated
|
||||
min-filtering and removal of large triangles, then we detect the vertex with
|
||||
the smallest depth, which in its horizontal slice is sufficiently closer to the
|
||||
camera than the other pixels in that slice. For the UND dataset this gives us
|
||||
reliably a point on the tip or ridge of the nose. The heuristic worked for 939
|
||||
out of 953 Scans, in the remaining 16 scans we marked the nose manually. The
|
||||
GavabDB database has the scans already aligned and the tip of the nose is at
|
||||
the origin. We used this information for the GavabDB experiments. The same
|
||||
regularisation parameters were used for all experiments, even though the
|
||||
GavabDB data is more noisy than the UND data. The parameters were set manually
|
||||
based on a few scans from the GavabDB Database. We used 100 principal identity
|
||||
components and 30 expression components for all experiments.
|
||||
|
||||
In the experiments the distances between all scans were calculated, and we
|
||||
measured recognition and retrieval rates by treating every scan once as the
|
||||
probe and all other scans as the gallery. Both databases were used
|
||||
independently.
|
||||
|
||||
\subsection{Retrieval Measures}
|
||||
We measure similarity between faces in parameter space as the angle between the
|
||||
face parameters in Mahalanobis space, which has proven to have high recognition
|
||||
rates~\cite{blanz03:face_rec}. The distance measure is
|
||||
\begin{align}
|
||||
s(\VEC\alpha_1, \VEC\alpha_2) &= \arccos\left(\frac{\VEC\alpha_1^T\VEC\alpha_2}{\norm{\VEC\alpha_1}\norm{\VEC\alpha_2}}\right)\qquad.
|
||||
\end{align}
|
||||
We observed that the angular measure gives slightly larger recognition rates
|
||||
than the Mahalanobis distance. The Mahalanobis angle has the effect of
|
||||
regarding all caricatures of a face, which lie on a ray from the origin towards
|
||||
any identity, as the same identity. We also evaluated other measures, but found
|
||||
them to be consistently worse than the Mahalanobis angle.
|
||||
|
||||
\subsection{Results}
|
||||
As expected, the two datasets behave differently because of the presence of
|
||||
expressions in the examples.
|
||||
|
||||
\subsubsection{UND}
|
||||
For the UND database we have good recognition rates with the neutral
|
||||
model. The mean cumulative normalized gain curve in
|
||||
Figure~\ref{fig:mcg} shows for varying retrieval depth the number of
|
||||
correctly retrieved scans divided by the maximal number of scans that could be
|
||||
retrieved at this level. From this it can be seen that the first match is
|
||||
always the correct match, if there is any match in the database. But for some
|
||||
probes no example is in the gallery. Therefore for face recognition we have to
|
||||
threshold the maximum allowed distance to be able to reject impostors. Varying
|
||||
the distance threshold leads to varying false acceptance rates (FAR) and false
|
||||
rejection rates (FRR), which are shown in Figure~\ref{fig:impostor}. Even
|
||||
though we have been tuning the model to the GavabDB dataset and not the UND
|
||||
dataset our recognition rates at any FAR rate are as good or better than the
|
||||
best results from the face recognition vendor test. This shows, that our basic
|
||||
face recognition method without expression modelling gives convincing results.
|
||||
Now we analyze how the expression modelling impacts recognition results on this
|
||||
expression-less database. If face and expression space are not orthogonal, then
|
||||
adding invariance towards expressions should make the recognition rates
|
||||
decrease. In fact, we observe that the recognition results are slightly lower,
|
||||
but only by a marginal amount, and still on par with the results from the face
|
||||
recognition vendor test. Let us now turn towards the expression database, where
|
||||
we expect to see an increase in recognition rate due to the expression model.
|
||||
|
||||
\subsubsection{GavabDB}
|
||||
The recognition rates on the GavabDB without expression model are not quite as
|
||||
good as for the expression-less UND dataset, so here we hope to find some
|
||||
improvement by using expression normalization. And indeed, the closest point
|
||||
recognition rate with only the neutral model is 96.25\% which can be improved
|
||||
to 98.36\% by adding the expression model. Also the FAR/FRR values decrease
|
||||
considerably. The largest improvement can be seen in retrieval performance,
|
||||
displayed in the precision recall curves in
|
||||
Figure~\ref{fig:precision_expression} and mean cumulative normalized gain
|
||||
curves in Figure~\ref{fig:mcg}. This is because there are multiple examples in
|
||||
the gallery, so finding a single match is relatively easy. But retrieving all
|
||||
examples from the database, even those with strong expressions, is only made
|
||||
possible by the expression model.
|
||||
|
||||
%\emph{TODO: Try also $k$-NN, that should give 100\% recognition rate on the
|
||||
%GavabDB too.}
|
||||
|
||||
\section{Speed}
|
||||
Though the method as presented operates at only approximately 40 seconds per
|
||||
query, it has the potential for speedup. It is possible to parallelize the
|
||||
closest point estimation and the optimisation, and more elaborate fitting
|
||||
algorithms including multiresolution schemes can be developed. The speed also
|
||||
depends on the number of vertices and components, for the results presented
|
||||
here 11000 vertices and 100 neutral plus 30 expression components were fitted.
|
||||
|
||||
\section{Conclusion}
|
||||
We have used a 3D Morphable Model with a separating expression model to develop
|
||||
an expression-invariant face recognition algorithm. We have shown, that the
|
||||
system has excellent recognition rates on difficult expression data and data
|
||||
taken in a cooperative environment. The introduction of expression invariance
|
||||
did not incur a significant loss of precision on easier neutral data. The strong prior
|
||||
knowledge of the 3DMM allows robust handling of noisy data and allowed us to
|
||||
build a fully automatic face recognition system. We also introduced a relatively
|
||||
efficient fitting algorithm, which, as it has the potential for
|
||||
paralellisation, could be made even faster.
|
||||
|
||||
Note that, as we do establish correspondence between the model and the scans,
|
||||
it is trivial to add image based classification for datasets where a calibrated
|
||||
photo is available. This can be done by comparing the rectified textures,
|
||||
which should result in even higher recognition rates. It is also important to
|
||||
note that the expression normalization described here for range data can be
|
||||
applied equally well to other modalities, using any of the proposed 3DMM
|
||||
fitting algorithms.
|
||||
|
||||
In the future we plan to include the additional texture cues and make the
|
||||
method faster, such that it is applicable in real world scenarios where a
|
||||
processing time of 40 seconds per probe is still a problem. Furthermore we
|
||||
would like to investigate more sophisticated fitting algorithms and a morphable
|
||||
model with a larger expression space.
|
||||
|
||||
%\section*{Acknowledgement}
|
||||
%The authors wish to thank P.\ Paysan for the data
|
||||
%acquisition. This work was supported in part by a grant from Microsoft
|
||||
%Research and the Swiss National Science Foundation (200021-103814 and NCCR COME project 5005-66380).
|
||||
|
||||
{\small
|
||||
\bibliographystyle{ieee}
|
||||
%%use following if all content of bibtex file should be shown
|
||||
%\nocite{*}
|
||||
\bibliography{shrec_08}
|
||||
}
|
||||
\end{document}
|
||||
|
||||
|
||||
@@ -1,125 +0,0 @@
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
Package color not loaded in conjunction with
|
||||
terminal option `colourtext'%
|
||||
}{See the gnuplot documentation for explanation.%
|
||||
}{Either use 'blacktext' in gnuplot or load the package
|
||||
color.sty in LaTeX.}%
|
||||
\renewcommand\color[2][]{}%
|
||||
}%
|
||||
\providecommand\includegraphics[2][]{%
|
||||
\GenericError{(gnuplot) \space\space\space\@spaces}{%
|
||||
Package graphicx or graphics not loaded%
|
||||
}{See the gnuplot documentation for explanation.%
|
||||
}{The gnuplot epslatex terminal needs graphicx.sty or graphics.sty.}%
|
||||
\renewcommand\includegraphics[2][]{}%
|
||||
}%
|
||||
\providecommand\rotatebox[2]{#2}%
|
||||
\@ifundefined{ifGPcolor}{%
|
||||
\newif\ifGPcolor
|
||||
\GPcolortrue
|
||||
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|
||||
\@ifundefined{ifGPblacktext}{%
|
||||
\newif\ifGPblacktext
|
||||
\GPblacktextfalse
|
||||
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|
||||
% define a \g@addto@macro without @ in the name:
|
||||
\let\gplgaddtomacro\g@addto@macro
|
||||
% define empty templates for all commands taking text:
|
||||
\gdef\gplbacktext{}%
|
||||
\gdef\gplfronttext{}%
|
||||
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|
||||
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|
||||
% no textcolor at all
|
||||
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||||
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|
||||
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||||
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||||
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||||
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||||
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|
||||
% gray
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||||
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||||
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||||
\expandafter\def\csname LTw\endcsname{\color{white}}%
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\expandafter\def\csname LTb\endcsname{\color{black}}%
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\expandafter\def\csname LTa\endcsname{\color{black}}%
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\expandafter\def\csname LT0\endcsname{\color{black}}%
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\expandafter\def\csname LT1\endcsname{\color{black}}%
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\expandafter\def\csname LT6\endcsname{\color{black}}%
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||||
\expandafter\def\csname LT7\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT8\endcsname{\color{black}}%
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||||
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|
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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|
||||
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|
||||
\csname LTb\endcsname%
|
||||
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|
||||
\csname LTb\endcsname%
|
||||
\put(918,1980){\makebox(0,0)[r]{\strut{} 0.08}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(1026,360){\makebox(0,0){\strut{} 0}}%
|
||||
\csname LTb\endcsname%
|
||||
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|
||||
\csname LTb\endcsname%
|
||||
\put(2502,360){\makebox(0,0){\strut{} 0.01}}%
|
||||
\csname LTb\endcsname%
|
||||
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|
||||
\csname LTb\endcsname%
|
||||
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|
||||
\csname LTb\endcsname%
|
||||
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|
||||
\csname LTb\endcsname%
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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||||
/ID [<278901DCE0FAFA98C196E505CDF67DDA><278901DCE0FAFA98C196E505CDF67DDA>]
|
||||
>>
|
||||
startxref
|
||||
2525
|
||||
%%EOF
|
||||
@@ -1,115 +0,0 @@
|
||||
% GNUPLOT: LaTeX picture with Postscript
|
||||
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|
||||
\fontfamily{phv}%
|
||||
\selectfont
|
||||
\makeatletter
|
||||
\providecommand\color[2][]{%
|
||||
\GenericError{(gnuplot) \space\space\space\@spaces}{%
|
||||
Package color not loaded in conjunction with
|
||||
terminal option `colourtext'%
|
||||
}{See the gnuplot documentation for explanation.%
|
||||
}{Either use 'blacktext' in gnuplot or load the package
|
||||
color.sty in LaTeX.}%
|
||||
\renewcommand\color[2][]{}%
|
||||
}%
|
||||
\providecommand\includegraphics[2][]{%
|
||||
\GenericError{(gnuplot) \space\space\space\@spaces}{%
|
||||
Package graphicx or graphics not loaded%
|
||||
}{See the gnuplot documentation for explanation.%
|
||||
}{The gnuplot epslatex terminal needs graphicx.sty or graphics.sty.}%
|
||||
\renewcommand\includegraphics[2][]{}%
|
||||
}%
|
||||
\providecommand\rotatebox[2]{#2}%
|
||||
\@ifundefined{ifGPcolor}{%
|
||||
\newif\ifGPcolor
|
||||
\GPcolortrue
|
||||
}{}%
|
||||
\@ifundefined{ifGPblacktext}{%
|
||||
\newif\ifGPblacktext
|
||||
\GPblacktexttrue
|
||||
}{}%
|
||||
% define a \g@addto@macro without @ in the name:
|
||||
\let\gplgaddtomacro\g@addto@macro
|
||||
% define empty templates for all commands taking text:
|
||||
\gdef\gplbacktext{}%
|
||||
\gdef\gplfronttext{}%
|
||||
\makeatother
|
||||
\ifGPblacktext
|
||||
% no textcolor at all
|
||||
\def\colorrgb#1{}%
|
||||
\def\colorgray#1{}%
|
||||
\else
|
||||
% gray or color?
|
||||
\ifGPcolor
|
||||
\def\colorrgb#1{\color[rgb]{#1}}%
|
||||
\def\colorgray#1{\color[gray]{#1}}%
|
||||
\expandafter\def\csname LTw\endcsname{\color{white}}%
|
||||
\expandafter\def\csname LTb\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LTa\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT0\endcsname{\color[rgb]{1,0,0}}%
|
||||
\expandafter\def\csname LT1\endcsname{\color[rgb]{0,1,0}}%
|
||||
\expandafter\def\csname LT2\endcsname{\color[rgb]{0,0,1}}%
|
||||
\expandafter\def\csname LT3\endcsname{\color[rgb]{1,0,1}}%
|
||||
\expandafter\def\csname LT4\endcsname{\color[rgb]{0,1,1}}%
|
||||
\expandafter\def\csname LT5\endcsname{\color[rgb]{1,1,0}}%
|
||||
\expandafter\def\csname LT6\endcsname{\color[rgb]{0,0,0}}%
|
||||
\expandafter\def\csname LT7\endcsname{\color[rgb]{1,0.3,0}}%
|
||||
\expandafter\def\csname LT8\endcsname{\color[rgb]{0.5,0.5,0.5}}%
|
||||
\else
|
||||
% gray
|
||||
\def\colorrgb#1{\color{black}}%
|
||||
\def\colorgray#1{\color[gray]{#1}}%
|
||||
\expandafter\def\csname LTw\endcsname{\color{white}}%
|
||||
\expandafter\def\csname LTb\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LTa\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT0\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT1\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT2\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT3\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT4\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT5\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT6\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT7\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT8\endcsname{\color{black}}%
|
||||
\fi
|
||||
\fi
|
||||
\setlength{\unitlength}{0.0500bp}%
|
||||
\begin{picture}(5760.00,2520.00)%
|
||||
\gplgaddtomacro\gplbacktext{%
|
||||
\csname LTb\endcsname%
|
||||
\put(810,540){\makebox(0,0)[r]{\strut{} 0}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(810,900){\makebox(0,0)[r]{\strut{} 0.5}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(810,1260){\makebox(0,0)[r]{\strut{} 1}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(810,1620){\makebox(0,0)[r]{\strut{} 1.5}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(810,1980){\makebox(0,0)[r]{\strut{} 2}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(918,360){\makebox(0,0){\strut{} 0}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(1825,360){\makebox(0,0){\strut{} 0.2}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(2732,360){\makebox(0,0){\strut{} 0.4}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(3640,360){\makebox(0,0){\strut{} 0.6}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(4547,360){\makebox(0,0){\strut{} 0.8}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(5454,360){\makebox(0,0){\strut{} 1}}%
|
||||
\put(180,1260){\rotatebox{90}{\makebox(0,0){\strut{}FRR \%}}}%
|
||||
\put(3186,90){\makebox(0,0){\strut{}FAR \%}}%
|
||||
\put(3186,2250){\makebox(0,0){\strut{}\bf \normalsize GavabDB: Recognition Performance}}%
|
||||
}%
|
||||
\gplgaddtomacro\gplfronttext{%
|
||||
\csname LTb\endcsname%
|
||||
\put(4635,1827){\makebox(0,0)[r]{\strut{}neutral model}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(4635,1647){\makebox(0,0)[r]{\strut{}expression model}}%
|
||||
}%
|
||||
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|
||||
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|
||||
\gplfronttext
|
||||
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|
||||
\endgroup
|
||||
@@ -1,127 +0,0 @@
|
||||
% GNUPLOT: LaTeX picture with Postscript
|
||||
\begingroup
|
||||
\fontfamily{phv}%
|
||||
\selectfont
|
||||
\makeatletter
|
||||
\providecommand\color[2][]{%
|
||||
\GenericError{(gnuplot) \space\space\space\@spaces}{%
|
||||
Package color not loaded in conjunction with
|
||||
terminal option `colourtext'%
|
||||
}{See the gnuplot documentation for explanation.%
|
||||
}{Either use 'blacktext' in gnuplot or load the package
|
||||
color.sty in LaTeX.}%
|
||||
\renewcommand\color[2][]{}%
|
||||
}%
|
||||
\providecommand\includegraphics[2][]{%
|
||||
\GenericError{(gnuplot) \space\space\space\@spaces}{%
|
||||
Package graphicx or graphics not loaded%
|
||||
}{See the gnuplot documentation for explanation.%
|
||||
}{The gnuplot epslatex terminal needs graphicx.sty or graphics.sty.}%
|
||||
\renewcommand\includegraphics[2][]{}%
|
||||
}%
|
||||
\providecommand\rotatebox[2]{#2}%
|
||||
\@ifundefined{ifGPcolor}{%
|
||||
\newif\ifGPcolor
|
||||
\GPcolortrue
|
||||
}{}%
|
||||
\@ifundefined{ifGPblacktext}{%
|
||||
\newif\ifGPblacktext
|
||||
\GPblacktexttrue
|
||||
}{}%
|
||||
% define a \g@addto@macro without @ in the name:
|
||||
\let\gplgaddtomacro\g@addto@macro
|
||||
% define empty templates for all commands taking text:
|
||||
\gdef\gplbacktext{}%
|
||||
\gdef\gplfronttext{}%
|
||||
\makeatother
|
||||
\ifGPblacktext
|
||||
% no textcolor at all
|
||||
\def\colorrgb#1{}%
|
||||
\def\colorgray#1{}%
|
||||
\else
|
||||
% gray or color?
|
||||
\ifGPcolor
|
||||
\def\colorrgb#1{\color[rgb]{#1}}%
|
||||
\def\colorgray#1{\color[gray]{#1}}%
|
||||
\expandafter\def\csname LTw\endcsname{\color{white}}%
|
||||
\expandafter\def\csname LTb\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LTa\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT0\endcsname{\color[rgb]{1,0,0}}%
|
||||
\expandafter\def\csname LT1\endcsname{\color[rgb]{0,1,0}}%
|
||||
\expandafter\def\csname LT2\endcsname{\color[rgb]{0,0,1}}%
|
||||
\expandafter\def\csname LT3\endcsname{\color[rgb]{1,0,1}}%
|
||||
\expandafter\def\csname LT4\endcsname{\color[rgb]{0,1,1}}%
|
||||
\expandafter\def\csname LT5\endcsname{\color[rgb]{1,1,0}}%
|
||||
\expandafter\def\csname LT6\endcsname{\color[rgb]{0,0,0}}%
|
||||
\expandafter\def\csname LT7\endcsname{\color[rgb]{1,0.3,0}}%
|
||||
\expandafter\def\csname LT8\endcsname{\color[rgb]{0.5,0.5,0.5}}%
|
||||
\else
|
||||
% gray
|
||||
\def\colorrgb#1{\color{black}}%
|
||||
\def\colorgray#1{\color[gray]{#1}}%
|
||||
\expandafter\def\csname LTw\endcsname{\color{white}}%
|
||||
\expandafter\def\csname LTb\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LTa\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT0\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT1\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT2\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT3\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT4\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT5\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT6\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT7\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT8\endcsname{\color{black}}%
|
||||
\fi
|
||||
\fi
|
||||
\setlength{\unitlength}{0.0500bp}%
|
||||
\begin{picture}(5760.00,2520.00)%
|
||||
\gplgaddtomacro\gplbacktext{%
|
||||
\csname LTb\endcsname%
|
||||
\put(810,540){\makebox(0,0)[r]{\strut{} 75}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(810,828){\makebox(0,0)[r]{\strut{} 80}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(810,1116){\makebox(0,0)[r]{\strut{} 85}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(810,1404){\makebox(0,0)[r]{\strut{} 90}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(810,1692){\makebox(0,0)[r]{\strut{} 95}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(810,1980){\makebox(0,0)[r]{\strut{} 100}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(918,360){\makebox(0,0){\strut{} 0}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(1372,360){\makebox(0,0){\strut{} 2}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(1825,360){\makebox(0,0){\strut{} 4}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(2279,360){\makebox(0,0){\strut{} 6}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(2732,360){\makebox(0,0){\strut{} 8}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(3186,360){\makebox(0,0){\strut{} 10}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(3640,360){\makebox(0,0){\strut{} 12}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(4093,360){\makebox(0,0){\strut{} 14}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(4547,360){\makebox(0,0){\strut{} 16}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(5000,360){\makebox(0,0){\strut{} 18}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(5454,360){\makebox(0,0){\strut{} 20}}%
|
||||
\put(180,1260){\rotatebox{90}{\makebox(0,0){\strut{}MNCG \%}}}%
|
||||
\put(3186,90){\makebox(0,0){\strut{}$@(x)$}}%
|
||||
\put(3186,2250){\makebox(0,0){\strut{}\bf \normalsize GavabDB: Mean Normalized Cumulative Gain}}%
|
||||
}%
|
||||
\gplgaddtomacro\gplfronttext{%
|
||||
\csname LTb\endcsname%
|
||||
\put(4635,873){\makebox(0,0)[r]{\strut{}neutral model}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(4635,693){\makebox(0,0)[r]{\strut{}expression model}}%
|
||||
}%
|
||||
\gplbacktext
|
||||
\put(0,0){\includegraphics{shrec_mncg}}%
|
||||
\gplfronttext
|
||||
\end{picture}%
|
||||
\endgroup
|
||||
@@ -1,117 +0,0 @@
|
||||
% GNUPLOT: LaTeX picture with Postscript
|
||||
\begingroup
|
||||
\fontfamily{phv}%
|
||||
\selectfont
|
||||
\makeatletter
|
||||
\providecommand\color[2][]{%
|
||||
\GenericError{(gnuplot) \space\space\space\@spaces}{%
|
||||
Package color not loaded in conjunction with
|
||||
terminal option `colourtext'%
|
||||
}{See the gnuplot documentation for explanation.%
|
||||
}{Either use 'blacktext' in gnuplot or load the package
|
||||
color.sty in LaTeX.}%
|
||||
\renewcommand\color[2][]{}%
|
||||
}%
|
||||
\providecommand\includegraphics[2][]{%
|
||||
\GenericError{(gnuplot) \space\space\space\@spaces}{%
|
||||
Package graphicx or graphics not loaded%
|
||||
}{See the gnuplot documentation for explanation.%
|
||||
}{The gnuplot epslatex terminal needs graphicx.sty or graphics.sty.}%
|
||||
\renewcommand\includegraphics[2][]{}%
|
||||
}%
|
||||
\providecommand\rotatebox[2]{#2}%
|
||||
\@ifundefined{ifGPcolor}{%
|
||||
\newif\ifGPcolor
|
||||
\GPcolortrue
|
||||
}{}%
|
||||
\@ifundefined{ifGPblacktext}{%
|
||||
\newif\ifGPblacktext
|
||||
\GPblacktexttrue
|
||||
}{}%
|
||||
% define a \g@addto@macro without @ in the name:
|
||||
\let\gplgaddtomacro\g@addto@macro
|
||||
% define empty templates for all commands taking text:
|
||||
\gdef\gplbacktext{}%
|
||||
\gdef\gplfronttext{}%
|
||||
\makeatother
|
||||
\ifGPblacktext
|
||||
% no textcolor at all
|
||||
\def\colorrgb#1{}%
|
||||
\def\colorgray#1{}%
|
||||
\else
|
||||
% gray or color?
|
||||
\ifGPcolor
|
||||
\def\colorrgb#1{\color[rgb]{#1}}%
|
||||
\def\colorgray#1{\color[gray]{#1}}%
|
||||
\expandafter\def\csname LTw\endcsname{\color{white}}%
|
||||
\expandafter\def\csname LTb\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LTa\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT0\endcsname{\color[rgb]{1,0,0}}%
|
||||
\expandafter\def\csname LT1\endcsname{\color[rgb]{0,1,0}}%
|
||||
\expandafter\def\csname LT2\endcsname{\color[rgb]{0,0,1}}%
|
||||
\expandafter\def\csname LT3\endcsname{\color[rgb]{1,0,1}}%
|
||||
\expandafter\def\csname LT4\endcsname{\color[rgb]{0,1,1}}%
|
||||
\expandafter\def\csname LT5\endcsname{\color[rgb]{1,1,0}}%
|
||||
\expandafter\def\csname LT6\endcsname{\color[rgb]{0,0,0}}%
|
||||
\expandafter\def\csname LT7\endcsname{\color[rgb]{1,0.3,0}}%
|
||||
\expandafter\def\csname LT8\endcsname{\color[rgb]{0.5,0.5,0.5}}%
|
||||
\else
|
||||
% gray
|
||||
\def\colorrgb#1{\color{black}}%
|
||||
\def\colorgray#1{\color[gray]{#1}}%
|
||||
\expandafter\def\csname LTw\endcsname{\color{white}}%
|
||||
\expandafter\def\csname LTb\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LTa\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT0\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT1\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT2\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT3\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT4\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT5\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT6\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT7\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT8\endcsname{\color{black}}%
|
||||
\fi
|
||||
\fi
|
||||
\setlength{\unitlength}{0.0500bp}%
|
||||
\begin{picture}(5760.00,2520.00)%
|
||||
\gplgaddtomacro\gplbacktext{%
|
||||
\csname LTb\endcsname%
|
||||
\put(810,540){\makebox(0,0)[r]{\strut{} 0}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(810,828){\makebox(0,0)[r]{\strut{} 20}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(810,1116){\makebox(0,0)[r]{\strut{} 40}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(810,1404){\makebox(0,0)[r]{\strut{} 60}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(810,1692){\makebox(0,0)[r]{\strut{} 80}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(810,1980){\makebox(0,0)[r]{\strut{} 100}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(918,360){\makebox(0,0){\strut{} 0}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(1825,360){\makebox(0,0){\strut{} 20}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(2732,360){\makebox(0,0){\strut{} 40}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(3640,360){\makebox(0,0){\strut{} 60}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(4547,360){\makebox(0,0){\strut{} 80}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(5454,360){\makebox(0,0){\strut{} 100}}%
|
||||
\put(180,1260){\rotatebox{90}{\makebox(0,0){\strut{}Precision \%}}}%
|
||||
\put(3186,90){\makebox(0,0){\strut{}Recall \%}}%
|
||||
\put(3186,2250){\makebox(0,0){\strut{}\bf \normalsize GavabDB: Precision Recall}}%
|
||||
}%
|
||||
\gplgaddtomacro\gplfronttext{%
|
||||
\csname LTb\endcsname%
|
||||
\put(2754,873){\makebox(0,0)[r]{\strut{}neutral model}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(2754,693){\makebox(0,0)[r]{\strut{}expression model}}%
|
||||
}%
|
||||
\gplbacktext
|
||||
\put(0,0){\includegraphics{shrec_pr}}%
|
||||
\gplfronttext
|
||||
\end{picture}%
|
||||
\endgroup
|
||||
@@ -1,125 +0,0 @@
|
||||
% GNUPLOT: LaTeX picture with Postscript
|
||||
\begingroup
|
||||
\fontfamily{phv}%
|
||||
\selectfont
|
||||
\makeatletter
|
||||
\providecommand\color[2][]{%
|
||||
\GenericError{(gnuplot) \space\space\space\@spaces}{%
|
||||
Package color not loaded in conjunction with
|
||||
terminal option `colourtext'%
|
||||
}{See the gnuplot documentation for explanation.%
|
||||
}{Either use 'blacktext' in gnuplot or load the package
|
||||
color.sty in LaTeX.}%
|
||||
\renewcommand\color[2][]{}%
|
||||
}%
|
||||
\providecommand\includegraphics[2][]{%
|
||||
\GenericError{(gnuplot) \space\space\space\@spaces}{%
|
||||
Package graphicx or graphics not loaded%
|
||||
}{See the gnuplot documentation for explanation.%
|
||||
}{The gnuplot epslatex terminal needs graphicx.sty or graphics.sty.}%
|
||||
\renewcommand\includegraphics[2][]{}%
|
||||
}%
|
||||
\providecommand\rotatebox[2]{#2}%
|
||||
\@ifundefined{ifGPcolor}{%
|
||||
\newif\ifGPcolor
|
||||
\GPcolortrue
|
||||
}{}%
|
||||
\@ifundefined{ifGPblacktext}{%
|
||||
\newif\ifGPblacktext
|
||||
\GPblacktextfalse
|
||||
}{}%
|
||||
% define a \g@addto@macro without @ in the name:
|
||||
\let\gplgaddtomacro\g@addto@macro
|
||||
% define empty templates for all commands taking text:
|
||||
\gdef\gplbacktext{}%
|
||||
\gdef\gplfronttext{}%
|
||||
\makeatother
|
||||
\ifGPblacktext
|
||||
% no textcolor at all
|
||||
\def\colorrgb#1{}%
|
||||
\def\colorgray#1{}%
|
||||
\else
|
||||
% gray or color?
|
||||
\ifGPcolor
|
||||
\def\colorrgb#1{\color[rgb]{#1}}%
|
||||
\def\colorgray#1{\color[gray]{#1}}%
|
||||
\expandafter\def\csname LTw\endcsname{\color{white}}%
|
||||
\expandafter\def\csname LTb\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LTa\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT0\endcsname{\color[rgb]{1,0,0}}%
|
||||
\expandafter\def\csname LT1\endcsname{\color[rgb]{0,1,0}}%
|
||||
\expandafter\def\csname LT2\endcsname{\color[rgb]{0,0,1}}%
|
||||
\expandafter\def\csname LT3\endcsname{\color[rgb]{1,0,1}}%
|
||||
\expandafter\def\csname LT4\endcsname{\color[rgb]{0,1,1}}%
|
||||
\expandafter\def\csname LT5\endcsname{\color[rgb]{1,1,0}}%
|
||||
\expandafter\def\csname LT6\endcsname{\color[rgb]{0,0,0}}%
|
||||
\expandafter\def\csname LT7\endcsname{\color[rgb]{1,0.3,0}}%
|
||||
\expandafter\def\csname LT8\endcsname{\color[rgb]{0.5,0.5,0.5}}%
|
||||
\else
|
||||
% gray
|
||||
\def\colorrgb#1{\color{black}}%
|
||||
\def\colorgray#1{\color[gray]{#1}}%
|
||||
\expandafter\def\csname LTw\endcsname{\color{white}}%
|
||||
\expandafter\def\csname LTb\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LTa\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT0\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT1\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT2\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT3\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT4\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT5\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT6\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT7\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT8\endcsname{\color{black}}%
|
||||
\fi
|
||||
\fi
|
||||
\setlength{\unitlength}{0.0500bp}%
|
||||
\begin{picture}(5760.00,2520.00)%
|
||||
\gplgaddtomacro\gplbacktext{%
|
||||
\csname LTb\endcsname%
|
||||
\put(918,540){\makebox(0,0)[r]{\strut{} 0}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(918,720){\makebox(0,0)[r]{\strut{} 0.01}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(918,900){\makebox(0,0)[r]{\strut{} 0.02}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(918,1080){\makebox(0,0)[r]{\strut{} 0.03}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(918,1260){\makebox(0,0)[r]{\strut{} 0.04}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(918,1440){\makebox(0,0)[r]{\strut{} 0.05}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(918,1620){\makebox(0,0)[r]{\strut{} 0.06}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(918,1800){\makebox(0,0)[r]{\strut{} 0.07}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(918,1980){\makebox(0,0)[r]{\strut{} 0.08}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(1026,360){\makebox(0,0){\strut{} 0}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(1764,360){\makebox(0,0){\strut{} 0.005}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(2502,360){\makebox(0,0){\strut{} 0.01}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(3240,360){\makebox(0,0){\strut{} 0.015}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(3978,360){\makebox(0,0){\strut{} 0.02}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(4716,360){\makebox(0,0){\strut{} 0.025}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(5454,360){\makebox(0,0){\strut{} 0.03}}%
|
||||
\put(180,1260){\rotatebox{90}{\makebox(0,0){\strut{}FRR}}}%
|
||||
\put(3240,90){\makebox(0,0){\strut{}FAR}}%
|
||||
\put(3240,2250){\makebox(0,0){\strut{}UND: Recognition Performance}}%
|
||||
}%
|
||||
\gplgaddtomacro\gplfronttext{%
|
||||
\csname LTb\endcsname%
|
||||
\put(4635,1827){\makebox(0,0)[r]{\strut{}neutral model}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(4635,1647){\makebox(0,0)[r]{\strut{}expression model}}%
|
||||
}%
|
||||
\gplbacktext
|
||||
\put(0,0){\includegraphics{und_FARFRR}}%
|
||||
\gplfronttext
|
||||
\end{picture}%
|
||||
\endgroup
|
||||
@@ -1,127 +0,0 @@
|
||||
% GNUPLOT: LaTeX picture with Postscript
|
||||
\begingroup
|
||||
\fontfamily{phv}%
|
||||
\selectfont
|
||||
\makeatletter
|
||||
\providecommand\color[2][]{%
|
||||
\GenericError{(gnuplot) \space\space\space\@spaces}{%
|
||||
Package color not loaded in conjunction with
|
||||
terminal option `colourtext'%
|
||||
}{See the gnuplot documentation for explanation.%
|
||||
}{Either use 'blacktext' in gnuplot or load the package
|
||||
color.sty in LaTeX.}%
|
||||
\renewcommand\color[2][]{}%
|
||||
}%
|
||||
\providecommand\includegraphics[2][]{%
|
||||
\GenericError{(gnuplot) \space\space\space\@spaces}{%
|
||||
Package graphicx or graphics not loaded%
|
||||
}{See the gnuplot documentation for explanation.%
|
||||
}{The gnuplot epslatex terminal needs graphicx.sty or graphics.sty.}%
|
||||
\renewcommand\includegraphics[2][]{}%
|
||||
}%
|
||||
\providecommand\rotatebox[2]{#2}%
|
||||
\@ifundefined{ifGPcolor}{%
|
||||
\newif\ifGPcolor
|
||||
\GPcolortrue
|
||||
}{}%
|
||||
\@ifundefined{ifGPblacktext}{%
|
||||
\newif\ifGPblacktext
|
||||
\GPblacktextfalse
|
||||
}{}%
|
||||
% define a \g@addto@macro without @ in the name:
|
||||
\let\gplgaddtomacro\g@addto@macro
|
||||
% define empty templates for all commands taking text:
|
||||
\gdef\gplbacktext{}%
|
||||
\gdef\gplfronttext{}%
|
||||
\makeatother
|
||||
\ifGPblacktext
|
||||
% no textcolor at all
|
||||
\def\colorrgb#1{}%
|
||||
\def\colorgray#1{}%
|
||||
\else
|
||||
% gray or color?
|
||||
\ifGPcolor
|
||||
\def\colorrgb#1{\color[rgb]{#1}}%
|
||||
\def\colorgray#1{\color[gray]{#1}}%
|
||||
\expandafter\def\csname LTw\endcsname{\color{white}}%
|
||||
\expandafter\def\csname LTb\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LTa\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT0\endcsname{\color[rgb]{1,0,0}}%
|
||||
\expandafter\def\csname LT1\endcsname{\color[rgb]{0,1,0}}%
|
||||
\expandafter\def\csname LT2\endcsname{\color[rgb]{0,0,1}}%
|
||||
\expandafter\def\csname LT3\endcsname{\color[rgb]{1,0,1}}%
|
||||
\expandafter\def\csname LT4\endcsname{\color[rgb]{0,1,1}}%
|
||||
\expandafter\def\csname LT5\endcsname{\color[rgb]{1,1,0}}%
|
||||
\expandafter\def\csname LT6\endcsname{\color[rgb]{0,0,0}}%
|
||||
\expandafter\def\csname LT7\endcsname{\color[rgb]{1,0.3,0}}%
|
||||
\expandafter\def\csname LT8\endcsname{\color[rgb]{0.5,0.5,0.5}}%
|
||||
\else
|
||||
% gray
|
||||
\def\colorrgb#1{\color{black}}%
|
||||
\def\colorgray#1{\color[gray]{#1}}%
|
||||
\expandafter\def\csname LTw\endcsname{\color{white}}%
|
||||
\expandafter\def\csname LTb\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LTa\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT0\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT1\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT2\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT3\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT4\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT5\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT6\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT7\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT8\endcsname{\color{black}}%
|
||||
\fi
|
||||
\fi
|
||||
\setlength{\unitlength}{0.0500bp}%
|
||||
\begin{picture}(5760.00,2520.00)%
|
||||
\gplgaddtomacro\gplbacktext{%
|
||||
\csname LTb\endcsname%
|
||||
\put(1026,540){\makebox(0,0)[r]{\strut{} 0.99}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(1026,828){\makebox(0,0)[r]{\strut{} 0.992}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(1026,1116){\makebox(0,0)[r]{\strut{} 0.994}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(1026,1404){\makebox(0,0)[r]{\strut{} 0.996}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(1026,1692){\makebox(0,0)[r]{\strut{} 0.998}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(1026,1980){\makebox(0,0)[r]{\strut{} 1}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(1134,360){\makebox(0,0){\strut{} 0}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(1566,360){\makebox(0,0){\strut{} 2}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(1998,360){\makebox(0,0){\strut{} 4}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(2430,360){\makebox(0,0){\strut{} 6}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(2862,360){\makebox(0,0){\strut{} 8}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(3294,360){\makebox(0,0){\strut{} 10}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(3726,360){\makebox(0,0){\strut{} 12}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(4158,360){\makebox(0,0){\strut{} 14}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(4590,360){\makebox(0,0){\strut{} 16}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(5022,360){\makebox(0,0){\strut{} 18}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(5454,360){\makebox(0,0){\strut{} 20}}%
|
||||
\put(180,1260){\rotatebox{90}{\makebox(0,0){\strut{}MNCG}}}%
|
||||
\put(3294,90){\makebox(0,0){\strut{}$@x$}}%
|
||||
\put(3294,2250){\makebox(0,0){\strut{}UND: Mean Normalized Cumulative Gain}}%
|
||||
}%
|
||||
\gplgaddtomacro\gplfronttext{%
|
||||
\csname LTb\endcsname%
|
||||
\put(4635,873){\makebox(0,0)[r]{\strut{}neutral model}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(4635,693){\makebox(0,0)[r]{\strut{}expression model}}%
|
||||
}%
|
||||
\gplbacktext
|
||||
\put(0,0){\includegraphics{und_MNCG}}%
|
||||
\gplfronttext
|
||||
\end{picture}%
|
||||
\endgroup
|
||||
@@ -1,117 +0,0 @@
|
||||
% GNUPLOT: LaTeX picture with Postscript
|
||||
\begingroup
|
||||
\fontfamily{phv}%
|
||||
\selectfont
|
||||
\makeatletter
|
||||
\providecommand\color[2][]{%
|
||||
\GenericError{(gnuplot) \space\space\space\@spaces}{%
|
||||
Package color not loaded in conjunction with
|
||||
terminal option `colourtext'%
|
||||
}{See the gnuplot documentation for explanation.%
|
||||
}{Either use 'blacktext' in gnuplot or load the package
|
||||
color.sty in LaTeX.}%
|
||||
\renewcommand\color[2][]{}%
|
||||
}%
|
||||
\providecommand\includegraphics[2][]{%
|
||||
\GenericError{(gnuplot) \space\space\space\@spaces}{%
|
||||
Package graphicx or graphics not loaded%
|
||||
}{See the gnuplot documentation for explanation.%
|
||||
}{The gnuplot epslatex terminal needs graphicx.sty or graphics.sty.}%
|
||||
\renewcommand\includegraphics[2][]{}%
|
||||
}%
|
||||
\providecommand\rotatebox[2]{#2}%
|
||||
\@ifundefined{ifGPcolor}{%
|
||||
\newif\ifGPcolor
|
||||
\GPcolortrue
|
||||
}{}%
|
||||
\@ifundefined{ifGPblacktext}{%
|
||||
\newif\ifGPblacktext
|
||||
\GPblacktextfalse
|
||||
}{}%
|
||||
% define a \g@addto@macro without @ in the name:
|
||||
\let\gplgaddtomacro\g@addto@macro
|
||||
% define empty templates for all commands taking text:
|
||||
\gdef\gplbacktext{}%
|
||||
\gdef\gplfronttext{}%
|
||||
\makeatother
|
||||
\ifGPblacktext
|
||||
% no textcolor at all
|
||||
\def\colorrgb#1{}%
|
||||
\def\colorgray#1{}%
|
||||
\else
|
||||
% gray or color?
|
||||
\ifGPcolor
|
||||
\def\colorrgb#1{\color[rgb]{#1}}%
|
||||
\def\colorgray#1{\color[gray]{#1}}%
|
||||
\expandafter\def\csname LTw\endcsname{\color{white}}%
|
||||
\expandafter\def\csname LTb\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LTa\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT0\endcsname{\color[rgb]{1,0,0}}%
|
||||
\expandafter\def\csname LT1\endcsname{\color[rgb]{0,1,0}}%
|
||||
\expandafter\def\csname LT2\endcsname{\color[rgb]{0,0,1}}%
|
||||
\expandafter\def\csname LT3\endcsname{\color[rgb]{1,0,1}}%
|
||||
\expandafter\def\csname LT4\endcsname{\color[rgb]{0,1,1}}%
|
||||
\expandafter\def\csname LT5\endcsname{\color[rgb]{1,1,0}}%
|
||||
\expandafter\def\csname LT6\endcsname{\color[rgb]{0,0,0}}%
|
||||
\expandafter\def\csname LT7\endcsname{\color[rgb]{1,0.3,0}}%
|
||||
\expandafter\def\csname LT8\endcsname{\color[rgb]{0.5,0.5,0.5}}%
|
||||
\else
|
||||
% gray
|
||||
\def\colorrgb#1{\color{black}}%
|
||||
\def\colorgray#1{\color[gray]{#1}}%
|
||||
\expandafter\def\csname LTw\endcsname{\color{white}}%
|
||||
\expandafter\def\csname LTb\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LTa\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT0\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT1\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT2\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT3\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT4\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT5\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT6\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT7\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT8\endcsname{\color{black}}%
|
||||
\fi
|
||||
\fi
|
||||
\setlength{\unitlength}{0.0500bp}%
|
||||
\begin{picture}(5760.00,2520.00)%
|
||||
\gplgaddtomacro\gplbacktext{%
|
||||
\csname LTb\endcsname%
|
||||
\put(810,540){\makebox(0,0)[r]{\strut{} 0}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(810,828){\makebox(0,0)[r]{\strut{} 0.2}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(810,1116){\makebox(0,0)[r]{\strut{} 0.4}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(810,1404){\makebox(0,0)[r]{\strut{} 0.6}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(810,1692){\makebox(0,0)[r]{\strut{} 0.8}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(810,1980){\makebox(0,0)[r]{\strut{} 1}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(918,360){\makebox(0,0){\strut{} 0}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(1825,360){\makebox(0,0){\strut{} 0.2}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(2732,360){\makebox(0,0){\strut{} 0.4}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(3640,360){\makebox(0,0){\strut{} 0.6}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(4547,360){\makebox(0,0){\strut{} 0.8}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(5454,360){\makebox(0,0){\strut{} 1}}%
|
||||
\put(180,1260){\rotatebox{90}{\makebox(0,0){\strut{}Precision}}}%
|
||||
\put(3186,90){\makebox(0,0){\strut{}Recall}}%
|
||||
\put(3186,2250){\makebox(0,0){\strut{}UND: Precision Recall}}%
|
||||
}%
|
||||
\gplgaddtomacro\gplfronttext{%
|
||||
\csname LTb\endcsname%
|
||||
\put(2754,873){\makebox(0,0)[r]{\strut{}neutral model}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(2754,693){\makebox(0,0)[r]{\strut{}expression model}}%
|
||||
}%
|
||||
\gplbacktext
|
||||
\put(0,0){\includegraphics{und_PR}}%
|
||||
\gplfronttext
|
||||
\end{picture}%
|
||||
\endgroup
|
||||
@@ -1,115 +0,0 @@
|
||||
% GNUPLOT: LaTeX picture with Postscript
|
||||
\begingroup
|
||||
\fontfamily{phv}%
|
||||
\selectfont
|
||||
\makeatletter
|
||||
\providecommand\color[2][]{%
|
||||
\GenericError{(gnuplot) \space\space\space\@spaces}{%
|
||||
Package color not loaded in conjunction with
|
||||
terminal option `colourtext'%
|
||||
}{See the gnuplot documentation for explanation.%
|
||||
}{Either use 'blacktext' in gnuplot or load the package
|
||||
color.sty in LaTeX.}%
|
||||
\renewcommand\color[2][]{}%
|
||||
}%
|
||||
\providecommand\includegraphics[2][]{%
|
||||
\GenericError{(gnuplot) \space\space\space\@spaces}{%
|
||||
Package graphicx or graphics not loaded%
|
||||
}{See the gnuplot documentation for explanation.%
|
||||
}{The gnuplot epslatex terminal needs graphicx.sty or graphics.sty.}%
|
||||
\renewcommand\includegraphics[2][]{}%
|
||||
}%
|
||||
\providecommand\rotatebox[2]{#2}%
|
||||
\@ifundefined{ifGPcolor}{%
|
||||
\newif\ifGPcolor
|
||||
\GPcolortrue
|
||||
}{}%
|
||||
\@ifundefined{ifGPblacktext}{%
|
||||
\newif\ifGPblacktext
|
||||
\GPblacktexttrue
|
||||
}{}%
|
||||
% define a \g@addto@macro without @ in the name:
|
||||
\let\gplgaddtomacro\g@addto@macro
|
||||
% define empty templates for all commands taking text:
|
||||
\gdef\gplbacktext{}%
|
||||
\gdef\gplfronttext{}%
|
||||
\makeatother
|
||||
\ifGPblacktext
|
||||
% no textcolor at all
|
||||
\def\colorrgb#1{}%
|
||||
\def\colorgray#1{}%
|
||||
\else
|
||||
% gray or color?
|
||||
\ifGPcolor
|
||||
\def\colorrgb#1{\color[rgb]{#1}}%
|
||||
\def\colorgray#1{\color[gray]{#1}}%
|
||||
\expandafter\def\csname LTw\endcsname{\color{white}}%
|
||||
\expandafter\def\csname LTb\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LTa\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT0\endcsname{\color[rgb]{1,0,0}}%
|
||||
\expandafter\def\csname LT1\endcsname{\color[rgb]{0,1,0}}%
|
||||
\expandafter\def\csname LT2\endcsname{\color[rgb]{0,0,1}}%
|
||||
\expandafter\def\csname LT3\endcsname{\color[rgb]{1,0,1}}%
|
||||
\expandafter\def\csname LT4\endcsname{\color[rgb]{0,1,1}}%
|
||||
\expandafter\def\csname LT5\endcsname{\color[rgb]{1,1,0}}%
|
||||
\expandafter\def\csname LT6\endcsname{\color[rgb]{0,0,0}}%
|
||||
\expandafter\def\csname LT7\endcsname{\color[rgb]{1,0.3,0}}%
|
||||
\expandafter\def\csname LT8\endcsname{\color[rgb]{0.5,0.5,0.5}}%
|
||||
\else
|
||||
% gray
|
||||
\def\colorrgb#1{\color{black}}%
|
||||
\def\colorgray#1{\color[gray]{#1}}%
|
||||
\expandafter\def\csname LTw\endcsname{\color{white}}%
|
||||
\expandafter\def\csname LTb\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LTa\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT0\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT1\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT2\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT3\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT4\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT5\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT6\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT7\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT8\endcsname{\color{black}}%
|
||||
\fi
|
||||
\fi
|
||||
\setlength{\unitlength}{0.0500bp}%
|
||||
\begin{picture}(5760.00,2520.00)%
|
||||
\gplgaddtomacro\gplbacktext{%
|
||||
\csname LTb\endcsname%
|
||||
\put(810,540){\makebox(0,0)[r]{\strut{} 0}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(810,900){\makebox(0,0)[r]{\strut{} 0.5}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(810,1260){\makebox(0,0)[r]{\strut{} 1}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(810,1620){\makebox(0,0)[r]{\strut{} 1.5}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(810,1980){\makebox(0,0)[r]{\strut{} 2}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(918,360){\makebox(0,0){\strut{} 0}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(1825,360){\makebox(0,0){\strut{} 0.2}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(2732,360){\makebox(0,0){\strut{} 0.4}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(3640,360){\makebox(0,0){\strut{} 0.6}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(4547,360){\makebox(0,0){\strut{} 0.8}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(5454,360){\makebox(0,0){\strut{} 1}}%
|
||||
\put(180,1260){\rotatebox{90}{\makebox(0,0){\strut{}FRR \%}}}%
|
||||
\put(3186,90){\makebox(0,0){\strut{}FAR \%}}%
|
||||
\put(3186,2250){\makebox(0,0){\strut{}\bf \normalsize UND: Recognition Performance}}%
|
||||
}%
|
||||
\gplgaddtomacro\gplfronttext{%
|
||||
\csname LTb\endcsname%
|
||||
\put(4635,1827){\makebox(0,0)[r]{\strut{}neutral model}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(4635,1647){\makebox(0,0)[r]{\strut{}expression model}}%
|
||||
}%
|
||||
\gplbacktext
|
||||
\put(0,0){\includegraphics{und_far_frr}}%
|
||||
\gplfronttext
|
||||
\end{picture}%
|
||||
\endgroup
|
||||
@@ -1,127 +0,0 @@
|
||||
% GNUPLOT: LaTeX picture with Postscript
|
||||
\begingroup
|
||||
\fontfamily{phv}%
|
||||
\selectfont
|
||||
\makeatletter
|
||||
\providecommand\color[2][]{%
|
||||
\GenericError{(gnuplot) \space\space\space\@spaces}{%
|
||||
Package color not loaded in conjunction with
|
||||
terminal option `colourtext'%
|
||||
}{See the gnuplot documentation for explanation.%
|
||||
}{Either use 'blacktext' in gnuplot or load the package
|
||||
color.sty in LaTeX.}%
|
||||
\renewcommand\color[2][]{}%
|
||||
}%
|
||||
\providecommand\includegraphics[2][]{%
|
||||
\GenericError{(gnuplot) \space\space\space\@spaces}{%
|
||||
Package graphicx or graphics not loaded%
|
||||
}{See the gnuplot documentation for explanation.%
|
||||
}{The gnuplot epslatex terminal needs graphicx.sty or graphics.sty.}%
|
||||
\renewcommand\includegraphics[2][]{}%
|
||||
}%
|
||||
\providecommand\rotatebox[2]{#2}%
|
||||
\@ifundefined{ifGPcolor}{%
|
||||
\newif\ifGPcolor
|
||||
\GPcolortrue
|
||||
}{}%
|
||||
\@ifundefined{ifGPblacktext}{%
|
||||
\newif\ifGPblacktext
|
||||
\GPblacktexttrue
|
||||
}{}%
|
||||
% define a \g@addto@macro without @ in the name:
|
||||
\let\gplgaddtomacro\g@addto@macro
|
||||
% define empty templates for all commands taking text:
|
||||
\gdef\gplbacktext{}%
|
||||
\gdef\gplfronttext{}%
|
||||
\makeatother
|
||||
\ifGPblacktext
|
||||
% no textcolor at all
|
||||
\def\colorrgb#1{}%
|
||||
\def\colorgray#1{}%
|
||||
\else
|
||||
% gray or color?
|
||||
\ifGPcolor
|
||||
\def\colorrgb#1{\color[rgb]{#1}}%
|
||||
\def\colorgray#1{\color[gray]{#1}}%
|
||||
\expandafter\def\csname LTw\endcsname{\color{white}}%
|
||||
\expandafter\def\csname LTb\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LTa\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT0\endcsname{\color[rgb]{1,0,0}}%
|
||||
\expandafter\def\csname LT1\endcsname{\color[rgb]{0,1,0}}%
|
||||
\expandafter\def\csname LT2\endcsname{\color[rgb]{0,0,1}}%
|
||||
\expandafter\def\csname LT3\endcsname{\color[rgb]{1,0,1}}%
|
||||
\expandafter\def\csname LT4\endcsname{\color[rgb]{0,1,1}}%
|
||||
\expandafter\def\csname LT5\endcsname{\color[rgb]{1,1,0}}%
|
||||
\expandafter\def\csname LT6\endcsname{\color[rgb]{0,0,0}}%
|
||||
\expandafter\def\csname LT7\endcsname{\color[rgb]{1,0.3,0}}%
|
||||
\expandafter\def\csname LT8\endcsname{\color[rgb]{0.5,0.5,0.5}}%
|
||||
\else
|
||||
% gray
|
||||
\def\colorrgb#1{\color{black}}%
|
||||
\def\colorgray#1{\color[gray]{#1}}%
|
||||
\expandafter\def\csname LTw\endcsname{\color{white}}%
|
||||
\expandafter\def\csname LTb\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LTa\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT0\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT1\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT2\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT3\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT4\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT5\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT6\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT7\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT8\endcsname{\color{black}}%
|
||||
\fi
|
||||
\fi
|
||||
\setlength{\unitlength}{0.0500bp}%
|
||||
\begin{picture}(5760.00,2520.00)%
|
||||
\gplgaddtomacro\gplbacktext{%
|
||||
\csname LTb\endcsname%
|
||||
\put(918,540){\makebox(0,0)[r]{\strut{} 99.5}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(918,828){\makebox(0,0)[r]{\strut{} 99.6}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(918,1116){\makebox(0,0)[r]{\strut{} 99.7}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(918,1404){\makebox(0,0)[r]{\strut{} 99.8}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(918,1692){\makebox(0,0)[r]{\strut{} 99.9}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(918,1980){\makebox(0,0)[r]{\strut{} 100}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(1026,360){\makebox(0,0){\strut{} 0}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(1469,360){\makebox(0,0){\strut{} 2}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(1912,360){\makebox(0,0){\strut{} 4}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(2354,360){\makebox(0,0){\strut{} 6}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(2797,360){\makebox(0,0){\strut{} 8}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(3240,360){\makebox(0,0){\strut{} 10}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(3683,360){\makebox(0,0){\strut{} 12}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(4126,360){\makebox(0,0){\strut{} 14}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(4568,360){\makebox(0,0){\strut{} 16}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(5011,360){\makebox(0,0){\strut{} 18}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(5454,360){\makebox(0,0){\strut{} 20}}%
|
||||
\put(180,1260){\rotatebox{90}{\makebox(0,0){\strut{}MNCG \%}}}%
|
||||
\put(3240,90){\makebox(0,0){\strut{}$@(x)$}}%
|
||||
\put(3240,2250){\makebox(0,0){\strut{}\bf \normalsize UND: Mean Normalized Cumulative Gain}}%
|
||||
}%
|
||||
\gplgaddtomacro\gplfronttext{%
|
||||
\csname LTb\endcsname%
|
||||
\put(4635,873){\makebox(0,0)[r]{\strut{}neutral model}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(4635,693){\makebox(0,0)[r]{\strut{}expression model}}%
|
||||
}%
|
||||
\gplbacktext
|
||||
\put(0,0){\includegraphics{und_mncg}}%
|
||||
\gplfronttext
|
||||
\end{picture}%
|
||||
\endgroup
|
||||
@@ -1,117 +0,0 @@
|
||||
% GNUPLOT: LaTeX picture with Postscript
|
||||
\begingroup
|
||||
\fontfamily{phv}%
|
||||
\selectfont
|
||||
\makeatletter
|
||||
\providecommand\color[2][]{%
|
||||
\GenericError{(gnuplot) \space\space\space\@spaces}{%
|
||||
Package color not loaded in conjunction with
|
||||
terminal option `colourtext'%
|
||||
}{See the gnuplot documentation for explanation.%
|
||||
}{Either use 'blacktext' in gnuplot or load the package
|
||||
color.sty in LaTeX.}%
|
||||
\renewcommand\color[2][]{}%
|
||||
}%
|
||||
\providecommand\includegraphics[2][]{%
|
||||
\GenericError{(gnuplot) \space\space\space\@spaces}{%
|
||||
Package graphicx or graphics not loaded%
|
||||
}{See the gnuplot documentation for explanation.%
|
||||
}{The gnuplot epslatex terminal needs graphicx.sty or graphics.sty.}%
|
||||
\renewcommand\includegraphics[2][]{}%
|
||||
}%
|
||||
\providecommand\rotatebox[2]{#2}%
|
||||
\@ifundefined{ifGPcolor}{%
|
||||
\newif\ifGPcolor
|
||||
\GPcolortrue
|
||||
}{}%
|
||||
\@ifundefined{ifGPblacktext}{%
|
||||
\newif\ifGPblacktext
|
||||
\GPblacktexttrue
|
||||
}{}%
|
||||
% define a \g@addto@macro without @ in the name:
|
||||
\let\gplgaddtomacro\g@addto@macro
|
||||
% define empty templates for all commands taking text:
|
||||
\gdef\gplbacktext{}%
|
||||
\gdef\gplfronttext{}%
|
||||
\makeatother
|
||||
\ifGPblacktext
|
||||
% no textcolor at all
|
||||
\def\colorrgb#1{}%
|
||||
\def\colorgray#1{}%
|
||||
\else
|
||||
% gray or color?
|
||||
\ifGPcolor
|
||||
\def\colorrgb#1{\color[rgb]{#1}}%
|
||||
\def\colorgray#1{\color[gray]{#1}}%
|
||||
\expandafter\def\csname LTw\endcsname{\color{white}}%
|
||||
\expandafter\def\csname LTb\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LTa\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT0\endcsname{\color[rgb]{1,0,0}}%
|
||||
\expandafter\def\csname LT1\endcsname{\color[rgb]{0,1,0}}%
|
||||
\expandafter\def\csname LT2\endcsname{\color[rgb]{0,0,1}}%
|
||||
\expandafter\def\csname LT3\endcsname{\color[rgb]{1,0,1}}%
|
||||
\expandafter\def\csname LT4\endcsname{\color[rgb]{0,1,1}}%
|
||||
\expandafter\def\csname LT5\endcsname{\color[rgb]{1,1,0}}%
|
||||
\expandafter\def\csname LT6\endcsname{\color[rgb]{0,0,0}}%
|
||||
\expandafter\def\csname LT7\endcsname{\color[rgb]{1,0.3,0}}%
|
||||
\expandafter\def\csname LT8\endcsname{\color[rgb]{0.5,0.5,0.5}}%
|
||||
\else
|
||||
% gray
|
||||
\def\colorrgb#1{\color{black}}%
|
||||
\def\colorgray#1{\color[gray]{#1}}%
|
||||
\expandafter\def\csname LTw\endcsname{\color{white}}%
|
||||
\expandafter\def\csname LTb\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LTa\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT0\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT1\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT2\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT3\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT4\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT5\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT6\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT7\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT8\endcsname{\color{black}}%
|
||||
\fi
|
||||
\fi
|
||||
\setlength{\unitlength}{0.0500bp}%
|
||||
\begin{picture}(5760.00,2520.00)%
|
||||
\gplgaddtomacro\gplbacktext{%
|
||||
\csname LTb\endcsname%
|
||||
\put(810,540){\makebox(0,0)[r]{\strut{} 0}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(810,828){\makebox(0,0)[r]{\strut{} 20}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(810,1116){\makebox(0,0)[r]{\strut{} 40}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(810,1404){\makebox(0,0)[r]{\strut{} 60}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(810,1692){\makebox(0,0)[r]{\strut{} 80}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(810,1980){\makebox(0,0)[r]{\strut{} 100}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(918,360){\makebox(0,0){\strut{} 0}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(1825,360){\makebox(0,0){\strut{} 20}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(2732,360){\makebox(0,0){\strut{} 40}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(3640,360){\makebox(0,0){\strut{} 60}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(4547,360){\makebox(0,0){\strut{} 80}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(5454,360){\makebox(0,0){\strut{} 100}}%
|
||||
\put(180,1260){\rotatebox{90}{\makebox(0,0){\strut{}Precision \%}}}%
|
||||
\put(3186,90){\makebox(0,0){\strut{}Recall \%}}%
|
||||
\put(3186,2250){\makebox(0,0){\strut{}\bf \normalsize UND: Precision Recall}}%
|
||||
}%
|
||||
\gplgaddtomacro\gplfronttext{%
|
||||
\csname LTb\endcsname%
|
||||
\put(2754,873){\makebox(0,0)[r]{\strut{}neutral model}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(2754,693){\makebox(0,0)[r]{\strut{}expression model}}%
|
||||
}%
|
||||
\gplbacktext
|
||||
\put(0,0){\includegraphics{und_pr}}%
|
||||
\gplfronttext
|
||||
\end{picture}%
|
||||
\endgroup
|
||||