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To reduce the dimensionality and improve the significativeness of the features, only the
features with maximal relevance and minimal redundancy have been selected using a feature
selection analysis. In particular, feature selection is performed using the minimal redundancy
maximal relevance (mRMR) model (Peng et al., 2005). For a given classification task, the
aim of mRMR is to select a subset of features by taking into account the ability of features to
identify the classification label, as well as the redundancy among the features. These concepts
are defined in terms of the mutual information between features.
In our approach, the mRMR algorithm is applied to the set of 10112-dimensional feature
vectors representing the faces. Each vector v f
f 10112 ) is constructed by concate-
nating the 128-dimensional SIFT descriptors computed at the face keypoints, orderly from 1 to
79. A data discretization into three levels is applied to the vectors as preprocessing step. This
is obtained by computing the mean value
=
( f 1 ,...,
σ k for every feature
f k . Then, discretized values f k are obtained. The overall set of discretized feature vectors is
used to feed the mRMR algorithm so as to determine the features which are most relevant in
discriminating between different facial expressions of 3D face scans of different subjects.
The facial expression recognition problem is a multiclassification task that is faced as a
combination of separated instances of one-versus-all classification subproblems. For each
subproblem, face scans showing one expression are assumed as targets (positive examples),
whereas all the other scans with any different expression are considered as negative examples.
Repeatedly, the target expression is changed among the six basic expressions provided by the
BU-3DFE database, hence, the sets of positive and negative examples change. Because of
this, mRMR feature selection is performed independently for each classification subproblem.
In general, this results into different features providing the minimal redundancy and maximal
relevance for the purpose of discriminating across different facial expressions. Then, just the
most relevant features identified for every expression are retained from the original feature
vectors in order to train the classifiers. This results into vectors v expr
f
μ k and the standard deviation
( f p 1 ,...,
f p Nexpr ), where
=
p Nexpr are the indices of the features components selected in the original vector, and
the subscript the label of a particular expression.
The selected features are then used to perform facial expression recognition using a maxima
rule between six one-versus - all SVM classifiers, each with a radial basis function kernel of
standard deviation equal to one (the publicly available SVMLight implementation of SVM
has been used: http://svmlight.joachims.org/).
p 1 ,...,
5.5 4D Facial Expression Recognition
The use of 4D data for face analysis applications is still at its nascent stages, with no research
on face recognition from sequences of 3D face scans and very little research focusing on
facial expression recognition. The first approach addressing the problem of facial expression
recognition from dynamic sequences of 3D scans was proposed by Sun et al. Sun and Yin
(2008). Their approach basically relies on the use of a generic deformable 3D model whose
changes are tracked both in space and time in order to extract a spatio-temporal descriptor
of the face. In the temporal analysis, a vertex flow tracking technique is applied to adapt the
3D deformable model to each frame of the 3D face sequences, and the vertex flow estimation
is derived by establishing point to point correspondences between 3D meshes on the basis
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