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Image Representationsfor Facial Expression Coding
been observed in spontaneous behavior. An automated system would make facial
expression measurement more widely accessible as a research tool for behavioral science and medicine. Such a system would also have application in human-computer
interaction tools and low bandwidth facial animation coding.
A number of systems have appeared in the computer vision literature for classifying
facial expressions into a few basic categories of emotion, such as happy, sad, or
surprised. While such approaches are important, an objective and detailed measure
of facial activity such as FACS is needed for basic research into facial behavior. In a
system being developed concurrently for automatic facial action coding, Cohn and
colleagues (7) employ feature point tracking of a select set of image points. Techniques employing 2-D image filters have proven to be more effective than featurebased representations for face image analysis [e.g. (6)]. Here we examine image
analysis techniques that densely analyze graylevel information in the face image.
This work surveys and compares techniques for face image analysis as applied to
automated FACS encoding.' The analysis focuses on methods for face image representation in which image graylevels are described as a linear superposition of basis
images. The techniques were compared on a common image testbed using common
similarity measures and classifiers.
We compared four representations in which the basis images were learned from
the statistics of the face image ensemble. These include unsupervised learning
techniques such as principal component analysis (PCA), and local feature analysis (LFA), which are learned from the second-order dependences among the image
pixels, and independent component analysis (ICA) which is learned from the highorder dependencies as well. We also examined a representation obtained through
supervised learning on the second-order image statistics, Fisher's linear discriminants (FLD). Classification performances with these data-driven basis images were
compared to Gabor wavelets, in which the basis images were pre-defined. We examined properties of optimal basis images, where optimal was defined in terms of
classification.
Generalization to novel faces was evaluated using leave-one-out cross-validation.
Two basic classifiers were employed: nearest neighbor and template matching, where
the templates were the mean feature vectors for each class. Two similarity measures
were employed for each classifier: Euclidean-distance and cosine of the angle between
feature vectors.
Inner brow raiser
Outer brow raiser
Brow lowa
Figure 1: a. The facial muscles underlying six of the 46 facial actions. b. Cropped
face images and &images for three facial actions (AU7s).
'A detailed description of this work appears in (8).
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Image Representations for Facial Expression Coding
Figure 2: a. First 4 PCA basis images. b. Four ICA basis images. The ICA basis
images are local, spatially opponent, and adaptive. c. Gabor kernels are local,
spatially opponent, and predefined. d. First 4 local PCA basis images.
We begin with the matrix P containing the principal component eigenvectors in
its columns, and Xi are the corresponding eigenvalues. Each row of the matrix K
serves as an element of the LFA image dictionary2
K = P V P ~ where V = D-4 =
where X i are the eigenvalues. The rows of K were found to have spatially local properties, and are "topographic" in the sense that they are indexed by spatial location
(15). The dimensionality of the LFA representation was reduced by employing an
iterative sparsification algorithm based on multiple linear regression described in
(15)The LFA representation attained 81.1% correct classification performance. Best
performance was obtained using the first 155 kernels, the cosine similarity measure,
and nearest neighbor classifier. Classification performance using LFA was not significantly different from the performance using PCA. Although a face recognition
algorithm based on the principles of LFA outperformed Eigenfaces in the March
1995 FERET competition, the exact algorithm has not been disclosed. Our results
suggest that an aspect of the algorithm other than the LFA representation accounts
for the difference in performance.
3.3
Independent Component Analysis (ICA)
Representations such as Eigenfaces, LFA, and FLD are based on the second-order
dependencies among the pixels, but are insensitive to the high-order dependencies.
High-order dependencies are relationships that cannot be described by a linear predictor. Independent component analysis (ICA) learns the high-order dependencies
in addition to the second-order dependencies among the pixels.
2 ~ image
n
dictionary is a set of images that decomposes other images, e.g. through
inner product. Here it finds the coefficients for the basis set K-'
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