Low-dimensional representations of sensory signals are key to solving many of the computational problems encountered in high-level vision. Principal Component Analysis has been used in the past to derive practically useful compact representations for di erent classes of objects. One major objection to the applicability of PCA is that it invariably leads to global, nontopographic representations that are not amenable to further processing and are not biologically plausible. In this paper we present a new mathematical construction|Local Feature Analysis (LFA)|for deriving local topographic representations for any class of objects. The LFA representations are sparse-distributed and, hence, are e ectively low-dimensional and retain all the advantages of the compact representations of the PCA. But unlike the global eigenmodes, they give a description of objects in terms of statistically derived local features and their positions. We illustrate the theory by using it to extract local features for three ensembles|2D images of faces without background, 3D surfaces of human heads, and nally 2D faces on a background. The resulting local representations have powerful applications in head segmentation and face recognition.

No abstract

Low-dimensional representations of sensory signals are key to solving many of the computational problems encountered in high-level vision. Principal Component Analysis (PCA) has been used in the past to derive such compact representations for the object class of human faces. Here, with an interpretation of PCA as a probabilistic model, we employ two objective criteria to study its generalization properties in the context of large frontal-pose face databases. We find that the eigenfaces, the eigenspectrum, and the generalization depend strongly on the ensemble composition and size, with statistics for populations as large as 5500, still not stationary. Further, the assumption of mirror symmetry of the ensemble improves the quality of the results substantially in the low-statistics regime, and is also essential in the high-statistics regime. We employ a perceptual criterion and argue that, even with large statistics, the dimensionality of the PCA subspace necessary for adequate representation of the identity information in relatively tightly cropped faces is in the 400-700 range, and we show that a dimensionality of 200 is inadequate. Finally, we discuss some of the shortcomings of PCA and suggest possible solutions.

No abstract

No abstract