The global dimensionality of face space

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.

Estimation of Face Depths by Conditional Densities

“…For example, in row (b), the recovered faces are all plausible though blurred, and reflect the lighting and pose of the original. So far as identity and expression are concerned, however, they tend towards the mean, as would be expected given the dimensionality requirements for identification and expression analysis [7]. Reconstructions improve with increasing probe size, though wherever there are large areas missing, the fill-in again has the property of being appropriate in both geometry and shading and therefore plausible, but neutral so far as expression is concerned.…”

Facial Image Super Resolution Using Weighted Patch Pairs

“…This process is almost impossible unless we moderate the problem by narrowing down the domain into a specific application which in this special case is the human face domain. Since face images are well structured and have similar appearance, they span a small subset in the high dimensional image space [14]. This similarity can be more obvious when comparing texture and color of the skin or the shape of the eyes, nose, lips and the space between them in human facial images within the same race, sex and age.…”

Automatic Detection of the Optimal Acceptance Threshold in a Face Verification System

“…In this case, selection of facial features and kernels is an open issue. The second approach, based on Elastic Bunch Graph Matching (EBGM) [7] and similar methods, use wavelet transformation to obtain local description of the face and a graph to obtain a global face description. In the scientific literature several results with different research algorithms have been published.…”