Volterrafaces: Discriminant analysis using Volterra kernels

In this paper we present a novel face classification system where we represent face images as a spatial arrangement of image patches, and seek a smooth nonlinear functional mapping for the corresponding patches such that in the range space, patches of the same face are close to one another, while patches from different faces are far apart, in L
₂
sense. We accomplish this using Volterra kernels, which can generate successively better approximations to any smooth nonlinear functional. During learning, for each set of corresponding patches we recover a Volterra kernel by minimizing a goodness functional defined over the range space of the sought functional. We show that for our definition of the goodness functional, which minimizes the ratio between intraclass distances and interclass distances, the problem of generating Volterra approximations, to any order, can be posed as a generalized eigenvalue problem. During testing, each patch from the test image that is classified independently, casts a vote towards image classification and the class with the maximum votes is chosen as the winner. We demonstrate the effectiveness of the proposed technique in recognizing faces by extensive experiments on Yale, CMU PIE and Extended Yale B benchmark face datasets and show that our technique consistently outperforms the state-of-the-art in learning based face discrimination.