Volterrafaces: Discriminant analysis using Volterra kernels

Abstract

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 non-linear 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 non-linear 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 intra-class distances and inter-class 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.

Nearest neighbor classifier generalization through spatially constrained filters

“…: It should be noted that there has been some previous work performed in literature on the topic of learning filters for vision tasks such as object alignment and classification [13,14,15]. The paper closest in spirit to our own, can be found in the seminal work of Kumar et al [15] concerning discriminant analysis using Volterra kernels (specifically when a first order approximation of the kernel is employed). Like our approach, the authors present an approach that applies discriminant analysis to sub-patches in an image, rather than the whole image itself.…”

“…Their approach exhibits impressive empirical performance for a number of NN facial identity tasks compared to current state of the art. Although similar conceptually, our work di↵ers substantially to the work of Kumar et al [15]. First, our work is centrally motivated by the connection between filters as a distance metric in the Fourier domain.…”

“…First, our work is centrally motivated by the connection between filters as a distance metric in the Fourier domain. Unlike [15] we provide theoretical insight into the uniqueness of filters with respect to linear NN classification. Finally, our work is focused on investigating the role of filters with spatial constraints in encoding generalizations into classifiers whereas [15] concentrated solely on classification performance.…”

Local Generic Representation for Face Recognition with Single Sample per Person

“…Patch/block based methods [16][8] [17][18] [19] partition each face image into several patches/blocks, and then perform feature extraction and classification on them. First, patches can be viewed as independent samples for feature extraction [16] [8].…”

Discriminative Data Transform for Image Feature Extraction and Classification

“…Second, we design another learning-based method to further transform the extracted feature descriptor for more accurate image classification. Our method is inspired by the recent studies on face recognition [7,8], in which the images are transformed with learned filters to obtain more discriminative features. We extend the LBP-based filter learning [8] to the BRIEF feature and descriptor transform.…”