Gabor functions have wide-spread applications both in analyzing the visual cortex of mammalians and in designing machine vision algorithms. It is known that the receptive field of neurons of V1 layer in the visual cortex can be accurately modeled by Gabor functions. In addition, Gabor functions are extensively used for feature extraction in machine vision tasks. In this paper, we prove that Gabor functions are translation-invariant positive-definite kernels and show that the problem of image representation with Gabor functions can be formulated as infinite kernel learning regression. Specifically, we use the stabilized infinite kernel learning regression algorithm that has already been introduced for learning translation-invariant positive-definite kernels and has enough flexibility and generality to embrace the class of Gabor kernels. The algorithm yields a representation of the image as a support vector expansion with a compound kernel that is a finite mixture of Gabor functions. The problem with this representation is that all Gabor functions are present at all support vector pixels. Using LASSO, we propose a method for sparse representation of an image with Gabor functions in which each Gabor function is positioned at a very sparse set of pixels. As a practical application, we introduce a novel method for learning a dataset-specific set of Gabor filters that can be used subsequently for feature extraction. Our experiments on CMU-PIE and Extended Yale B datasets show that use of the learned Gabor filters significantly improves the recognition accuracy of a recently introduced face recognition algorithm.

Keywords