Overcomplete image representations for texture analysis

Abstract

Computer vision has played an important role in many scientific and technological areas mainly because modern society highlights vision over other senses. At the same time, application requirements and complexity have also increased, so that in many cases, the optimal solution depends on the intrinsic characteristics of the problem. Therefore, it is difficult to propose a universal image model. In parallel, advances in understanding the human visual system have allowed to suggest sophisticated models that incorporate simple phenomena. This dissertation aims to investigate characteristics of vision such as over-representation and orientation of receptive fields to develop a bio-inspired image model for texture analysis. Fourier analysis is the most common way to characterize images in the space-frequency domain, however, this type of expansion is limited. As an alternative, a more general and powerful methodology based on the so-called overcomplete methods was used. Starting from the studies of Gabor [1], Daugman [2], and Hubel and Wiesel [3], the author proposes an overcomplete image model that takes advantage of redundant information such as greater flexibility in approximations (for instance, an image can be decomposed onto multiple bases) and the increased stability of the representation, namely less sensitive to noise. Another advantage is that it is possible to explain high-dimensional data in terms of a concise set of primitive features. The equivalence between the experimental findings on orientation selectivity of visual cortical neurons and the structure of Gabor functions allow to claim that this proposal is biologically inspired.