A Nonlinear Model of Visual Information Processing Based on Discrete Maximal Overlap Wavelets

Abstract

The purpose of this paper is to give a new computational model of early visual information processing, and to simulate by using the model the occurrence of visual illusions. The model proposed in this paper is constructed as a maximal overlap biorthogonal wavelet filter bank equipped with a nonlinear processing modeled after ''contrast induction'' effect (for the definition, see Section 3). This model provides good computer simulations of the occurrence of many lightness illusions such as the Mach band, the Hermann grid, the Chevreul illusion, and other related illusions. Moreover, also the café wall illusion is studied by using the model.

2D tight framelets with orientation selectivity suggested by vision science

“…We refer our paper [9] why MOGMRA is suitable for studying mathematical models of visual information processing. See [10] and [11] for maximal overlap multiresolution analysis for wavelets.…”

Finite Discrete, Shift-Invariant, Directional Filterbanks for Visual Information Processing, I : Construction

“…Indeed real visual information processing is carried out not only by simple cells in V1, but also by horizontal connection of neurons, and the latter is global and nonlinear processing; the nonlinear processing will break tightness and even perfect reconstruction property. In fact, in the previous paper [1], we gave a mathematical formulation of such a global, nonlinear processing, and constructed a model by bringing the nonlinear effect to a maximal overlap, bi-orthogonal, separable wavelet filterbank. Further, using this model, we gave good computer simulations of occurrence of certain visual illusions.…”

“…Separable wavelets which we adopted in [1] have only three directions: horizontal, vertical and diagonal. Therefore, in order to study vision by mathematical method more precisely, we need to construct nonlinear models based on our 2D filterbanks with better orientation selectivity.…”

“…Since these filterbanks do not possess enough orientation selectivity, in the next section we make 2D filterbanks with good orientation selectivity from the filterbanks described in this section. As was pointed out in the previous paper by the first author [1], the shift-invariant filterbanks are desirable experimentally more than maximal decimated ones for studying nonlinear models of vision. Hence we intend to give 2D filterbanks this property.…”

Framelet analysis of some geometrical illusions

“…In that paper we used maximal overlap version of a biorthogonal wavelet constructed in Cohen et al [6]. We refer [1] for nonlinear analysis of Cafe Wall illusion and twisted cords.…”