Recovering the Shape from Texture Using Lognormal Filters

Abstract

How does the visual cortex extract perspective information from textured surfaces? To answer this question, we propose a biologically plausible algorithm based on a simplified model of the visual processing. First, new log-normal filters are presented in replacement of the classical Gabor filters. Particularly, these filters are separable in frequency and orientation and this characteristic is used to derive a robust method to estimate the local mean frequency in the image. Based on this new approach, a local decomposition of the image into patches, after a retinal pre-treatment, leads to the estimation of the local frequency variation all over the surface. The analytical relation between the local frequency and the geometrical parameters of the surface, under perspective projection, is derived and finally allows to solve the so-called problem of recovering the shape from the texture. The accuracy of the method is evaluated and discussed on different kind of textures, both regular and irregular, and also on natural scenes.