Stereo Algorithm with Anisotropic Reaction-Diffusion Systems
Atsushi Nomura, Koichi Okada, Hidetoshi Miike, Yoshiki Mizukami, Makoto Ichikawa, Tatsunari Sakurai · InTech eBooks · 2012
Stereo Visioncorrespondence problem and to obtain a dense stereo disparity map, they proposed imposing two constraints: uniqueness and continuity on the disparity map.The uniqueness constraint states that a point on the stereo disparity map has a unique disparity level except for transparent surfaces and object boundaries having multiple disparity levels.The continuity constraint states that neighboring grid points share the same or similar disparity levels except object boundaries.Marr and Poggio designed the grid system so as to satisfy the two constraints, by connecting neighboring cells cooperatively for the continuity constraint, and by connecting multi-layered grid systems exclusively for the uniqueness constraint.Psychological and biophysical research results have affected the computer vision research including the cooperative algorithm.According to the Gestalt psychology [10,11], when the human visual system captures an image consisting of small figures such as short lines and small crosses, it perceives a group of neighboring elements sharing the same or similar visual properties [12].The Gestalt psychologists originally found this phenomenon and clearly stated the laws of closure, similarity, proximity, symmetry, continuity and common fate.In addition, previous biophysical research results showed that biological cells respond to external stimuli and exhibit a nonlinear excitation-inhibition process.Therefore, we understand that these previous results have affected the cooperative algorithm by Marr and Poggio.We can find similarities between the continuity constraint and the perceptual grouping exhibiting the laws of similarity, proximity and continuity, and between behavior of artificial cells in the cooperative algorithm and the cell responses in the excitation-inhibition process.We previously presented several reaction-diffusion algorithms for segmentation and stereo disparity detection under the concept of reaction-diffusion systems [13,14].A reaction-diffusion system refers to the system of diffusively coupled elements exhibiting an excitation-inhibition process [15].The reaction-diffusion system is mathematically described with a set of time-evolving partial differential equations consisting of diffusion terms and reaction ones.By numerically computing the reaction-diffusion system, we can simulate spatio-temporal phenomena such as pulse propagation observed in natural and biological systems, for example, in biological information transmission processes.We can expect that the pulse propagation phenomenon in a reaction-diffusion system serves as the continuity constraint in the stereo correspondence problem, and thus we proposed a stereo algorithm consisting of exclusively connected multi-layered reaction-diffusion systems [14].In addition, inspired by the strong inhibitory diffusion causing Turing patterns [16], and suggested by a lateral inhibition mechanism in a biological visual system [17], we have imposed the strong inhibitory diffusion on the reaction-diffusion stereo algorithm.This chapter presents recent advances in the reaction-diffusion stereo algorithm introducing anisotropy in diffusion processes.After quickly reviewing previous related work achieved in several different areas of psychology, stereo algorithms, reaction-diffusion and physiology in Section 2, we describe elementary stereo geometry, the cooperative algorithm and a reaction-diffusion system as preliminaries in Section 3.Then, we proceed to the original reaction-diffusion stereo algorithm with isotropic diffusion processes and its recent advances introducing anisotropic diffusion processes in Section 4. The section also presents the cooperative algorithm revised with a reaction-diffusion system.Then, we demonstrate comparison among the reaction-diffusion stereo algorithms including the original and