Reaction-Diffusion Algorithm for Vision Systems

Vision systems require fundamental algorithms of image processing and vision computing. Algorithms of edge detection, grouping and stereo disparity detection are typical examples. Marr and his collaborators proposed several effective algorithms of edge detection and stereo disparity detection, in particular, in a computational approach (Marr, 1982). Marr and Hildreth had previously proposed an edge detection algorithm (Marr and Hildreth, 1980), in which edge points were defined as those having a high brightness gradient over space. They utilized the Gaussian filter combined with the Laplacian one; the Gaussian filter removes noise components, and the Laplacian filter senses a brightness gradient. They additionally proposed an alternative algorithm that utilizes difference of two Gaussian filters having two different space constants of excitation and inhibition. Both of these two algorithms utilize the Gaussian filter; the output of the filter is equivalent to the solution of the diffusion equation. Their proposal highly attracted other researchers’ attention, resulting in the development of many edge detection algorithms starting from the Gaussian filter or the diffusion equation, in which, for example, anisotropy was introduced into the diffusion equation (Perona & Malik, 1990). Regarding stereo disparity detection, Marr and Poggio proposed “the cooperative algorithm” (Marr and Poggio, 1976; Marr et al., 1978). Stereo cameras project a target point located in a three-dimensional world onto two points on their left and right image planes; stereo disparity refers to the difference of the two points. A stereo disparity map helps to reconstruct the three-dimensional world and thus has many applications in vision systems. To construct a reliable stereo disparity map, Marr and Poggio made two important constraints, one of which is that spatial adjacent points on a stereo disparity map must have similar disparity levels. This constraint allows us to propagate disparity information in a spatial local area. Therefore, the cooperative algorithm for the stereo disparity detection utilizes an information propagation mechanism, which roughly refers to the mechanism of diffusion. Using this cooperative algorithm, other researchers have proposed several methods of stereo disparity detection (Zitnick & Kanade, 2000). There are several interesting approaches to image processing and vision computing not only in the field of computer science, but also in the natural sciences. Kuhnert et al. demonstrated that a chemical reaction system solves the typical image processing tasks of edge detection