Stereo Algorithm with Reaction-Diffusion Equations

Three-dimensional depth reconstruction from a pair of stereo images needs to find reliable stereo correspondence between left and right images. Stereo disparity refers to difference of positions between two corresponding points on the stereo images. Although there are many possibilities in finding the stereo correspondence, the human vision system successfully reconstructs three-dimensional depth distribution with binocular vision. Thus, we can expect that solving the stereo correspondence problem brings a key mechanism to understand the human vision system. The human vision system can solve the stereo correspondence problem from random-dot stereograms, which refer to a pair of stereo images consisting of only a randomly dotted pattern. Julesz demonstrated that the randomly dotted pattern is enough for the human vision system to solve the stereo correspondence problem (Julesz, 1960). When the human vision system is exposed to random-dot stereograms, it perceives three-dimensional structure emerging spontaneously. This implies that the human vision system has a module being able to detect stereo disparity from only a randomly dotted pattern and not requiring key information such as edges and feature points, which generally appear in natural scenes. Several researchers presented stereo algorithms to solve the stereo correspondence problem from random-dot stereograms in the early period of computer vision research. In particular, Marr and Poggio presented a representative stereo algorithm named the cooperative algorithm (Marr & Poggio, 1976). Their motivation to approach the stereo correspondence problem exists in the biological aspect of the human vision system; their algorithm consists of multi-layered cell networks. Their most important proposal to the stereo algorithm is the two famous constraints: continuity and uniqueness. The authors have been approaching several subjects in image processing and computer vision research, by utilizing reaction-diffusion equations as a biologically motivated tool (Nomura et al., 2007). We call the group of algorithms utilizing reaction-diffusion equations the reaction-diffusion algorithm. The previous research done by the authors presented several algorithms for edge detection, segmentation (grouping) and stereo disparity detection by utilizing the FitzHugh-Nagumo type reaction-diffusion equations. This chapter presents a stereo algorithm utilizing multi-sets of the FitzHugh-Nagumo type reaction-diffusion equations. We associate each set of the equations with each of possible disparity levels; a particular grid point of the set represents existence or non-existence of its associated disparity level. The filling-in process originally built in the reaction-diffusion O pe n A cc es s D at ab as e w w w .ite ch on lin e. co m