Stereo Vision Using Cost-Relaxation with 3D Support Regions

In this paper a new stereo algorithm is presented for computing dense disparity maps from stereo image pairs using a cost relaxation approach, where the disparity map is the momentary state of a dynamic system. Following biologically motivated cooperative approaches a disparity space is defined with cooperating probability variables. In a first step a correlation based similarity measure is performed to initialize the relaxation process. Due to a very simple mathematical formulation, the relaxation itself could be realized as an optimization of a global cost function taking into account both the stereoscopic continuity constraint and considerations of the pixel similarity. The continuity constraint is implemented using a 3D Gaussian-weighted local support area of coupling probability variables which interact during the relaxation process. A special construction of the global cost function guarantees the existence of a unique global minimum of the cost function, which can be easily found with the help of a standard numerical procedure. In a post-processing step occlusions are detected and a sub-pixel precise disparity map is computed.