Dynamic Programming on the Multidimensional Grid and Fast Search Algorithm for Energy Minimization in Stereo and Optical Flow

— In this paper, a recursive algorithm that considerably reduces the computational complexity of the minimum search problem has been presented. The mentioned reduction is especially significant if the disparity space is 2D or 3D. The proposed method can be applied in the well-known dynamic programming (DP) approach for stereo and motion. In this case, the general 2D problem of the global discrete energy minimization has been reduced to several mutually independent sub-problems of one-dimensional minimization, and an exact solution has been obtained for each sub-problem. A new modification of DP techniques, which we call extended dynamic programming for energy minimization (EDP), has been also presented in this paper. The EDP method is used if an approximation of the general 2D discrete energy minimization problem is considered. In this case, the proposed recursive minimum search (RMS) algorithm is an essential part of the EDP method. Using the EDP algorithm, we have obtained a lower energy than the graph cuts expansion technique on stereo and motion problems.