Viterbi algorithm as an alternative to energy minimization for stereo image matching

The correspondence problem in image matching is an ill-defined one. It is difficult to match two stereo images to produce an accurate depth map without applying some sort of constraints to the matching process. Matching is made especially difficult near discontinuities and occlusions in the images. A popular method of applying constraints to image matching is energy minimisation. However, this technique is computationally expensive and is not guaranteed to finish at an optimal solution. This paper describes the use of a least cost path finding algorithm called the Viterbi algorithm as an alternative to energy minimisation. The Viterbi algorithm operates on individual horizontal scanlines and uses a cost function to find the optimum "path" of nodes through disparity space from one side of the image to the other. Constraints can be applied by restricting the possible movements of the path or by modifying the cost function. The Viterbi algorithm, unlike energy minimisation, is not an iterative process and is guaranteed to find the path that has the least possible cost. The implementation of the Viterbi algorithm described in this paper uses constraints that were developed to make the image matching robust in the presence of discontinuities and occlusions. Results are shown for both synthetic and real-world stereo pairs.