A Hierarchical Symmetric Stereo Algorithm Using Dynamic Programming

In this paper, a new hierarchical stereo algorithm is presented. The algorithm matches individual pixels in corresponding scanlines by minimizing a cost function. Several cost functions are compared. The algorithm achieves a tremendous gain in speed and memory requirements by implementing it hierarchically. The images are downsampled an optimal number of times and the disparity map of a lower level is used as ‘offset’ disparity map at a higher level. An important contribution consists of the complexity analysis of the algorithm. It is shown that this complexity is independent of the disparityrange. This result is also used to determine the optimal number of downsample levels. This speed gain results in the ability to use more complex (compute intensive) cost functions that deliver high quality disparity maps. Another advantage of this algorithm is that cost functions can be chosen independent of the optimisation algorithm. The algorithm in this paper is symmetric, i.e. exactly the same matches are found if left and right image are swapped. Finally, the algorithm was carefully implemented so that a minimal amount of memory is used. It has proven its efficiency on large images with a high disparity range as well as its quality. Examples are given in this paper.