General stereo image matching using symmetric complex wavelets

General stereo image matching provides an adequate but hard problem with sufficient complexity, with which the potential of wavelets may be exploited to a full extend. An ideal stereo image matching algorithm is supposed to be invariant to the scale, translation, rotation, and partial correspondence between two given stereo images. While the multi-resolution of wavelets is good at scale adaptivity, we also require the wavelet transform and pyramids to be translation- and rotation-invariant. This paper is intended to serve for three purposes: (1) To present the general problem of stereo image matching in a sufficient depth and extent, so that pure wavelet mathematicians could think on adequate and efficient solutions, (2) To present a complete algorithm for top-down image matching including surface reconstruction by using wavelet pyramids, (3) To search for a wavelet family optimal for image matching. It is expected that a family of adequately designed wavelets could provide a generic and robust solution to the stereo image matching problem, which could be an important breakthrough in computer vision, photogrammetry, and pattern recognition.