Matching 3-D arcs

We present a new algorithm for efficient matching of 3-D polygonal arcs. The algorithm is based on the decomposition of the arcs into sets of corresponding line segments with equal lengths. We derive a closed-form solution for the transformation that gives the best match between two sets of corresponding line segments (best in the sense of an L₂ norm distance measure), which enables the development of efficient arc matching algorithm. We apply this algorithm to the problem of finding a match between a short are and a piece of a long arc in real and synthetic images, and compare the results with alternative techniques in the literature