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We describe an efficient procedure for reassembling unknown two-dimensional objects that have been broken or torn into a large number of irregular fragments, a problem that often arises in archaeology, art restoration, forensics, and other disciplines. The procedure compares the curvature-encoded fragment outlines, at progressively increasing scales of resolution, using an incremental dynamic programming sequence-matching algorithm. The total cost gets reduced by a factor proportional to the mean number of samples per segment, which makes the method viable for problems of practical size (thousands of fragments). The performance of our method is illustrated with an artificial but realistic example.
Leitão et al. (Sun,) studied this question.