The matching of two-dimensional shapes is an important problem with applications in domains as diverse as biometrics, industry, medicine and anthropology. The distance measure used must be invariant to many distortions, including scale, offset, noise, partial occlusion, etc. Most of these distortions are relatively easy to handle, either in the representation of the data or in the similarity measure used. However rotation invariance seems to be uniquely difficult. Current approaches typically try to achieve rotation invariance in the representation of the data, at the expense of discrimination ability, or in the distance measure, at the expense of efficiency. In this work we show that we can take the slow but accurate approaches and dramatically speed them up. On real world problems our technique can take current approaches and make them four orders of magnitude faster, without false dismissals. Moreover, our technique can be used with any of the dozens of existing shape representations and with all the most popular distance measures including Euclidean distance, Dynamic Time Warping and Longest Common Subsequence
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