Fast Best-Match Shape Searching in Rotation Invariant Metric Spaces

The matching of two-dimensional shapes is an important problem with applications in domains as diverse as biometrics, industry, medicine and zoology. 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 explore the metric properties of the rotation invariant distance measures and propose an algorithm for fast similarity searching in the shape space. The algorithm is demonstrated to introduce a dramatic speed-up over the current approaches, and is guaranteed to introduce no false dismissals. The technique avoids a large percentage of the comparisons between a query and the elements at hand, which makes it especially attractive when large shape collections are available and indexing is required.