Among the visual features of multimedia content, shape is of particular interest because humans can often recognize objects solely on the basis of shape. Over the past three decades, there has been a great deal of research on shape analysis, focusing mostly on shape indexing, clustering, and classification. In this work, we introduce the new problem of finding shape discords, the most unusual shapes in a collection. We motivate the problem by considering the utility of shape discords in diverse domains including zoology, microscopy, anthropology, and medicine. While the brute force search algorithm has quadratic time complexity, we avoid this untenable lethargy by using locality-sensitive hashing to estimate similarity between shapes which enables us to reorder the search more efficiently and thus extract the maximum benefit from an admissible pruning strategy we introduce. An extensive experimental evaluation demonstrates that our approach is empirically linear in time.
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