Supporting anthropological research with efficient rotation invariant shape similarity measurement

The matching of two-dimensional shapes is an important problem with many applications in anthropology. Examples of objects that anthropologists are interested in classifying, clustering and indexing based on shape include bone fragments, projectile points (arrowheads/spearpoints), petroglyphs and ceramics. Interest in matching such objects originates from the fundamental question for many biological anthropologists and archaeologists: how can we best quantify differences and similarities? This interest is fuelled in part by a movement that notes: 'an increasing number of archaeologists are showing interest in employing Darwinian evolutionary theory to explain variation in the material record'. Aiding such research efforts with computers requires a shape similarity measure that is 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 poor 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. We show the applications of our work to several important problems in anthropology, including clustering and indexing of skulls, projectile points and petroglyphs.