Partial Matching of Planar Polygons Under Translation and Rotation

Curve matching is an important computational task for domains such as: reconstruction of archaeological fragments, forensics investigation, measuring melodic similarity, and model-based object recognition. There are a variety of measures and algorithmic approaches used to address the curve matching problem including: shape signature strings with substring matching, geometric hashing, and Hausdorff distance approaches. In this paper we propose an approach that uses a turning function representation of the shape and also uses a L2 measure for comparing matches. The novel algorithm presented finds the best match along some fixed length portions of two polygons where the polygons may be arbitrarily translated and rotated. The algorithm’s time complexity is O(mn(n+m)) where n and m are the numbers of verticies in the perimeters being matched. The utility of the algorithm is demonstrated in the reconstruction of a small jigsaw puzzle.