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Adaptive Locally Affine-Invariant Shape Matching

Matching deformable objects using their shapes is an important problem in computer vision since shape is perhaps the most distinguishable characteristic of an object. The problem is difficult due to many factors such as intra-class variations, local deformations, articulations, viewpoint changes and missed and extraneous contour portions due to errors in shape extraction. While small local deformations has been handled in the literature by allowing some leeway in the matching of individual contour points via methods such as Chamfer distance and Hausdorff distance, handling more severe deformations and articulations has been done by applying local geometric corrections such as similarity or affine. However, determining which portions of the shape should be used for the geometric corrections is very hard, although some methods have been tried. In this paper, we address this problem by an efficient search for the group of contour segments to be clustered together for a geometric correction using Dynamic Programming by essentially searching for the segmentations of two shapes that lead to the best matching between them. At the same time, we allow portions of the contours to remain unmatched to handle missing and extraneous contour portions. Experiments indicate that our method outperforms other algorithms, especially when the shapes to be matched are more complex.