AbstractWe present a novel approach to matching and recognition of 2D shapes, which uses a chord-based shape representation and matches shapes by finding correspondences between chords. Given a 2D shape, we choose its basis chord such that both end points of the chord have high probability of being present under occlusion. Then the shape is transformed and represented in an internal reference frame uniquely defined by the basis chord. In this chord-based reference frame, we capture the coordinate distribution of all shape points using a point density graph. When a second shape is being matched against the first shape, we pursue a chord on the second shape based on which the second shape’s point density graph is the closest to that of the first shape. To avoid exhaustive search of all chords on the second shape, we use the Chord Length Distributions of the two shapes to prune a dominant portion of the search space. The distance between two point density graphs is measured using a symmetrized Kullback-Leibler divergence. Then when the correspondence between a pair of chords is established, a unique similarity transform is determined to match the two shapes so that the corresponding chords are aligned. Finally, we employ a hierarchical approach to extend our method to include Affine transformations. Matching and Recognition results from the Brown SIID project shapes, the MNIST dataset of handwritten digits, and the SQUID fish database, demonstrate our algorithm’s performance, its invariance properties and its robustness to occlusion, articulation, missing gaps, and spurious structures on shapes.
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