Shape recognition has applications in computer vision tasks such as industrial automated inspection and automatic target recognition. When objects are occluded, many recognition methods that use global information will fail. To recognize partially occluded objects, we represent each object by a Set of landmarks. The landmarks of an object are points of interest which have important shape attributes and are usually obtained from the object boundary. In this study, we use high curvature points along an object boundary as the landmarks of the object. Given a scene consisting of partially occluded objects, the hypothesis of a model object in the scene is verified by matching the landmarks of an object with those in the scene. A measure of similarity between two landmarks, one from a model and the other from a scene, is needed to perform this matching. One such local shape measure is the sphericity of a triangular transformation mapping the model landmark and its two neighboring landmarks to the scene landmark and its two neighboring landmarks. Sphericity is in general defined for a diffeomorphism. Its invariant properties under a group of transformation, namely, translation, rotation, and scaling are derived. The sphericity of a triangular transformation is shown to be a robust local shape measure in the sense that minor distortion in the landmarks does not significantly alter its value. To match landmarks between a model and a scene, a table of compatibility, where each entry of the table is the sphericity value derived from the mapping of a model landmark to a scene landmark, is constructed. A hopping dynamic programming procedure which switches between a forward and a backward dynamic programming procedure is applied to guide the landmark matching through the compatibility table. The location of the model in the scene is estimated with a least squares fit among the matched landmarks. A heuristic measure is then computed to decide if the model is in the scene.
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