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Shape Vocabulary: A Robust and Efficient Shape Representation for Shape Matching

In this paper, a learning-based shape descriptor for shape matching is demonstrated. Formulated in a bag-of-words like framework, the proposed method summarizes the local features extracted from certain shape to generate a integrated representation. It contributes to the speed-up of shape matching, since the distance metric in the vector space analysis can be directly applied to compare the constructed global descriptors, eliminating the time consuming stage of local feature matching. Similar to the philosophy in spatial pyramid matching, a strategy for feature division is applied in the phase of encoded feature pooling and vocabulary learning, which helps to construct a more discriminative descriptor incorporating both global and local information. Also, a local contour-based feature extraction method is designed for 2D shapes, while significant properties of the local contours are inspected for the design of feature division rules. The designed local feature extraction method and the feature division rules manage to reduce the variances of shape representation due to the changes in rotation. In addition to 2D shape, we also present a simple and natural method to extend the proposed method to the scenario of 3D shape representation. The proposed shape descriptor is validated on several benchmark data sets for evaluating 2D and 3D shape matching algorithms, and it is observed that the investigated shape descriptor maintains superior discriminative power as well as high time efficiency.