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Shape Matching under Affine Transformation (SMAT) is an important issue in shape analysis. Most of the existing SMAT methods are sensitive to noise or complicated because they usually need to extract the edge points or compute the high order function of the shape. To solve these problems, a new SMAT method which combines the low order shape normalization and the multi-scale area integral features is proposed. First, the shapes with affine transformation are normalized into their orthogonal representations according to the moments and an equivalent resample. This procedure transforms the shape by several linear operations: translations, scaling, and rotation, following by a resample operation. Second, the Multi-Scale Area Integral Features (MSAIF) of the shapes which are invariant to the orthogonal transformation (rotation and reflection transformation) are extracted. The MSAIF is a signature achieved through concatenating the area integral feature at a range of scales from fine to coarse. The area integral feature is an integration of the feature values, which are computed by convoluting the shape with an isotropic kernel and taking the complement, over the shape domain following by the normalization using the area of the shape. Finally, the matching of different shapes is performed according to the dissimilarity which is measured with the optimal transport distance. The performance of the proposed method is tested on the car dataset and the multi-view curve dataset. Experimental results show that the proposed method is efficient and robust, and can be used in many shape analysis works.
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