We present a probabilistic approach to shape matching which is invariant to rotation,\ud translation and scaling. Shapes are represented by unlabeled point sets, so\ud discontinuous boundaries and non-boundary points do not pose a problem. Occlusions,\ud significant dissimilarities between shapes and image clutter are explained by\ud a ‘background model’ and hence, their impact on the overall match is limited. By\ud simultaneously learning a part decomposition of both shapes, we are able to successfully\ud match shapes that differ as a result of independent part transformations\ud – a form of variation common amongst real objects of the same class. The effectiveness\ud of the matching algorithm is demonstrated using the benchmark MPEG-7\ud data set and real images
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