BARTOLI, PIZARRO, LOOG: STRATIFIED GENERALIZED PROCRUSTES ANALYSIS 1 Stratified Generalized Procrustes Analysis1
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چکیده
This paper deals with generalized procrustes analysis. This is the problem of registering a set of shape data by finding a reference shape and global rigid transformations given point correspondences. The transformed shape data must align with the reference shape as best possible. This is a difficult problem. The classical approach computes alternatively the reference shape, usually as the average of the transformed shapes, and each transformation in turn. We propose a stratified approach inspired by recent results obtained in Structurefrom-Motion. Our stratified approach offers a statistically grounded framework for obtaining both the transformations and the reference shape at once in two steps. First, we compute a reference shape and affine transformations. Second, we upgrade these transformations to the sought after similarity or euclidean transformations. In practice each of these two steps involves solving a non-convex optimization problem. We provide convex approximations and closed-form solutions. As opposed to the classical alternation approach, our stratified approach processes data in batch. It gracefully deals with missing data. We provide results on synthetic and real data sets. Compared to the alternation schema, our algorithm obtains lower error in both affine and euclidean cases, especially for shapes with high deformations.
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تاریخ انتشار 2010