Riemannian Geometry Approach for Minimizing Distortion and its Applications
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Given an affine transformation T, we define its Fisher distortion Dist_F(T). We show that the Fisher distortion has Riemannian metric structure and provide an algorithm for finding mean distorting transformation – namely – for a given set {T_i}_i=1^N of affine transformations, find an affine transformation T that minimize the overall distortion ∑_i=1^NDist_F^2(T^-1T_i). The mean distorting transformation can be useful in some fields – in particular, we apply it for rendering affine panoramas.
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