Riemannian Geometry Approach for Minimizing Distortion and its Applications

Code

• github.com/dozeri83/mean_pos_def
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Abstract

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 _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.

Reproductions