Riemannian Geometry Approach for Minimizing Distortion and its Applications

arXiv2207.12038MaRDI QIDQ6405926

Author name not available (Why is that?)

Publication date: 25 July 2022

Abstract: Given an affine transformation $T$, we define its Fisher distortion $Dis{t}_F(T)$. 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 $su{m}_{i=1}^{N}Dis{t}_F^2(T^{-1}{T}_i).$ The mean distorting transformation can be useful in some fields -- in particular, we apply it for rendering affine panoramas.

Has companion code repository: https://github.com/dozeri83/mean_pos_def

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