Riemannian Geometry Approach for Minimizing Distortion and its Applications

Dror Ozeri

paper

Riemannian Geometry Approach for Minimizing Distortion and its Applications

arXiv:2207.12038

Abstract

Given an affine transformation $T$ , we define its Fisher distortion $D i s t_{F} (T)$ . 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 $\sum_{i = 1}^{N} D i s t_{F}^{2} (T^{- 1} T_{i}) .$ The mean distorting transformation can be useful in some fields -- in particular, we apply it for rendering affine panoramas.