Riemannian Geometry Approach for Minimizing Distortion and its Applications

• URL: http://arxiv.org/abs/2207.12038v3
• Date: Thu, 28 Jul 2022 06:56:50 GMT
• Title: Riemannian Geometry Approach for Minimizing Distortion and its Applications
• Authors: Dror Ozeri
• Abstract summary: We find an affine transformation $T$ that minimize the overall distortion $sum_i=1NDist_F2(T-1T_i)$. The transformation can be useful in some fields -- in particular, we apply it for rendering affine panoramas.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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 $\{T_{i}\}_{i=1}^N$ of affine transformations, find an affine transformation $T$ that minimize the overall distortion $\sum_{i=1}^NDist_F^{2}(T^{-1}T_{i}).$ The mean distorting transformation can be useful in some fields -- in particular, we apply it for rendering affine panoramas.

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