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Riemannian Geometry Approach for Minimizing Distortion and its Applications
Dror Ozeri
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 {Tᵢ}ᵢ₌₁ᴺ of affine transformations, find an affine transformation T that minimize the overall distortion ∑ᵢ₌₁ᴺDist_F²(T⁻¹Tᵢ). The mean distorting transformation can be useful in some fields -- in particular, we apply it for rendering affine panoramas.
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