Riemannian Geometry Approach for Minimizing Distortion and its Applications

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 ${\sum }_{i=1}^{N}Dis{t}_F^2(T^{-1}{T}_i)\mathrm{.}$ The mean distorting transformation can be useful in some fields – in particular, we apply it for rendering affine panoramas.