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Given an affine transformation $T$, we define its Fisher distortion$Dist_F(T)$. We show that the Fisher distortion has Riemannian metric structureand provide an algorithm for finding mean distorting transformation -- namely-- for a given set $\{T_{i}\}_{i=1}^N$ of affine transformations, find anaffine transformation $T$ that minimize the overall distortion$\sum_{i=1}^NDist_F^{2}(T^{-1}T_{i}).$ The mean distorting transformation canbe useful in some fields -- in particular, we apply it for rendering affinepanoramas.

Riemannian Geometry Approach for Minimizing Distortion and its Applications