Riemannian Geometry Approach for Minimizing Distortion and its Applications
This work addresses distortion minimization in affine transformations, with applications in fields like computer vision, but appears incremental as it builds on existing geometric approaches.
The paper tackles the problem of minimizing distortion for affine transformations by defining a Fisher distortion measure with Riemannian metric structure and providing an algorithm to compute a mean distorting transformation that minimizes overall distortion, applied to rendering affine panoramas.
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.