When Patches Match -- A Statistical View on Matching under Illumination Variation

We discuss matching measures (scores and residuals) for comparing image patches under unknown affine photometric (=intensity) transformations. In contrast to existing methods, we derive a fully symmetric matching measure which reflects the fact that both copies of the signal are affected by measurement errors (´noise´), not only one. As it turns out, this evolves into an Eigen system problem, however a simple direct solution for all entities of interest can be given. We strongly advocate for constraining the estimated gain ratio and the estimated mean value offset to realistic ranges, thus preventing the matching scheme from locking into unrealistic correspondences.