On the Source of Asymmetry in Image Registration Problems

Most image registration problems are formulated in an asymmetric fashion. Given a pair of images, one is implicitly or explicitly regarded as template, and warped onto the other to match. In this paper, we focus on this seemingly arbitrary choice of the roles, and reveal how it may lead to biased warp estimates in the presence of relative scaling. We present a principled way of selecting for the template, and explain why only the correct asymmetric form, with the potential inclusion of a blurring step, can yield unbiased estimators. Our analysis also shows that commonly-used symmetrization/regularization of the warps may actually lead to biased estimators. We experimentally validate our analysis by measuring the bias of L1 and L2 norm motion estimators when the template choice is wrong, and conclude that image registration is inherently an asymmetric problem.