A variational approach for correspondence finding between three rectified images

We present a variational approach for the computation of dense correspondence between three rectified images. Using rectification allows reducing the problem to a single parameter functional. Classically, the functional is composed of a data term and a regularization term. We introduce an improved model, where the pixel wise data term is combined with a template matching approach, which is well adapted to the case of rectified images. This modification increases the accuracy significantly. The minimization is practically handled by solving the Euler-Lagrange equation. In our setting, the Euler-Lagrange equation is replaced by a parabolic evolution equation. Under general assumptions, we prove that this equation has a single asymptotic state, that is obtained by any initial guess.