Intensity-Unbiased Force Computation for Variational Motion Estimation

We show that the sum of squared differences, commonly used as a dissimilarity measure in variational methods is biased towards high gradients and large intensity differences, and that it can affect drastically the quality of motion estimation techniques such as deformable registration. We propose a method which solves that problem by recalling that the Euler-Lagrange equation of the dissimilarity measure yields a force term, and computing the direction and the magnitude of these forces independently. This results in a simple, efficient, and robust method, which is intensity-unbiased. We compare our method with the SSD-based standard approach on both synthetic and real medical 2D data, and show that our approach performs better.