Variational methods for multimodal image matching

Matching images of different modalities can be achieved by the maximization of suitable statistical similarity measures within a given class of geometric transformations. Handling complex, nonrigid deformations in this context turns out to be particularly difficult and has attracted much attention in the last few years. The thrust of this paper is that many of the existing methods for nonrigid monomodal registration that use simple criteria for comparing the intensities (e. g. SSD) can be extended to the multimodal case where more complex intensity similarity measures are necessary. To this end, we perform a formal computation of the variational gradient of a hierarchy of statistical similarity measures, and use the results to generalize a recently proposed and very effective optical flow algorithm (L. Alvarez, J. Weickert, and J. Sanchez, 2000, Technical Report, and IJCV 39(1):41-56) to the case of multimodal image registration. Our method readily extends to the case of locally computed similarity measures, thus providing the flexibility to cope with spatial non-stationarities in the way the intensities in the two images are related. The well posedness of the resulting equations is proved in a complementary work (O.D. Faugeras and G. Hermosillo, 2001, Technical Report 4235, INRIA) using well established techniques in functional analysis. We briefly describe our numerical implementation of these equations and show results on real and synthetic data.