Multimodal image registration using Laplacian commutators

Veronika A Zimmer, Miguel Angel Gonzalez Ballester, Gemma Piella

Abstract:

The fusion and combination of images from multiple modalities is important in many applications. Typically,
this process consists of the alignment of the images and the combination of the complementary information.
In this work, we focused on the former part and propose a multimodal image distance measure based on the
commutativity of graph Laplacians. The eigenvectors of the image graph Laplacian, and thus the graph Laplacian
itself, capture the intrinsic structure of the image’s modality. Using Laplacian commutativity as a criterion of
image structure preservation, we adapt the problem of finding the closest commuting operators to multimodal
image registration. Hence, by using the relation between simultaneous diagonalization and commutativity of
matrices, we compare multimodal image structures by means of the commutativity of their graph Laplacians.
In this way, we avoid spectrum reordering schemes or additional manifold alignment steps which are necessary
to ensure the comparability of eigenspaces across modalities. We show on synthetic and real datasets that this
approach is applicable to dense rigid and non-rigid image registration. Results demonstrated that the proposed
measure is able to deal with very challenging multimodal datasets and compares favorably to normalized mutual
information, a de facto similarity measure for multimodal image registration.