Abstract:
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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 |