Manifold Learning for Multi-Modal Image Registration

The standard approach to multi-modal registration is to apply sophisticated similarity metrics such as mutual information. The disadvantage of these measures, in contrast to simple L1 or L2 norm, is the increased computational complexity and consequently the prolongation of the registration time. An alternative approach, which has so far not yet gained much attention in the literature, is to find image representations, so called structural representations, that allow for the direct application of L1 and L2 norm. Recently, entropy images [26] were proposed as a simple structural representation of images for multi-modal registration. In this article, we propose the application of manifold learning, more precisely Laplacian eigenmaps, to learn the structural representation. It has the theoretical advantage of presenting an optimal approximation to one of the criteria for a structural description. Laplacian eigenmaps search for similar patches in high-dimensional patch space and embed the manifold in a low-dimensional space under preservation of locality. This can be interpreted as the identification of internal similarities in images. In our experiments, we show that the internal similarity across images is comparable and notice very good registration results for the new structural representation.