C. Wachinger, N. Navab Entropy and Laplacian Images: Structural Representations for Multi-Modal Registration Medical Image Analysis, Volume 16, Issue 1, January 2012, Pages 1–17. (bib)
	The standard approach to multi-modal registration is to apply sophisticated similarity metrics such as mutual information. The disadvantage of these metrics, in comparison to measuring the intensity difference with \eg L1 or L2 distance, is the increase in computational complexity and consequently the increase in runtime of the registration. An alternative approach, which has not yet gained much attention in the literature, is to find image representations, so called structural representations, that allow for the application of the L1 and L2 distance for multi-modal images. This has not only the advantage of a faster similarity calculation but enables also the application of more sophisticated optimization strategies. In this article, we theoretically analyze the requirements for structural representations. Further, we introduce two approaches to create such representations, which are based on the calculation of patch entropy and manifold learning, respectively. While the application of entropy has practical advantages in terms of computational complexity, the usage of manifold learning has theoretical advantages, by presenting an optimal approximation to one of the theoretical requirements. We perform experiments on multiple datasets for rigid, deformable, and groupwise registration with good results with respect to both, runtime and quality of alignment.
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