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Much biomedical and medical research relies on the collection of ever-larger amounts of image data (both 2D images and 3D volumes, as well as time-series) and increasingly from multiple sources. Image registration, the process of finding correspondences between images based on the affinity of features of interest, is often required as a vital step towards the final analysis, which may consist of a comparison of images, measurement of movement, or fusion of complementary information. The contributions in this work are centered around reliable image registration methods for both 2D and 3D images with the aim of wide applicability: similarity and distance measures between images for image registration, algorithms for efficient computation of these, and other commonly used measures for both local and global optimization frameworks, and representations for multimodal image registration where the appearance and structures present in the images may vary dramatically.

The main contributions are: (i) distance measures for affine symmetric intensity image registration, combining intensity and spatial information based on the notion of alpha-cuts from fuzzy set theory; (ii) the extension of the affine registration method to more flexible deformable transformation models, leading to the framework Intensity and Spatial Information-Based Deformable Image Registration (INSPIRE); (iii) two efficient algorithms for computing the proposed distances and their spatial gradients and thereby enabling local gradient-based optimization; (iv) a contrastive representation learning method, Contrastive Multimodal Image Representation for Registration (CoMIR), utilizing deep learning techniques to obtain common representations that can be registered using methods designed for monomodal scenarios; (v) efficient algorithms for global optimization of mutual information and similarities of normalized gradient fields; (vi) a comparative study exploring the applicability of modern image-to-image translation methods to facilitate multimodal registration; (vii) the Stochastic Distance Transform, using the theory of discrete random sets to offer improved noise-insensitivity to distance computations; (viii) extensive evaluation of the proposed image registration methods on a number of different datasets mainly from (bio)medical imaging, where they exhibit excellent performance, and reliability, suggesting wide utility.