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A lot of research has been done during the past 20 years in the area of medical image registration for obtaining detailed, important, and complementary information from two or more images and aligning them into a single, more informative image. Nature of the transformation and domain of the transformation are two important medical image registration techniques that deal with characters of objects (motions) in images. This article presents a detailed survey of the registration techniques that belong to both categories with detailed elaboration on their features, issues, and challenges. An investigation estimating similarity and dissimilarity measures and performance evaluation is the main objective of this work. This article also provides reference knowledge in a compact form for researchers and clinicians looking for the proper registration technique for a particular application.