  The goal of image registration is to establish spatial correspondence between
two or more images, traditionally through dense displacement fields (DDFs) or
parametric transformations (e.g., rigid, affine, and splines). Rethinking the
existing paradigms of achieving alignment via spatial transformations, we
uncover an alternative but more intuitive correspondence representation: a set
of corresponding regions-of-interest (ROI) pairs, which we demonstrate to have
sufficient representational capability as other correspondence representation
methods.Further, it is neither necessary nor sufficient for these ROIs to hold
specific anatomical or semantic significance. In turn, we formulate image
registration as searching for the same set of corresponding ROIs from both
moving and fixed images - in other words, two multi-class segmentation tasks on
a pair of images. For a general-purpose and practical implementation, we
integrate the segment anything model (SAM) into our proposed algorithms,
resulting in a SAM-enabled registration (SAMReg) that does not require any
training data, gradient-based fine-tuning or engineered prompts. We
experimentally show that the proposed SAMReg is capable of segmenting and
matching multiple ROI pairs, which establish sufficiently accurate
correspondences, in three clinical applications of registering prostate MR,
cardiac MR and abdominal CT images. Based on metrics including Dice and target
registration errors on anatomical structures, the proposed registration
outperforms both intensity-based iterative algorithms and DDF-predicting
learning-based networks, even yielding competitive performance with
weakly-supervised registration which requires fully-segmented training data.
