A Majorization-Minimization Algorithm for Neuroimage Registration

SIAM Journal on Imaging Sciences, Volume 17, Issue 1, Page 273-300, March 2024.
Abstract. Intensity-based image registration is critical for neuroimaging tasks, such as 3D reconstruction, times-series alignment, and common coordinate mapping. The gradient-based optimization methods commonly used to solve this problem require a careful selection of step-length. This limitation imposes substantial time and computational costs. Here we propose a gradient-independent rigid-motion registration algorithm based on the majorization-minimization (MM) principle. Each iteration of our intensity-based MM algorithm reduces to a simple point-set rigid registration problem with a closed form solution that avoids the step-length issue altogether. The details of the algorithm are presented, and an error bound for its more practical truncated form is derived. The performance of the MM algorithm is shown to be more effective than gradient descent on simulated images and Nissl stained coronal slices of mouse brain. We also compare and contrast the similarities and differences between the MM algorithm and another gradient-free registration algorithm called the block-matching method. Finally, extensions of this algorithm to more complex problems are discussed.