Regularity-guaranteed transformation estimation in medical image registration

In addition to seeking geometric correspondence between the inputs, a legitimate image registration algorithm should also keep the estimated transformation meaningful or regular. In this paper, we present a mathematically sound formulation that explicitly controls the deformation to keep each grid in a meaningful shape over the entire geometric matching procedure. The deformation regularity conditions are enforced by maintaining all the moving neighbors as non-twist grids. In contrast to similar works, our model differentiates and formulates the convex and concave update cases under an efficient and straightforward point-line/surface orientation framework, and uses equality constraints to guarantee grid regularity and prevent folding. Experiments on MR images are presented to show the improvements made by our model over the popular Demon's and DCT-based registration algorithms.