Mid-space-independent deformable image registration

Abstract

Aligning images in a mid-space is a common approach to ensuring that deformable image registration is symmetric – that it does not depend on the arbitrary ordering of the input images. The results are, however, generally dependent on the mathematical definition of the mid-space. In particular, the set of possible solutions is typically restricted by the constraints that are enforced on the transformations to prevent the mid-space from drifting too far from the native image spaces. The use of an implicit atlas has been proposed as an approach to mid-space image registration. In this work, we show that when the atlas is aligned to each image in the native image space, the data term of implicit-atlas-based deformable registration is inherently independent of the mid-space. In addition, we show that the regularization term can be reformulated independently of the mid-space as well. We derive a new symmetric cost function that only depends on the transformation morphing the images to each other, rather than to the atlas. This eliminates the need for anti-drift constraints, thereby expanding the space of allowable deformations. We provide an implementation scheme for the proposed framework, and validate it through diffeomorphic registration experiments on brain magnetic resonance images.

Tasks

Reproductions