Image registration estimates spatial correspondences between image pairs. These estimates are typically obtained via numerical optimization or regression by a deep network. A desirable property is that a correspondence estimate (e.g., the true oracle correspondence) for an image pair is maintained under deformations of the input images. Formally, the estimator should be equivariant to a desired class of image transformations. In this work, we present careful analyses of equivariance properties in the context of multi-step deep registration networks. Based on these analyses we 1) introduce the notions of [U, U] equivariance (network equivariance to the same deformations of the input images) and [W, U] equivariance (where input images can undergo different deformations); we 2) show that in a suitable multistep registration setup it is sufficient for overall [W, U] equivariance if the first step has [W, U] equivariance and all others have [U, U] equivariance; we 3) show that common displacement-predicting networks only exhibit [U, U] equivariance to translations instead of the more powerful [W, U ] equivariance; and we 4) show how to achieve multistep [W, U] equivariance via a coordinate-attention mechanism combined with displacement-predicting networks. Our approach obtains excellent practical performance for 3D abdomen, lung, and brain medical image registration. We match or outperform state-of-the-art (SOTA) registration approaches on all the datasets with a particularly strong performance for the challenging abdomen registration.

We present an approach to learning regular spatial transformations between image pairs in the context of medical image registration. Contrary to optimization-based registration techniques and many modern learning-based methods, we do not directly penalize transformation irregularities but instead promote transformation regularity via an inverse consistency penalty. We use a neural network to predict a map between a source and a target image as well as the map when swapping the source and target images. Different from existing approaches, we compose these two resulting maps and regularize deviations of the Jacobian of this composition from the identity matrix. This regularizer - GradICON - results in much better convergence when training registration models compared to promoting inverse consistency of the composition of maps directly while retaining the desirable implicit regularization effects of the latter. We achieve state-of-the-art registration performance on a variety of real-world medical image datasets using a single set of hyperparameters and a single non-dataset-specific training protocol. Code is available at https://github.com/uncbiag/ICON.

Transport processes are ubiquitous. They are, for example, at the heart of optical flow approaches; or of perfusion imaging, where blood transport is assessed, most commonly by injecting a tracer. An advection-diffusion equation is widely used to describe these transport phenomena. Our goal is estimating the underlying physics of advection-diffusion equations, expressed as velocity and diffusion tensor fields. We propose a learning framework (YETI) building on an auto-encoder structure between 2D and 3D image time-series, which incorporates the advection-diffusion model. To help with identifiability, we develop an advection-diffusion simulator which allows pre-training of our model by supervised learning using the velocity and diffusion tensor fields. Instead of directly learning these velocity and diffusion tensor fields, we introduce representations that assure incompressible flow and symmetric positive semi-definite diffusion fields and demonstrate the additional benefits of these representations on improving estimation accuracy. We further use transfer learning to apply YETI on a public brain magnetic resonance (MR) perfusion dataset of stroke patients and show its ability to successfully distinguish stroke lesions from normal brain regions via the estimated velocity and diffusion tensor fields.