GraDIRN: Learning Iterative Gradient Descent-based Energy Minimization for Deformable Image Registration

We present a Gradient Descent-based Image Registration Network (GraDIRN) for learning deformable image registration by embedding gradient-based iterative energy minimization in a deep learning framework. Traditional image registration algorithms typically use iterative energy-minimization optimization to find the optimal transformation between a pair of images, which is time-consuming when many iterations are needed. In contrast, recent learning-based methods amortize this costly iterative optimization by training deep neural networks so that registration of one pair of images can be achieved by fast network forward pass after training. Motivated by successes in image reconstruction techniques that combine deep learning with the mathematical structure of iterative variational energy optimization, we formulate a novel registration network based on multi-resolution gradient descent energy minimization. The forward pass of the network takes explicit image dissimilarity gradient steps and generalized regularization steps parameterized by Convolutional Neural Networks (CNN) for a fixed number of iterations. We use auto-differentiation to derive the forward computational graph for the explicit image dissimilarity gradient w.r.t. the transformation, so arbitrary image dissimilarity metrics and transformation models can be used without complex and error-prone gradient derivations. We demonstrate that this approach achieves state-of-the-art registration performance while using fewer learnable parameters through extensive evaluations on registration tasks using 2D cardiac MR images and 3D brain MR images.