Adaptive Riemannian Optimization for Multi-Scale Diffeomorphic Matching

The paper proposes FireANTs, the first multi-scale Adaptive Riemannian Optimization algorithm for dense diffeomorphic image matching. One of the most critical and understudied aspects of diffeomorphic image matching algorithms are its highly ill-conditioned nature. We quantitatively capture the extent of ill-conditioning in a typical MRI matching task, motivating the need for an adaptive optimization algorithm for diffeomorphic matching. To this end, FireANTs generalizes the concept of momentum and adaptive estimates of the Hessian to mitigate this ill-conditioning in the non-Euclidean space of diffeomorphisms. Unlike common non-Euclidean manifolds, we also formalize considerations for multi-scale optimization of diffeomorphisms. Our rigorous mathematical results and operational contributions lead to a state-of-the-art dense matching algorithm that can be applied to generic image data with remarkable accuracy and robustness. We demonstrate consistent improvements in image matching performance across a spectrum of community-standard medical and biological correspondence matching challenges spanning a wide variety of image modalities, anatomies, resolutions, acquisition protocols, and preprocessing pipelines. This improvement is supplemented by 300x to 3200x speedup over existing CPU-based state-of-the-art algorithms. For the first time, we perform diffeomorphic matching of sub-micron mouse isocortex volumes at native resolution, and generate a 25µm mouse brain atlas in under 25 minutes. Our fast implementation also enables hyperparameter studies that were intractable with existing correspondence matching algorithms.