FireANTs: Adaptive Riemannian Optimization for Multi-Scale Diffeomorphic Matching

2024-04-01

AI Summary

To address the challenging dense diffeomorphic registration problem in medical and biological imaging—characterized by cross-scale variations, large deformations, and high ill-posedness—this paper proposes the first adaptive Riemannian optimization algorithm tailored for multi-scale diffeomorphic manifolds. Methodologically, it innovatively extends momentum-based acceleration and Hessian-adaptive estimation to non-Euclidean manifolds, establishing a formal multi-scale optimization framework; additionally, it introduces a quantitative ill-posedness analysis to guide optimization of dense deformation fields. Experimentally, on ultra-high-resolution (sub-micron) mouse cortical registration, the method achieves state-of-the-art accuracy and robustness, accelerates inference by 300×–3200× over baseline approaches, and enables large-scale hyperparameter studies previously infeasible due to computational constraints.

Technology Category

• Machine Learning: Learning with Manifolds
• Search and Optimization: Non-convex Optimization
• Computer Vision: Learning & Optimization for CV

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

Abstract

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 from 300x up to 3200x speedup over existing state-of-the-art algorithms. For the first time, we perform diffeomorphic matching of sub-micron mouse cortex volumes at native resolution. Our fast implementation also enables hyperparameter studies that were intractable with existing correspondence matching algorithms.

Problem

• Image Matching
• Optimization Algorithm
• Medical Imaging

Innovation

• FireANTs
• Image Registration
• High Speed Optimization