将可逆形变场扩展到矩阵群，提升大变形图像配准效果
Stationary Velocity Fields on Matrix Groups for Deformable Image Registration
- 基于矩阵群构造稳定速度场，增强形变建模能力
- 在脑部MRI跨患者配准中实现更优的大变形恢复
- 适合医学图像配准、需要大形变建模的研究者
平稳速度场（SVF）方法可构建可逆形变场，常用于图像配准，尤其适合作为机器学习网络后的模块。然而其在大变形场景下表现受限。本文将SVF推广至矩阵群，特别是$\ ext{SE}(3)$，使欧氏变换集中在低频部分，从而更易恢复大运动。为此扩展了流方程，并给出了存在性充分条件。进一步证明了分解条件，支持采用缩放-平方法高效数值积分。在人体脑部3D MRI的跨患者配准任务上进行了数值验证。
原文摘要 · Abstract (English)
The stationary velocity field (SVF) approach allows to build parametrizations of invertible deformation fields, which is often a desirable property in image registration. Its expressiveness is particularly attractive when used as a block following a machine learning-inspired network. However, it can struggle with large deformations. We extend the SVF approach to matrix groups, in particular $\SE(3)$. This moves Euclidean transformations into the low-frequency part, towards which network architectures are often naturally biased, so that larger motions can be recovered more easily. This requires an extension of the flow equation, for which we provide sufficient conditions for existence. We further prove a decomposition condition that allows us to apply a scaling-and-squaring approach for efficient numerical integration of the flow equation. We numerically validate the approach on inter-patient registration of 3D MRI images of the human brain.
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