用Adam优化器加速医学影像表面配准，兼顾速度与鲁棒性
AdamFlow: Adam-based Wasserstein Gradient Flows for Surface Registration in Medical Imaging
- 将表面网格视为概率分布，用切片Wasserstein距离衡量差异
- 提出AdamFlow算法，实现对数线性复杂度的高效优化
- 在多种解剖结构上表现优异，适合需要快速高精度配准的场景
表面配准在医学影像解剖形状分析中至关重要。现有方法常面临效率与鲁棒性的权衡：局部点匹配方法计算高效但易受噪声和初始化影响；全局点集对齐方法虽鲁棒但计算成本高。为此，本文提出一种快速表面配准方法，将表面网格建模为概率测度，将表面配准转化为分布优化问题。采用具有对数线性复杂度的高效切片Wasserstein距离度量两网格间差异。提出新型优化方法AdamFlow，将经典的Adam优化器从欧氏空间推广至概率空间，以最小化切片Wasserstein距离。理论上分析了AdamFlow的渐近收敛性，并在多种解剖结构上的仿射与非刚性配准任务中实证其优越性能。
原文摘要 · Abstract (English)
Surface registration plays an important role for anatomical shape analysis in medical imaging. Existing surface registration methods often face a trade-off between efficiency and robustness. Local point matching methods are computationally efficient, but vulnerable to noise and initialisation. Methods designed for global point set alignment tend to incur a high computational cost. To address the challenge, here we present a fast surface registration method, which formulates surface meshes as probability measures and surface registration as a distributional optimisation problem. The discrepancy between two meshes is measured using an efficient sliced Wasserstein distance with log-linear computational complexity. We propose a novel optimisation method, AdamFlow, which generalises the well-known Adam optimisation method from the Euclidean space to the probability space for minimising the sliced Wasserstein distance. We theoretically analyse the asymptotic convergence of AdamFlow and empirically demonstrate its superior performance in both affine and non-rigid surface registration across various anatomical structures.
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