# AdamFlow: Adam-based Wasserstein Gradient Flows for Surface Registration in Medical Imaging Source: [AdamFlow: Adam-based Wasserstein Gradient Flows for Surface Registration in Medical Imaging]() Collection index: [llms.txt]() Data updated: 2026-04-04T05:00:11.701Z Authors: Qiang Ma, Qingjie Meng, Xin Hu, Yicheng Wu, Wenjia Bai Published: 2026-04-02T17:29:54.000Z ## Abstract 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. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. - [Non-rigid Surface Registration on Liver (ASSD, HD90)](): Non-rigid Surface Registration; Liver; ASSD (mm): 0.72. - [Non-rigid Surface Registration on Pancreas (ASSD, HD90)](): Non-rigid Surface Registration; Pancreas; ASSD (mm): 0.415. - [Non-rigid Surface Registration on Left ventricle (ASSD, HD90)](): Non-rigid Surface Registration; Left ventricle; ASSD (mm): 0.402. - [Affine Surface Registration on Liver (ASSD, HD90)](): Affine Surface Registration; Liver; ASSD (mm): 7.452. - [Affine Surface Registration on Pancreas (ASSD, HD90)](): Affine Surface Registration; Pancreas; ASSD (mm): 5.381. - [Affine Surface Registration on Left ventricle (ASSD, HD90)](): Affine Surface Registration; Left ventricle; ASSD (mm): 1.932. - [Affine Surface Registration on Liver](): Affine Surface Registration; Liver; Runtime (s): 2.65. - [Affine Surface Registration on Pancreas](): Affine Surface Registration; Pancreas; Runtime (s): 3.07. - [Affine Surface Registration on Left ventricle](): Affine Surface Registration; Left ventricle; Runtime (second): 1.72. - [Non-rigid Surface Registration on Liver](): Non-rigid Surface Registration; Liver; Runtime (s): 2.55. - [Non-rigid Surface Registration on Pancreas](): Non-rigid Surface Registration; Pancreas; Runtime (s): 1.48. - [Non-rigid Surface Registration on Left ventricle](): Non-rigid Surface Registration; Left ventricle; Runtime (s): 0.42. ## Original sources and implementation [Original paper]() [PDF]()