AdamFlow: Adam-based Wasserstein Gradient Flows for Surface Registration in Medical Imaging
This work addresses the problem of fast and robust surface registration for anatomical shape analysis in medical imaging, representing an incremental improvement by adapting Adam optimization to a new domain.
The paper tackles the trade-off between efficiency and robustness in surface registration for medical imaging by formulating it as a distributional optimization problem using sliced Wasserstein distance, and introduces AdamFlow, a novel optimization method that achieves superior performance in both affine and non-rigid registration with log-linear computational complexity.
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.