A Convex Optimization Framework for Regularized Geodesic Distances
A Convex Optimization Framework for Regularized Geodesic Distances
复制标题
DOI：
10.1145/3588432.3591523
复制
发表时间：
2023-05
期刊：
影响因子：
--
通讯作者：
M. Edelstein;Nestor Guillen;J. Solomon;M. Ben-Chen
中科院分区：
文献类型：
--
作者：
M. Edelstein;Nestor Guillen;J. Solomon;M. Ben-Chen
我们提出了一个用于计算正则化测地距离的通用凸优化问题。我们证明，在正则化器的温和条件下，该问题是很好地提出的。我们提出了三种不同的正则化器，并提供了特殊情况下的解析解，以及相应的高效优化算法。此外，我们展示了如何通过在乘积流形上制定问题来推广所有对情况的方法，这会导致对称距离。我们的正则化距离在鲁棒性和易于校准方面优于现有方法。
We propose a general convex optimization problem for computing regularized geodesic distances. We show that under mild conditions on the regularizer the problem is well posed. We propose three different regularizers and provide analytical solutions in special cases, as well as corresponding efficient optimization algorithms. Additionally, we show how to generalize the approach to the all pairs case by formulating the problem on the product manifold, which leads to symmetric distances. Our regularized distances compare favorably to existing methods, in terms of robustness and ease of calibration.