基于鲁棒切线瓦瑟斯坦距离的多尺度非刚性点云配准方法
Multi-scale Non-Rigid Point Cloud Registration Using Robust Sliced-Wasserstein Distance via Laplace-Beltrami Eigenmap
AI总结：
本文提出利用拉普拉斯-贝蒾特征映射和鲁棒切线瓦瑟斯坦距离进行多尺度非刚性点云配准，通过不同尺度的n值实现快速且鲁棒的配准过程。
摘要：
本文提出计算模型和算法用于具有非刚性变换的点云配准。首先，通过拉普拉斯-贝蒾特征映射，将采样自某些欧几里得空间R^D的点云转换为嵌入R^n的新点云，利用LB算子内在定义的前n个特征值和特征函数。LB特征映射在原流形的等距变换下是不变的。然后，设计基于最优传输理论的计算模型和算法，以概率形式进行转换后的点云配准，提供通用性和灵活性以处理一般点云设置。我们的方法使用鲁棒切线瓦瑟斯坦距离，即不同方向上的投影瓦瑟斯坦距离的平均值，并结合刚性变换以处理拉普拉斯-贝蒾特征映射引入的歧义。通过从较小的n值开始，提供快速且鲁棒的配准（基于粗尺度特征）以及更精细尺度配准的良好初始猜测，再到较大的n值，我们的方法为多尺度非刚性点云配准提供了高效、鲁棒且准确的解决方案。
英文摘要：
In this work, we propose computational models and algorithms for point cloud registration with non-rigid transformation. First, point clouds sampled from manifolds originally embedded in some Euclidean space $\mathbb{R}^D$ are transformed to new point clouds embedded in $\mathbb{R}^n$ by Laplace-Beltrami(LB) eigenmap using the $n$ leading eigenvalues and corresponding eigenfunctions of LB operator defined intrinsically on the manifolds. The LB eigenmap are invariant under isometric transformation of the original manifolds. Then we design computational models and algorithms for registration of the transformed point clouds in distribution/probability form based on the optimal transport theory which provides both generality and flexibility to handle general point clouds setting. Our methods use robust sliced-Wasserstein distance, which is as the average of projected Wasserstein distance along different directions, and incorporate a rigid transformation to handle ambiguities introduced by the Laplace-Beltrami eigenmap. By going from smaller $n$, which provides a quick and robust registration (based on coarse scale features) as well as a good initial guess for finer scale registration, to a larger $n$, our method provides an efficient, robust and accurate approach for multi-scale non-rigid point cloud registration.
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