In this paper, we introduce and study matching methods based on distance
profiles. For the matching of point clouds, the proposed method is easily
implementable by solving a linear program, circumventing the computational
obstacles of quadratic matching. Also, we propose and analyze a flexible way to
execute location-to-location matching using distance profiles. Moreover, we
provide a statistical estimation error analysis in the context of
location-to-location matching using empirical process theory. Furthermore, we
apply our method to a certain model and show its noise stability by
characterizing conditions on the noise level for the matching to be successful.
Lastly, we demonstrate the performance of the proposed method and compare it
with some existing methods using synthetic and real data.

本论文介绍和研究了基于距离轮廓的匹配方法。对于点云匹配，所提出的方法通过求解线性规划来实现，避免了二次匹配的计算障碍。同时，我们提出并分析了一种灵活的位置对位置匹配方法，使用了距离轮廓进行执行。此外，我们在位置对位置匹配中使用实证过程理论提供了统计估计误差分析。最后，我们将所提出的方法应用于一种模型，并通过表征噪声水平的条件展示了其噪声稳定性。最后，我们使用合成数据和真实数据展示了所提出方法的性能，并与一些现有方法进行了比较。