Point cloud matching, a crucial technique in computer vision, medical and
robotics fields, is primarily concerned with finding correspondences between
pairs of point clouds or voxels. In some practical scenarios, emphasizing local
differences is crucial for accurately identifying a correct match, thereby
enhancing the overall robustness and reliability of the matching process.
Commonly used shape descriptors have several limitations and often fail to
provide meaningful local insights on the paired geometries. In this work, we
propose a new technique, based on graph Laplacian eigenmaps, to match point
clouds by taking into account fine local structures. To deal with the order and
sign ambiguity of Laplacian eigenmaps, we introduce a new operator, called
Coupled Laplacian, that allows to easily generate aligned eigenspaces for
multiple rigidly-registered geometries. We show that the similarity between
those aligned high-dimensional spaces provides a locally meaningful score to
match shapes. We initially evaluate the performance of the proposed technique
in a point-wise manner, specifically focusing on the task of object anomaly
localization using the MVTec 3D-AD dataset. Additionally, we define a new
medical task, called automatic Bone Side Estimation (BSE), which we address
through a global similarity score derived from coupled eigenspaces. In order to
test it, we propose a benchmark collecting bone surface structures from various
public datasets. Our matching technique, based on Coupled Laplacian,
outperforms other methods by reaching an impressive accuracy on both tasks. The
code to reproduce our experiments is publicly available at
this https URL and in the Supplementary
Code.

基于图 Laplacian 特征映射和局部结构的点云匹配技术，通过引入 Coupled Laplacian 算子解决顺序和符号歧义，成功实现高度精确的形状匹配和异常定位。