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 about 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 (https://github.com/matteo-bastico/CoupLap), that allows to easily generate aligned eigenspaces for multiple registered geometries. We show that the similarity between those aligned high-dimensional spaces provides a locally meaningful score to match shapes. We firstly evaluate the performance of the proposed technique in a point-wise manner, focusing on the task of object anomaly localization on 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.

翻译：点云匹配作为计算机视觉、医学和机器人领域的一项关键技术，主要关注于寻找点云或体素对之间的对应关系。在某些实际场景中，强调局部差异对于准确识别正确匹配至关重要，从而提升匹配过程的整体鲁棒性和可靠性。常用的形状描述符存在若干局限性，往往无法提供关于配对几何结构的有意义的局部洞察。本文提出一种基于图拉普拉斯特征映射的新技术，通过考虑精细的局部结构来实现点云匹配。为处理拉普拉斯特征映射的阶次和符号模糊性问题，我们引入一种称为耦合拉普拉斯（https://github.com/matteo-bastico/CoupLap）的新算子，该算子能够为多个已配准的几何结构轻松生成对齐的特征空间。我们证明，这些对齐的高维空间之间的相似性可为形状匹配提供具有局部意义的评分。我们首先以逐点方式评估所提技术的性能，重点关注MVTec 3D-AD数据集上的物体异常定位任务。此外，我们定义了一项称为自动骨侧估计（BSE）的新医学任务，通过从耦合特征空间导出的全局相似度评分来解决该任务。为验证其有效性，我们提出了一个收集来自多个公开数据集的骨骼表面结构的基准测试集。实验表明，基于耦合拉普拉斯的匹配技术在两项任务上均以显著优势超越其他方法，达到了令人印象深刻的准确率。