As 3D point clouds become a cornerstone of modern technology, the need for sophisticated generative models and reliable evaluation metrics has grown exponentially. In this work, we first expose that some commonly used metrics for evaluating generated point clouds, particularly those based on Chamfer Distance (CD), lack robustness against defects and fail to capture geometric fidelity and local shape consistency when used as quality indicators. We further show that introducing samples alignment prior to distance calculation and replacing CD with Density-Aware Chamfer Distance (DCD) are simple yet essential steps to ensure the consistency and robustness of point cloud generative model evaluation metrics. While existing metrics primarily focus on directly comparing 3D Euclidean coordinates, we present a novel metric, named Surface Normal Concordance (SNC), which approximates surface similarity by comparing estimated point normals. This new metric, when combined with traditional ones, provides a more comprehensive evaluation of the quality of generated samples. Finally, leveraging recent advancements in transformer-based models for point cloud analysis, such as serialized patch attention, we propose a new architecture for generating high-fidelity 3D structures, the Diffusion Point Transformer (DiPT). We perform extensive experiments and comparisons on the ShapeNet dataset, showing that our model outperforms previous solutions, particularly in terms of quality of generated point clouds, achieving new state-of-the-art. Code available at https://github.com/matteobastico/DiffusionPointTransformer.

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 lo-cal differences is crucial for accurately identifying a cor-rect 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 geome-tries. 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 in-troduce a new operator, called Coupled Laplacian11Code: 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 man-ner, 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 Cou-pled Laplacian, outperforms other methods by reaching an impressive accuracy on both tasks.