Graph Smoothing for Enhanced Local Geometry Learning in Point Cloud Analysis

TL;DR

Graph-based point cloud learning often suffers from suboptimal graphs where boundary points form sparse connections and junction areas introduce noisy links, hindering reliable feature propagation. The authors introduce GSPoint, a framework that couples graph smoothing with enhanced local geometry learning. Graph smoothing balances node degrees using symmetric adjacency refinement and a von Neumann kernel-based multi-hop scheme, while local geometry learning injects adaptive shape features and cylindrical distribution cues into feature aggregation. Experiments on ModelNet40, ScanObjectNN, ShapeNetPart, and S3DIS demonstrate competitive or superior performance across classification and segmentation, with ablations validating the contributions and plug-in benefits for other methods. The work offers a robust approach to building geometry-aware neighborhoods in unstructured point clouds, improving real-world robustness and applicability.

Abstract

Graph-based methods have proven to be effective in capturing relationships among points for 3D point cloud analysis. However, these methods often suffer from suboptimal graph structures, particularly due to sparse connections at boundary points and noisy connections in junction areas. To address these challenges, we propose a novel method that integrates a graph smoothing module with an enhanced local geometry learning module. Specifically, we identify the limitations of conventional graph structures, particularly in handling boundary points and junction areas. In response, we introduce a graph smoothing module designed to optimize the graph structure and minimize the negative impact of unreliable sparse and noisy connections. Based on the optimized graph structure, we improve the feature extract function with local geometry information. These include shape features derived from adaptive geometric descriptors based on eigenvectors and distribution features obtained through cylindrical coordinate transformation. Experimental results on real-world datasets validate the effectiveness of our method in various point cloud learning tasks, i.e., classification, part segmentation, and semantic segmentation.

Figures (6)

• Figure 1: Illustration of sparse connection. The heatmaps of degree distribution indicates that (a) When the graph is constructed using the normal ball query, some boundary points exhibit sparse connection and out-degree values below 20, whereas some points have out-degree values exceeding 35. (b) Through our method, the number of points with extreme out-degree values is reduced.
• Figure 2: Illustration of noisy connection. The constructed point neighborhoods indicate that (a) By the normal ball query, the constructed point cloud neighborhood might exhibit noisy connection, e.g., the neighbors of a point encompasses both fuselage and wing points. (b) Through our method, the neighbors of the point are refined to include only points from the fuselage.
• Figure 3: The proposed framework of GSPoint. Our method involves two key parts in the point cloud feature extraction process, i.e., graph smoothing module and local geometry learning module. Note that, FPS indicates farthest point sampling.
• Figure 4: With normal ball query (upper row) $vs.$ With our graph smoothing (bottom row).
• Figure 5: xyz coordinate $vs.$ cylindrical coordinate.