Curvature Informed Furthest Point Sampling

TL;DR

A reinforcement learning-based sampling algorithm that enhances furthest point sampling by integrating curvature information, and establishes state-of-the-art results for classification, segmentation and shape completion, showcasing its robustness and adaptability.

Abstract

Point cloud representation has gained traction due to its efficient memory usage and simplicity in acquisition, manipulation, and storage. However, as point cloud sizes increase, effective down-sampling becomes essential to address the computational requirements of downstream tasks. Classical approaches, such as furthest point sampling (FPS), perform well on benchmarks but rely on heuristics and overlook geometric features, like curvature, during down-sampling. In this paper, We introduce a reinforcement learning-based sampling algorithm that enhances FPS by integrating curvature information. Our approach ranks points by combining FPS-derived soft ranks with curvature scores computed by a deep neural network, allowing us to replace a proportion of low-curvature points in the FPS set with high-curvature points from the unselected set. Existing differentiable sampling techniques often suffer from training instability, hindering their integration into end-to-end learning frameworks. By contrast, our method achieves stable end-to-end learning, consistently outperforming baseline models across multiple downstream geometry processing tasks. We provide comprehensive ablation studies, with both qualitative and quantitative insights into the effect of each feature on performance. Our algorithm establishes state-of-the-art results for classification, segmentation and shape completion, showcasing its robustness and adaptability.

Figures (5)

• Figure 1: 2048 points of a monitor downsampled to 256 points showing CFPS retains more structural information than traditional FPS. The scalar map shows curvature values increasing from white to red. Notice more higher curvature points with CFPS.
• Figure 2: Architecture diagram of the Curvature-aware Furthest Point Sampling (CFPS) pipeline. The pipeline involves swapping the least important points from the core set ($X_{core}$), selected by the Furthest Point Sampling (FPS) algorithm, with the most important points from the unselected points ($\bar{X}_{core}$). The importance of each point is determined by a joint ranking based on both curvature and FPS rank. The number of points to be exchanged between the core and non-core sets is determined by an exchange ratio predicted by a policy network.
• Figure 3: Comparison of downsampling methods across different objects. Each column represents the point cloud of a specific object (Desk, Chair, Monitor, Dressing Table), either the full point cloud or downsampled. The rows represent the downsampling method: Original Point Cloud, FPS, APES Local, APES Global, and CFPS (Our). The original pointcloud is of size 2048 and is downsampled to 256 points. The scalar map show curvature values increasing from white to red.
• Figure 4: Result of changing $nep$ number of exchange points on different classes in MVP dataset
• Figure 5: VRCNet Architecture for Shape Completion