Curvature Informed Furthest Point Sampling

TL;DR

This paper introduces a reinforcement learning-based point cloud sampling method that incorporates curvature information to improve down-sampling quality for downstream geometry tasks, outperforming classical methods.

Contribution

It presents a novel curvature-informed sampling algorithm that enhances furthest point sampling with reinforcement learning, enabling stable end-to-end training and superior performance.

Findings

Achieves state-of-the-art results in classification, segmentation, and shape completion.

Demonstrates stable end-to-end learning with curvature integration.

Outperforms baseline models across multiple geometry processing tasks.

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.