Heat field signatures reveal shape details in point clouds
Heat Field Signatures: From Point Clouds to Smooth Geometry
Machine Learning
Summary
Understanding the shapes and details inside collections of points in space can be hard because these points are irregular and don’t directly show smooth surfaces or shapes. This paper introduces Heat Field Signatures (HFS), a way to create smooth heat-like patterns around these points, making it easier to analyze shape features like size, direction, and texture. The authors show that HFS can work well across different types of biological and structural data, even improving protein shape classification by a large margin. This method connects raw points directly with geometry math without needing complex steps or extra learning.
What this means in practice
- •For biotech data engineers: Classify protein folds based only on 3D coordinates more accurately and efficiently using heat field signatures.
- •For 3d shape analysis developers: Enhance shape descriptors in point cloud processing pipelines by integrating heat field signatures for multiscale geometry detection.
Authors
Yuanqing Wang, Yapeng Tian, Baris Coskunuzer
Abstract
Bringing multiscale geometric analysis directly to irregular point clouds remains difficult: quantities such as local dimension, anisotropy, density variation, and geometric transitions are typically estimated through explicit neighborhood, manifold, or graph constructions, or left for neural networks to infer from coordinates. We introduce Heat Field Signatures (HFS), which lift a point cloud to a multiscale family of smooth ambient heat fields, providing a direct interface from discrete samples to geometric analysis. From this field, HFS computes closed-form global and local signatures directly from pairwise distances, capturing heat concentration, intrinsic dimension, anisotropy, and scale transitions. We further introduce the Heat Dimension Spectrum (HDS), a compact summary of multiscale geometric composition. HFS can be used as a closed-form descriptor, a lightweight learned representation, or a geometric feature channel for neural point-cloud models. Across synthetic and real-world benchmarks spanning subcellular, neuronal, tree, and protein data, HFS outperforms strong point-cloud and multiparameter-persistence baselines while substantially reducing end-to-end cost. On SCOP protein-fold classification, HFS improves over the strongest deep baseline by nearly $24$ percentage points using coordinates alone, while standalone HFS representations are exactly rotation-invariant by construction. More broadly, HFS turns a classical heat field into a practical interface for multiscale geometric analysis in modern point-cloud learning.