Learning to Tessellate: Point Cloud Generation via Recursive Spectral Partitioning
2026-08-03 • Computer Vision and Pattern Recognition
Computer Vision and Pattern Recognition
AI summaryⓘ
The authors present PointRSP, a new method for generating 3D point clouds that keeps the original shape’s structure intact. Instead of using random or simple ways to organize points, their method breaks down the shape into a tree-like structure based on its topology using spectral partitioning. This hierarchical layout helps the model understand and recreate shapes more accurately. They also introduce special techniques to better encode and generate these shapes step-by-step. Experiments show that PointRSP produces higher quality and more diverse 3D shapes compared to earlier methods.
Point cloudAutoregressive modelsSpectral partitioningTopology preservationBinary treeHierarchical representationLatent spacePositional encoding3D shape generation
Authors
Monan Sun, Bangzhen Liu, Huaidong Zhang, Shengfeng He
Abstract
Autoregressive models have emerged as an effective paradigm for point cloud generation. However, most existing approaches rely on heuristic tokenization strategies, such as spatial sorting or stochastic downsampling, which often disrupt intrinsic point cloud topology and weaken the structural coherence of the generated shapes. In this paper, we present PointRSP, an autoregressive framework that reformulates point cloud generation as a topology-preserving tessellation process via recursive spectral partitioning. Instead of constructing token sequences heuristically, we introduce a topology-aware partitioning autoencoder that decomposes an unstructured point cloud into a non-balanced binary tree through a hybrid recursive spectral partitioning strategy. This hierarchical representation provides a deterministic geometric blueprint that preserves topological relationships while capturing multiscale structural dependencies within a quantized latent space. To synthesize shapes in this space, we propose a dual-stream cascaded generator that jointly models structural evolution and feature synthesis. In addition, we design a geometry-calibrated positional encoding mechanism that anchors latent embeddings using multi-scale structural centers, which stabilizes cascaded generation during the early stages of structural formation. Extensive experiments show that PointRSP achieves state-of-the-art performance in generation quality and diversity, demonstrating strong generalization across complex 3D topologies.