Learning to Tessellate: Point Cloud Generation via Recursive Spectral Partitioning

2026-08-03

AI Summary

Existing autoregressive point cloud generation methods rely on heuristic tokenization schemes that often disrupt the intrinsic topological structure of point clouds, resulting in incoherent outputs. To address this limitation, this work proposes a topology-preserving generative framework based on recursive spectral partitioning. The approach employs a topology-aware partitioning autoencoder to construct an unbalanced binary tree hierarchy, yielding a deterministic geometric blueprint. A geometry-calibrated positional encoding mechanism is introduced to preserve multi-scale topological relationships, and a dual-stream cascaded generator is designed to jointly model structural evolution and feature synthesis. The proposed method achieves state-of-the-art performance in generation quality, diversity, and generalization to complex 3D topologies.

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.

Problem

• point cloud generation
• autoregressive models
• topology preservation
• structural coherence
• tokenization

Innovation

• recursive spectral partitioning
• topology-preserving tessellation
• autoregressive point cloud generation
• hierarchical latent representation
• geometry-calibrated positional encoding