P2Voxel: Pyramid Pivot Voxelization for 3D Mesh Tokenization

2026-08-01

AI Summary

This work addresses the challenge of efficiently and structurally encoding irregular triangular meshes by proposing a learnable geometric sampling method based on pyramid pivot voxelization. Guided by three key assumptions—local planarity, spatial complexity, and block reconstructability—the approach adaptively performs fine-grained sampling in geometrically complex regions while coarsely compressing smooth areas within a multi-resolution voxel space. A pyramid-structured variational autoencoder (VAE) is employed to learn local implicit token representations that are inherently reconstructable. The resulting compact and structured tokens achieve high-fidelity surface reconstruction while significantly improving token efficiency, thereby offering a high-quality mesh tokenization scheme for downstream 3D tasks.

Abstract

Triangle meshes provide explicit and accurate surface geometry, yet their irregular topology connectivity makes 3D mesh tokenization a geometric sampling problem: how to sample and organize geometric evidence into compact, structured and learnable tokens. Beyond field-centric volumetric sampling and edge-intersection surface sampling, we retarget mesh tokenization as \textit{local surface evidence sampling}: identifying the minimal geometric evidence inside each active voxel that is sufficient for deterministic surface recovery. To this end, we introduce \textbf{P2Voxel}, a pyramid pivot voxelization framework for compact and reconstruction-aware mesh tokenization. P2Voxel is built on three key innovations. Under the \textit{Local Planarity} assumption, Pivot Voxelization represents each active voxel with a surface pivot and an orientation sign, providing minimal local evidence that can induce the corner values required for deterministic reconstruction. Under the \textit{Spatial Complexity} assumption, Pyramid Pivot Voxelization exploits the spatial non-uniformity of real surfaces by allocating finer pivot tokens to geometrically complex regions while keeping smooth regions coarse and compact. Under the \textit{Block Reconstructability} assumption, a Pyramid VAE learns compact multi-resolution latent codes over locally reconstructable pivot blocks, avoiding the need to model the entire high-resolution voxelized shape as a dense global field. Together, these designs convert meshes into compact, structured, and learnable pyramid pivot tokens, enabling efficient mesh reconstruction for downstream 3D tasks.

Problem

• 3D mesh tokenization
• geometric sampling
• surface reconstruction
• voxelization
• structured representation

Innovation

• Pivot Voxelization
• Pyramid VAE
• Local Planarity
• Spatial Complexity
• Mesh Tokenization