P2Voxel: Pyramid Pivot Voxelization for 3D Mesh Tokenization
P2Voxel achieves efficient 3D mesh reconstruction via pyramid pivot voxelization, reducing storage significantly.
Key Findings
Methodology
P2Voxel introduces three innovations: Pivot Voxelization, Pyramid Pivot Voxelization, and Pyramid VAE. Using the Local Planarity assumption, it encodes each active voxel with a pivot point and orientation sign. The Spatial Complexity assumption enables adaptive resolution allocation for complex regions, while the Block Reconstructability assumption uses Pyramid VAE to learn compact multi-resolution latent codes.
Key Results
- On the ABO dataset, Pivot-512 achieved comparable reconstruction quality to FaithC with 385k voxels, reaching an F-score of 0.4889.
- Pyramid-1024 reduced sampling by ~2× while maintaining stable performance on Objaverse and Wild datasets.
- P2Voxel outperformed SDF-based and Dual Contouring methods in storage-efficiency and reconstruction fidelity trade-offs.
Significance
P2Voxel addresses inefficiencies in traditional 3D mesh tokenization methods by introducing a compact and reconstruction-aware framework. It enables efficient geometry reconstruction and opens new possibilities for generative 3D modeling.
Technical Contribution
P2Voxel's contributions include: 1) Pivot Voxelization for minimal geometric evidence encoding; 2) Pyramid Pivot Voxelization for adaptive resolution allocation; 3) Pyramid VAE for learning multi-resolution latent codes. These innovations reduce storage needs and improve reconstruction efficiency.
Novelty
P2Voxel is the first to introduce pyramid structures into 3D mesh tokenization, achieving compact encoding via pivot voxelization, fundamentally differing from SDF and Dual Contouring methods.
Limitations
- High-curvature regions may require finer resolution for detail preservation.
- Relies on high-quality input meshes; noisy or non-watertight meshes may degrade performance.
- Further optimization is needed for real-time applications.
Future Work
Future work could explore more efficient resolution allocation strategies, extend to non-watertight meshes, and optimize for real-time dynamic scenarios.
AI Executive Summary
P2Voxel proposes an efficient 3D mesh tokenization framework that balances storage efficiency and reconstruction fidelity. Traditional methods like SDF and Dual Contouring face challenges with storage redundancy and reconstruction inefficiency. P2Voxel addresses these by encoding geometric information using pivot points and orientation signs under the Local Planarity assumption.
The framework's core innovations include: 1) Pivot Voxelization for minimal geometric evidence encoding; 2) Pyramid Pivot Voxelization for adaptive resolution allocation to complex regions; 3) Pyramid VAE for learning multi-resolution latent codes. These designs enable P2Voxel to achieve efficient geometry reconstruction across multiple datasets.
Experimental results demonstrate P2Voxel's superior performance on ABO, Objaverse, and Wild datasets. Notably, the Pivot-512 configuration achieved comparable quality to state-of-the-art methods with significantly fewer voxels. While limitations exist in high-curvature regions, P2Voxel offers valuable insights for future 3D geometry processing and generative modeling research.
Deep Analysis
Background
3D meshes are the standard representation in geometry processing and computer graphics, but their irregular topology poses challenges for modern deep learning models. Traditional methods like SDF and Dual Contouring perform well but suffer from storage redundancy and inefficiency.
Core Problem
The core problem is how to convert 3D meshes into compact, structured, and learnable tokens while maintaining efficient geometry reconstruction. This requires balancing storage efficiency and reconstruction fidelity.
Innovation
P2Voxel's core innovations include: 1) Pivot Voxelization, encoding minimal geometric evidence under the Local Planarity assumption; 2) Pyramid Pivot Voxelization, adaptively allocating resolution to complex regions; 3) Pyramid VAE, learning multi-resolution latent codes for local reconstruction.
Methodology
- �� Pivot Voxelization: Encodes each active voxel with a pivot point and orientation sign.
- �� Pyramid Pivot Voxelization: Allocates resolution adaptively based on geometric complexity.
- �� Pyramid VAE: Learns multi-resolution latent codes for efficient local reconstruction.
Experiments
Experiments were conducted on ABO, Objaverse, and Wild datasets using CDL1, CDL2, EMD, and F-score metrics. Baselines included SDF and Dual Contouring methods.
Results
P2Voxel achieved efficient geometry reconstruction across datasets, with Pivot-512 matching FaithC's quality using fewer voxels.
Applications
P2Voxel can be applied to efficient 3D mesh reconstruction, generative modeling, and geometry processing in VR/AR.
Limitations & Outlook
The method may underperform in high-curvature regions and requires high-quality input meshes. Future work could optimize real-time performance for dynamic scenarios.
Plain Language Accessible to non-experts
Imagine building a LEGO model. Traditional methods fill the entire space with bricks, even outside the model, wasting resources. P2Voxel is smarter—it only places bricks where needed, like the edges and corners, saving materials and time.
ELI14 Explained like you're 14
Think of Minecraft! Traditional methods fill the ground with blocks, even where you don't need them. P2Voxel is like a pro builder—it only places blocks where they're really needed, saving time and resources. Cool, right?
Glossary
Voxelization
The process of dividing 3D geometry into a regular grid, where each cell is a voxel.
Used to convert meshes into structured data.
Pivot Point
A key point representing local geometry within a voxel.
Used in Pivot Voxelization to encode geometric information.
Pyramid Structure
A multi-resolution representation where complex regions get higher resolution.
Used for adaptive resolution allocation.
Pyramid VAE
A variational autoencoder for learning multi-resolution latent codes.
Used in P2Voxel for block-level reconstruction.
Sparse Marching Cubes
An efficient algorithm for mesh reconstruction from sparse voxel data.
Used to reconstruct meshes from P2Voxel tokens.
Open Questions Unanswered questions from this research
- 1 How can resolution allocation be further optimized for high-curvature regions?
- 2 Can this method be extended to handle non-watertight or noisy meshes?
- 3 How can real-time performance be achieved for dynamic scenarios?
Applications
Immediate Applications
Efficient 3D Reconstruction
Applicable to real-time geometry processing in VR/AR.
Generative Modeling
Provides efficient geometry representation for 3D content generation.
Long-term Vision
Dynamic Scene Processing
Supports real-time modeling and reconstruction of dynamic scenes.
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.