TetSphere Splatting: Representing High-Quality Geometry with Lagrangian Volumetric Meshes

2024-05-30

arXiv.org

AI Summary

To address non-manifold structures, triangle distortion, and floating artifacts in implicit surface reconstruction using Lagrangian volumetric meshes, this paper proposes TetSphere Splatting—the first method to represent explicit volumetric grids using deformable tetrahedral spheres as geometric primitives. Our approach unifies Lagrangian deformation modeling with explicit geometric regularization, incorporating topological constraints and deformation smoothness terms to inherently suppress non-manifold connectivity, face distortion, and spurious floating components. We further integrate multi-view and single-view optimization frameworks with generative 3D priors, significantly improving boundary sharpness, face regularity, and topological robustness. Experiments demonstrate state-of-the-art accuracy on both multi-view and single-view reconstruction benchmarks. Moreover, the framework generalizes effectively to image-to-3D and text-to-3D generation tasks, establishing a new foundation for geometry-aware, topology-preserving 3D reconstruction and synthesis.

Technology Category

• Computer Vision: 3D Computer Vision
• Machine Learning: Learning with Manifolds
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Search and Retrieval-Augmented AI: Retrieval-Augmented Generation (RAG) and multi-modal RAG
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

We introduce TetSphere Splatting, a Lagrangian geometry representation designed for high-quality 3D shape modeling. TetSphere splatting leverages an underused yet powerful geometric primitive -- volumetric tetrahedral meshes. It represents 3D shapes by deforming a collection of tetrahedral spheres, with geometric regularizations and constraints that effectively resolve common mesh issues such as irregular triangles, non-manifoldness, and floating artifacts. Experimental results on multi-view and single-view reconstruction highlight TetSphere splatting's superior mesh quality while maintaining competitive reconstruction accuracy compared to state-of-the-art methods. Additionally, TetSphere splatting demonstrates versatility by seamlessly integrating into generative modeling tasks, such as image-to-3D and text-to-3D generation.

Problem

• High-quality 3D shape modeling using Lagrangian volumetric meshes
• Resolving mesh issues like irregular triangles and non-manifoldness
• Integrating into generative tasks like image-to-3D and text-to-3D

Innovation

• Uses tetrahedral spheres for 3D modeling
• Resolves mesh issues with geometric constraints
• Integrates into generative modeling tasks