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

TL;DR

TetSphere splatting demonstrates versatility by seamlessly integrating into generative modeling tasks, such as image-to-3D and text-to-3D generation, by seamlessly integrating into generative modeling tasks.

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.

Figures (14)

• Figure 1: (a) Eulerian vs. Lagrangian geometry representations: Compared to Eulerian methods that rely on a fixed grid, TetSphere splatting, a Lagrangian method, uses a set of volumetric tetrahedral spheres that deform to represent the geometry. TetSphere splatting supports applications such as reconstruction, image-to-3D, and text-to-3D generation (b-d).
• Figure 2: Visual comparison of mesh quality across widely used shape representations, including NeRF nerf, FlexiCubes shen2023flexible (Eulerian), DMesh son2024dmesh, and Gaussian Splatting huang20242d (Lagrangian). These methods exhibit mesh quality issues, such as irregular or degenerated triangles, non-manifoldness, and floating artifacts. Our method demonstrates uniform surface triangles, improved mesh quality, and structure integrity.
• Figure 3: Overall pipeline: TetSphere splatting represents a 3D shape using a collection of TetSpheres. Each TetSphere is a tetrahedral sphere that can be deformed from its initial uniform state through deformation gradient. The deformation process is optimized by minimizing rendering loss and geometric energy terms.
• Figure 4: TetSphere splatting with deforming tetrahedral spheres. Color-coded regions represent the bi-harmonic energy values (red: high, blue: low) across tetrahedra, one of the geometric regularizations employed in our deformation optimization process.
• Figure 5: Qualitative results on multi-view reconstruction, with surface mesh visualizations and rendered normal maps. Our method excels over baseline methods regarding mesh quality, less bumpy surface, correct surface orientation, and accurately capturing slender and thin structures.