SDFRaster: Real-Time Mesh Reconstruction

• SDFRaster is a continuous signed distance field defined over a Delaunay tetrahedral mesh that combines efficient rasterization with differentiable marching tetrahedra for globally coherent surface extraction.
• It employs a joint photometric-geometric optimization with a multiresolution hash encoder and lightweight MLPs to generate high-quality, watertight meshes with reduced storage costs.
• Empirical evaluations on benchmarks like DTU and Tanks and Temples show SDFRaster achieves lower Chamfer distances and superior detail preservation compared to competing approaches.

SDFRaster is a rasterizable signed distance field (SDF) representation designed for real-time, end-to-end mesh reconstruction that achieves globally consistent surface extraction within the optimization loop. It addresses the limitations of rasterization-based volumetric rendering—which cannot directly extract globally coherent surfaces—and implicit SDF methods—which rely on computationally expensive ray marching—by unifying efficient rasterization with analytic mesh extraction. SDFRaster builds on a continuous SDF defined over a Delaunay tetrahedral mesh, integrates differentiable Marching Tetrahedra for direct mesh supervision, and employs a joint photometric-geometric optimization objective. Empirical evaluations on standard benchmarks, including DTU and Tanks and Temples, demonstrate SDFRaster's ability to generate high-quality, complete meshes with lower storage cost than competing approaches (Cui et al., 26 Apr 2026).

1. Continuous SDF Representation over Tetrahedral Grids

SDFRaster models a scene as a continuous signed distance function $f:\mathbb{R}^3\to\mathbb{R}$ over the domain defined by a Delaunay tetrahedral mesh $\mathcal{T}$ with vertices $\mathcal{V} = \{\mathbf{v}_i\}$. Each vertex $\mathbf{v}_i$ stores a feature computed by a multi-resolution hash encoder $E_\gamma$—as in Instant-NGP—and a per-vertex SDF value: $$\mathbf{z}_i = E_\gamma(\mathbf{v}_i), \qquad f_i = H_{\rm sdf}\bigl([\mathbf{z}_i, \mathbf{v}_i]\bigr),$$ where $H_{\rm sdf}$ is a small multilayer perceptron (MLP) head. SDF values at interior points $\mathbf{x}$ of a tetrahedron $t = (i_0, i_1, i_2, i_3)$ are obtained via barycentric interpolation: $$f(\mathbf{x}) = \sum_{k=0}^3 \lambda_k(\mathbf{x})\, f_{i_k},$$ yielding a globally continuous, piecewise-linear SDF. This approach restricts storage and computation to the mesh's vertices, producing a compact and expressive scene representation.

2. Rasterization and Alpha-Compositing Scheme

Rendering in SDFRaster proceeds by rasterizing each tetrahedron along camera rays and performing alpha-compositing. For a camera ray $\mathcal{T}$0, the algorithm identifies entry and exit parameters $\mathcal{T}$1 and $\mathcal{T}$2 for each tetrahedron $\mathcal{T}$3, computes the 3D endpoints $\mathcal{T}$4 and $\mathcal{T}$5, and evaluates signed distances at these points. Opacity is calculated using a logistic-CDF mapping: $\mathcal{T}$6 where $\mathcal{T}$7 and $\mathcal{T}$8 is a learnable sharpness controlling the transition. Appearance is modeled by assigning each tetrahedron a view-dependent base color $\mathcal{T}$9 and a linear color gradient $\mathcal{V} = \{\mathbf{v}_i\}$0 at the centroid $\mathcal{V} = \{\mathbf{v}_i\}$1, so that interior colors are given by: $\mathcal{V} = \{\mathbf{v}_i\}$2 Per-ray compositing is performed front-to-back: $\mathcal{V} = \{\mathbf{v}_i\}$3 where $\mathcal{V} = \{\mathbf{v}_i\}$4 is the segment color averaged between $\mathcal{V} = \{\mathbf{v}_i\}$5 and $\mathcal{V} = \{\mathbf{v}_i\}$6. Depth and normal maps are composited analogously, supporting both photometric and geometric supervision.

3. Differentiable Marching Tetrahedra and Mesh Extraction

To enable end-to-end mesh reconstruction and training, SDFRaster incorporates analytic, differentiable mesh extraction using standard Marching Tetrahedra. For each tetrahedron with mixed vertex SDF signs, 1 or 2 triangles are generated by locating isosurface crossings on edges via: $\mathcal{V} = \{\mathbf{v}_i\}$7 This expression is analytic with respect to SDF values and vertex positions, allowing mesh-based loss gradients to propagate directly into network parameters and mesh geometry. This integration eliminates the need for post-processing mesh extraction and guarantees global surface consistency throughout optimization.

4. Joint Optimization and Loss Functions

SDFRaster performs joint optimization over the hash-encoded SDF head $\mathcal{V} = \{\mathbf{v}_i\}$8, the appearance parameters $\mathcal{V} = \{\mathbf{v}_i\}$9, sharpness $\mathbf{v}_i$0, and vertex positions $\mathbf{v}_i$1. The loss function combines photometric, mesh consistency, and field regularization objectives: $\mathbf{v}_i$2 where:

• $\mathbf{v}_i$3 includes $\mathbf{v}_i$4 color difference and SSIM loss between rendered and ground-truth color,
• $\mathbf{v}_i$5 ensures consistency between field-rendered and mesh-extracted depth and normal maps,
• $\mathbf{v}_i$6 comprises depth-normal self-consistency, Eikonal regularization ($\mathbf{v}_i$7 at vertices), and curvature penalties.

Training proceeds for approximately 18,000 iterations per scene using Adam, with regular tetrahedral densification (adding centroids to high-variance cells) and pruning (removing low-importance vertices).

5. Implementation Considerations

SDFRaster’s grid is constructed by Delaunay tetrahedralization of seed points covering the scene bounding box, with dynamic densification and culling for adaptive resolution. The backbone consists of a shared 16-level multiresolution hash grid (per Instant-NGP) and two small MLPs for SDF and appearance (approximately 100,000 parameters each; total network size ≈0.5 M parameters). Typical DTU scenes fit within a 2 GB GPU memory footprint. Per-scene training times are ≈1.6 hours on RTX 4090 (DTU) and ≈6 hours on L40 (Tanks and Temples). SDFRaster is ≈6× faster than NeuS/VolSDF (>12 hours), but slower than rasterization-based Gaussian-splatting baselines (2DGS ≈9 min, SVRaster ≈5 min), with the distinction that it produces a globally consistent, watertight mesh (Cui et al., 26 Apr 2026).

6. Empirical Evaluation and Comparative Performance

On the DTU 15-scene benchmark, SDFRaster attains the lowest mean Chamfer distance among explicit methods (0.68 mm, compared to 0.71 mm for the next best), and on the Tanks and Temples subset (6 scenes), it achieves an average F1 of 0.43, outperforming methods such as SU GaR/EVER and matching or exceeding contemporary hybrids. Its extracted meshes are significantly smaller (186 MB) than those of competing approaches (GOF 605 MB, 2DGS 658 MB). Qualitatively, SDFRaster's meshes exhibit fewer holes, retain clean topology, and preserve thin structures (e.g., chair legs, railings) that are often lost in TSDF-fusion pipelines.

7. Significance and Methodological Distinctions

SDFRaster unifies:

• A compact, continuous SDF discretized by tetrahedralization,
• Ultra-efficient rasterization via per-tetrahedron alpha-compositing,
• Analytic, differentiable mesh extraction with Marching Tetrahedra, and
• A hybrid photometric-geometric optimization objective.

This combination enables high-fidelity, end-to-end mesh reconstruction without reliance on heuristic post-processing or expensive ray marching. A plausible implication is that SDFRaster offers a competitive solution for applications requiring efficient, globally coherent surface extraction from image collections or multiview data, particularly where compactness, mesh quality, and training runtime are paramount (Cui et al., 26 Apr 2026).