SDFoam: Signed-Distance Foam for explicit surface reconstruction

TL;DR

SDFoam tackles the challenge of accurate geometry within neural rendering by unifying an explicit Voronoi foam with a learnable SDF. By treating each Voronoi cell as a local SDF and deriving per-cell density from the SDF, the method enables differentiable ray tracing and direct, topology-preserving mesh extraction. The approach yields crisper, more complete surfaces with fewer floaters and maintains competitive rendering quality and training speed compared to RadiantFoam. Across multiple scenes, SDFoam delivers substantial gains in mesh reconstruction accuracy (Chamfer) while preserving photometric fidelity and enabling faster mesh extraction, bridging explicit geometry and neural radiance fields.

Abstract

Neural radiance fields (NeRF) have driven impressive progress in view synthesis by using ray-traced volumetric rendering. Splatting-based methods such as 3D Gaussian Splatting (3DGS) provide faster rendering by rasterizing 3D primitives. RadiantFoam (RF) brought ray tracing back, achieving throughput comparable to Gaussian Splatting by organizing radiance with an explicit Voronoi Diagram (VD). Yet, all the mentioned methods still struggle with precise mesh reconstruction. We address this gap by jointly learning an explicit VD with an implicit Signed Distance Field (SDF). The scene is optimized via ray tracing and regularized by an Eikonal objective. The SDF introduces metric-consistent isosurfaces, which, in turn, bias near-surface Voronoi cell faces to align with the zero level set. The resulting model produces crisper, view-consistent surfaces with fewer floaters and improved topology, while preserving photometric quality and maintaining training speed on par with RadiantFoam. Across diverse scenes, our hybrid implicit-explicit formulation, which we name SDFoam, substantially improves mesh reconstruction accuracy (Chamfer distance) with comparable appearance (PSNR, SSIM), without sacrificing efficiency.

Figures (13)

• Figure 1: Existing methods in literature reconstruct 3D scenes either by employing explicit or implicit geometry, each with their own advantages and drawbacks. Our method, SDFoam, jointly learns a signed distance field (SDF) and a 3D Voronoi Diagram (or foam), both of which are optimized during a ray-tracing process. Our method offers a good trade-off of rendering speed, visual fidelity and reconstruction accuracy. Our code and experiments are available at https://mmlab-cv.github.io/SDFoam.
• Figure 2: Ray traversal through Voronoi cells. The ray intersects the $n$-th cell (centered at site $p_n$) at positions $t_n$ (entry) and $t_{n+1}$ (exit), defining the segment length $\delta_n$. Spatial and visual information are piecewise constant within $\delta_n$. The ray $r$ is defined by its origin $o$ and direction $d$.
• Figure 3: SDFoam Architecture. A point cloud is initialized and refined over time by learning an SDF from its points. Their SDF values are then converted to density, which jointly with color and position parameters are used to learn a ray-traced scene. $\theta_{var}$ is a learnable variance parameters that allows to improve the SDF-to-density conversion over time, similar to wang2021neus.
• Figure 4: From a trained SDFoam scene, we have access to both the SDF and the Voronoi Diagram. We infer the SDF value for each cell site, extracting the surface voronois via a threshold. The relevant surface faces are selected by thresholding their vertices against a close to zero SDF value. Since the VD is non-overlapping by nature, we don't need to build additional connectivity at this step.
• Figure 5: Mesh reconstruction qualitative results. Top to bottom: ground truth, RF, SDFoam. Modelling the voronoi cells as local SDFs improves the consistency of the extracted surface, thus filling the typical holes derived from the ray-tracing procedure in RF.