A range scan records more than where a surface is: every measured ray also states where the surface is not. Most implicit reconstruction methods discard this, treating the scan as an unordered point cloud. We instead take the sensor origin of every point as input and fit a continuous 1-Lipschitz implicit field directly to the rays, supervising the first intersection found by differentiable sphere tracing rather than an unsigned distance to the points. Starting from a closed-form field enclosing the scene, depth supervision carves the surface inward toward the observations. The Lipschitz constraint turns visibility into a geometric certificate: positive field values along a measured ray guarantee a ball of empty space around it, so one-dimensional ray evidence becomes a three-dimensional free-space guarantee. The result is robust to acquisition noise, outliers and sparse sampling, and avoids hallucinating surfaces in regions the sensor has observed to be empty.
\mathcal{D} = \{(\mathbf{c}_i, \mathbf{p}_i)\}_{i=1}^{N}
\begin{alignedat}{2} &\mathbf{c}_i \in \mathbb{R}^3 \quad && \text{acquisition center} \\ &\mathbf{p}_i \in \mathbb{R}^3 \quad && \text{noisy measurement of } \mathcal{S}^\star \\ &\mathbf{d}_i = (\mathbf{p}_i - \mathbf{c}_i) / \lVert \mathbf{p}_i - \mathbf{c}_i \rVert \quad && \text{ray direction} \end{alignedat}
\text{reconstruct } \mathcal{S}^\star \text{ as } f_\theta^{-1}(0)
\begin{aligned} \min_{\theta} \;\; & \frac{1}{N}\sum_{i=1}^{N} \rho\bigl(t_i(\theta) - \lVert \mathbf{p}_i - \mathbf{c}_i \rVert\bigr) \\ \text{s.t.} \;\; & t_i(\theta) = \inf\,\{t \ge 0 : f_\theta(\mathbf{c}_i + t\,\mathbf{d}_i) = 0\} \end{aligned}
\begin{alignedat}{2} &\bullet\;\; f_\theta \quad && \text{1-Lipschitz MLP} \\ &\bullet\;\; \rho \quad && \text{robust penalty} \end{alignedat}
Reconstruction of the SRB Gargoyle scene in a clean setting. We use the positional encoding parameter L as a simple knob to study the fidelity–robustness trade-off: increasing L gives more fitting capacity but less robustness to corruption. Ours (L=6) captures finer geometric details.
Baselines: DiGS (Ben-Shabat et al., CVPR 2022) and DiffCD (Härenstam-Nielsen et al., ECCV 2024).
Reconstruction of the SRB Anchor scene with increasing scanner noise levels. The lower fitting capacity of Ours (L=0) makes it robust to noise.
Reconstruction of the SRB Anchor scene with increasing outlier ratios (0%, 5%, 10%, 20%) relative to the number of clean points. By enforcing visibility constraints and using a Huber loss, our method remains robust to outliers.
Sofa reconstruction from real-world LiDAR scans captured with an iPad Pro. Ours (L=2) produces a more faithful reconstruction, avoiding excessive smoothing and recovering fine geometric details such as the cushions.
This work was supported in part by the French government under management of Agence Nationale de la Recherche as part of the “France 2030” program, PR[AI]RIE-PSAI project, reference ANR-23-IACL-0008. J.P. was supported in part by the Louis Vuitton/ENS chair in artificial intelligence, the Institute of Information & Communications Technology Planning & Evaluation (IITP) grant funded by the Korean Government (MSIT) (No. RS-2024-00457882, National AI Research Lab Project), and a Global Distinguished Professorship at the Courant Institute of Mathematical Sciences and the Center for Data Science at New York University.
@article{lenain2026visibility,
title = {Surface Reconstruction from Range Scans Under Visibility Constraints},
author = {Lenain, Gabriel and Boyer, Edmond and Ponce, Jean},
journal = {arXiv preprint arXiv:2610.18005},
year = {2026}
}