Diffusion-Driven Inter-Outer Surface Separation for Point Clouds with Open Boundaries

We propose a diffusion-based algorithm for separating the inter and outer layer surfaces from double-layered point clouds, particularly those exhibiting the “double surface artifact” caused by truncation in Truncated Signed Distance Function (TSDF) fusion during indoor or medical 3D reconstruction. This artifact arises from asymmetric truncation thresholds, leading to erroneous inter and outer shells in the fused volume, which our method addresses by extracting the true inter layer to mitigate challenges like overlapping surfaces and disordered normals. We focus on point clouds with \emph{open boundaries} (i.e., sampled surfaces with topological openings/holes through which particles may escape), rather than point clouds with \emph{missing surface regions} where no samples exist. Our approach enables robust processing of both watertight and open-boundary models, achieving extraction of the inter layer from 20,000 inter and 20,000 outer points in approximately 10 seconds. This solution is particularly effective for applications requiring accurate surface representations, such as indoor scene modeling and medical imaging, where double-layered point clouds are prevalent, and it accommodates both closed (watertight) and open-boundary surface geometries. Our goal is \emph{post-hoc} inter/outer shell separation as a lightweight module after TSDF fusion; we do not aim to replace full variational or learning-based reconstruction pipelines.

💡 Research Summary

The paper addresses a common problem in Truncated Signed Distance Function (TSDF) fusion pipelines: the creation of spurious double‑layered surfaces (an inner “inter” shell and an outer shell) that arise from asymmetric truncation thresholds, especially when reconstructing thin structures such as walls or sheets. These artifacts hinder downstream tasks like mesh generation, SLAM, AR/VR, and medical visualization. Rather than redesigning the fusion process, the authors propose a lightweight, post‑hoc module that separates the true inner surface from the erroneous outer one using a physics‑inspired diffusion simulation.

The core idea is to treat the point cloud as a porous container and launch virtual particles that perform random walks inside it. A spherical “simulation ball” of radius R_ball starts from an interior seed point (usually the geometric center) and moves in straight‑line steps up to a maximum distance L_max. At each step the algorithm queries a kd‑tree for nearby points within the ball’s effective radius (R_eff = R_ball + margin). If no points are encountered, the ball proceeds forward; otherwise a collision is registered. The collision point’s local normal is approximated from its nearest neighbors, and the ball’s direction is reflected with a small random perturbation to emulate realistic scattering. Each collision contributes to a hit counter for the contacted point, and after a predefined number of collisions the point may become a new spawn location for subsequent particles. An outer “escape boundary” sphere, large enough to enclose the entire cloud, captures particles that exit through topological openings (holes). Once a particle reaches this boundary, its trajectory terminates.

The algorithm iterates this process, spawning new balls either from the original seed or from previously generated spawn points, until either a maximum number of balls has been simulated or the duplication rate (the fraction of newly discovered points) stabilizes near 0.99 for ten consecutive iterations. The set of points with high collision frequencies is taken as the inner surface; the outer shell is discarded. Because the method relies only on point positions (no normals, meshes, or volumetric grids), it works for both watertight and open‑boundary models.

Implementation details include:

• Loading the raw point cloud as a NumPy array and computing an average nearest‑neighbor distance R₀ for scale normalization.
• Using Open3D’s kd‑tree for fast radius searches.
• Defining parameters R_ball, L_max, and R_eff empirically (the paper reports successful separation for 40 k points in ~10 s on a standard CPU).
• After diffusion, applying Poisson surface reconstruction on the extracted inner points to obtain a clean mesh; small holes may remain where the original data were sparse or truly open.

The authors compare their approach to classic geometric methods (Poisson reconstruction, Ball‑Pivoting, Alpha Shapes, advancing front, Voronoi‑based techniques) and to recent neural implicit methods (NeRF, DeepSDF). Traditional geometric pipelines tend to enforce watertightness, merging thin layers and bridging gaps, while neural methods require heavy training, large GPU resources, and still struggle with thin double layers unless specifically trained for them. In contrast, the diffusion‑based method needs only a few hyper‑parameters, runs in seconds, and is robust to noise and non‑uniform sampling.

Experimental validation includes synthetic data with 20 k inner and 20 k outer points and real-world indoor and medical scans. Quantitatively, the method reduces inter‑outer mixing by over 85 % compared to naïve Poisson reconstruction, and qualitatively it preserves thin walls and genuine openings. Limitations are acknowledged: the algorithm’s performance depends on sufficient sampling of the inner surface, bounded hole sizes, and appropriate step sizes; extremely complex interiors or very large openings may cause excessive outer‑surface collisions, leading to misclassification. Moreover, the current CPU implementation may not scale to millions of points without parallelization.

In summary, the paper contributes a novel, physics‑inspired diffusion simulation for post‑fusion double‑shell separation that is simple, fast, and applicable to both closed and open‑boundary point clouds. It fills a practical gap in TSDF pipelines, offering a modular tool that can be integrated into existing workflows without retraining or redesigning the reconstruction pipeline. Future work could explore GPU acceleration, adaptive parameter selection, and integration with downstream tasks such as semantic segmentation or real‑time SLAM.