Separability Membrane: 3-D Active Contour for Point Cloud Surface Reconstruction
Gulpi Qorik Oktagalu Pratamasunu, Guoqing Hao, Kazuhiro Fukui · IEEE Access · 2026
Reconstructing surfaces from 3D point clouds is challenging when boundaries are ambiguous due to noise or outliers. Existing methods often rely on accurate normal estimation and geometric assumptions, making them sensitive to outliers or requiring large amounts of training data and explicit voxel grids with memory overhead and quantization artifacts, limiting generalization. This paper proposes the Separability Membrane, a robust 3D active contour for extracting surfaces from 3D point cloud objects. Our approach defines the surface of a 3D object as the boundary that maximizes the separability of point features, such as intensity, color, or local density, between its inner and outer regions based on Fisher’s ratio. Separability Membrane identifies surfaces by maximizing class while controlling surface rigidity through an adaptive B-spline surface that adjusts its properties based on both local and global separability. Our method estimates occupancy from k-NN densities without building grids, avoiding memory overhead and quantization while preserving volumetric reasoning benefits. Evaluations on a synthetic dataset and the 3DNet dataset show competitive performance on clean data (F-Score $0.979\pm 0.018$ ) and substantial gains under severe outliers ( $0.966\pm 0.028$ with region outliers, $0.953\pm 0.031$ with surface outliers). Qualitative validation on KITTI-360 further demonstrates effectiveness on real-world LiDAR data with natural sensor noise. Overall, the method consistently maintains over 95% F-Score in all tested outlier scenarios while reducing processing time by more than an order of magnitude compared to deep learning baselines.