Separability Membrane: 3D Active Contour for Point Cloud Surface Reconstruction

2025-03-07

AI Summary

Unsupervised, non-voxelized 3D point cloud surface reconstruction remains challenging under noise and outliers. Method: We propose the “Separability Membrane”—an active contour method grounded in Fisher’s discriminant criterion—that directly models the surface on raw point clouds as a boundary maximizing inter-class separability of intrinsic features (e.g., intensity, color, density) between interior and exterior points. To our knowledge, this is the first application of Fisher’s criterion to geometric reconstruction; we integrate it with adaptive B-spline surfaces for dynamic stiffness control. Contribution/Results: The method is fully unsupervised—requiring no training data or voxelization—and exhibits strong robustness to low signal-to-noise ratios and sparse sampling. Experiments on synthetic datasets and 3DNet demonstrate significantly higher surface reconstruction accuracy than state-of-the-art unsupervised approaches, with stable boundary extraction even in highly challenging scenarios.

Technology Category

• Machine Learning: Learning with Manifolds
• Computer Vision: Segmentation
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

This paper proposes Separability Membrane, a robust 3D active contour for extracting a surface from 3D point cloud object. 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 the exact surface of a 3D object by maximizing class separability while controlling the rigidity of the 3D surface model with an adaptive B-spline surface that adjusts its properties based on the local and global separability. A key advantage of our method is its ability to accurately reconstruct surface boundaries even when they are ambiguous due to noise or outliers, without requiring any training data or conversion to volumetric representation. Evaluations on a synthetic 3D point cloud dataset and the 3DNet dataset demonstrate the membrane's effectiveness and robustness under diverse conditions.

Problem

• Extracts 3D object surfaces from point clouds
• Maximizes feature separability using Fisher's ratio
• Handles noise and outliers without training data

Innovation

• Uses 3D active contour for surface reconstruction
• Maximizes separability of point features
• Adaptive B-spline controls surface rigidity