用特征可分性定义3D表面，无需训练即可精准重建点云表面。
Separability Membrane: 3D Active Contour for Point Cloud Surface Reconstruction
- 基于Fisher比最大化点特征可分性，定义表面边界。
- 在噪声和离群点下仍能准确提取模糊表面边界。
- 自适应B样条控制曲面刚度，适合复杂几何重建。
本文提出Separability Membrane，一种用于从3D点云中提取表面的鲁棒3D主动轮廓方法。该方法将3D物体表面定义为在内、外区域间最大化点特征（如强度、颜色或局部密度）可分性的边界，依据Fisher比率。通过最大化类别可分性并利用自适应B样条表面控制3D表面模型的刚性，该方法根据局部与全局可分性动态调整属性，从而精确识别3D物体的真实表面。其核心优势在于无需训练数据或体素化表示，即使在噪声或离群点干扰下仍能准确重建模糊表面边界。在合成3D点云数据集和3DNet数据集上的评估表明，该膜方法在多种条件下均表现出高效性与鲁棒性。
原文摘要 · Abstract (English)
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.
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