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.
Abstract (translated)
本文提出了一种名为“Separability Membrane”的鲁棒三维活动轮廓方法，用于从三维点云对象中提取表面。我们的方法将三维物体的表面定义为一个边界，该边界最大化了内侧和外侧区域之间基于费希尔比率（Fisher's ratio）计算出的点特征（如强度、颜色或局部密度）的可分离性。Separability Membrane 通过最大限度地提高类别间的可分性和利用自适应B样条曲面控制三维表面模型的刚度来精确识别三维物体的实际表面，该B样条曲面可以根据局部和全局可分离性的不同调整其属性。 我们的方法的一个关键优势在于它能够在噪声或异常值导致边界模糊的情况下准确重建表面边界，并且不需要任何训练数据或转换为体积表示。在合成三维点云数据集以及3DNet数据集上的评估证明了该膜的有效性和鲁棒性，即使是在各种不同的条件下也是如此。
URL
https://arxiv.org/abs/2503.05217
