Abstract
3D point cloud - a new signal representation of volumetric objects - is a discrete collection of triples marking exterior object surface locations in 3D space. Conventional imperfect acquisition processes of 3D point cloud - e.g., stereo-matching from multiple viewpoint images or depth data acquired directly from active light sensors - imply non-negligible noise in the data. In this paper, we adopt a previously proposed low-dimensional manifold model for the surface patches in the point cloud and seek self-similar patches to denoise them simultaneously using the patch manifold prior. Due to discrete observations of the patches on the manifold, we approximate the manifold dimension computation defined in the continuous domain with a patch-based graph Laplacian regularizer and propose a new discrete patch distance measure to quantify the similarity between two same-sized surface patches for graph construction that is robust to noise. We show that our graph Laplacian regularizer has a natural graph spectral interpretation, and has desirable numerical stability properties via eigenanalysis. Extensive simulation results show that our proposed denoising scheme can outperform state-of-the-art methods in objective metrics and can better preserve visually salient structural features like edges.
Abstract (translated)
三维点云（3d point cloud）——一种新的三维物体信号表示——是三维空间中标记外部物体表面位置的三重体的离散集合。传统的三维点云不完美的采集过程——例如，多视点图像的立体匹配或直接从有源光传感器获取的深度数据——意味着数据中存在不可忽略的噪声。本文对点云中的表面斑块采用了先前提出的低维流形模型，并利用斑块流形先验法寻找自相似的斑块，同时对其进行去噪。由于流形上的斑块的离散观测，我们用基于斑块的图拉普拉斯正则化器对连续域中定义的流形维数计算进行了近似，并提出了一种新的离散斑块距离测度，用以量化两个大小相同的曲面斑块之间的相似度，这种相似度对n具有鲁棒性。奥伊斯我们证明了我们的图拉普拉斯正则化器具有自然的图谱解释，并且通过本征分析具有理想的数值稳定性。大量的仿真结果表明，我们提出的去噪方案在目标度量方面优于最先进的方法，并且能够更好地保留边缘等明显的结构特征。
URL
https://arxiv.org/abs/1803.07252
