Acquisition, Restoration and Compression of 3D Geometric Data

本文研究的重点是三维点云数据的去噪。点云是物理对象(如人体)三维几何形状的非均匀离散样本的集合。在我们的方法中，利用图形信号处理的最新进展，我们设计了一个基于图的正则化项，称为重加权图拉普拉斯正则化(RGLR)来正则化原本不适定的反问题。RGLR具有许多理想的性质，包括：i)旋转不变，ii)分段光滑性的提升，以及iii)快速优化，其中RGLR可以通过迭代二次规划来高效地计算。实验结果表明，与已有的点云去噪方法相比，本文提出的基于RGLR的点云去噪方法在较低的复杂度下具有更好的去噪性能。

The focus of this research period is in the denoising of 3D point cloud. A point cloud is a collection of non-uniform discrete samples of 3D geometry of a physical object, such as human body.Leveraging on recent advances in graph signal processing, in our approach we design a graph-based regularization term called reweighted graph Laplacian regularization (RGLR) to regularize an otherwise ill-posed inverse problem. RGLR has a number of desirable properties, including: i) rotation-invariant, ii) promotion of piecewise-smoothness, and iii) fast optimization, where the RGLR can be computed efficient via iterative quadratic programming. Experimental results show that compared to existing point cloud denoising schemes, our proposed RGLR-based scheme has better performance at lower complexity.