Acquisition, Restoration and Compression of 3D Geometric Data

本课题的研究重点是三维点云的去噪。点云是物理对象（如人体）的非均匀离散三维几何样本的集合。利用图信号处理的最新进展，在我们的方法中，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），以正则化一个病态逆问题。RGLR具有许多理想的特性，包括：i)旋转不变性，ii)促进分段平滑，以及iii)快速优化，其中RGLR可以通过迭代二次规划有效地计算。实验结果表明，与现有的点云去噪方案相比，本文提出的基于rglr的点云去噪方案具有更好的性能和更低的复杂度。

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.