Robust surface reconstruction from highly noisy point clouds using distributed elastic networks

In this paper, a novel distributed elastic random weights network (DERWN) is proposed to achieve robust surface reconstruction from highly noisy point clouds sampled from real surface. The designed elastic regularization with l1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$l_{1}$$\end{document} and l2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$l_{2}$$\end{document} penalty items makes the network more resilient to noise and effectively capture the intrinsic shape of surface. Sparsity constraints of output weight vectors and threshold-based nodes removal are conducive to determining appropriate number of hidden nodes of network and optimizing the distribution of hidden nodes. The distributed optimization manner in DERWN on the basis of alternating direction method of multipliers solves the problem that traditional RWN learning algorithm suffers from the limitation of memory with large-scale data. The proposed DERWN achieves a solution to global problem by solving local subproblems coordinately. Experimental results show that the proposed DERWN algorithm can robustly reconstruct the unknown surface in case of highly noisy data with satisfying accuracy and smoothness.