Grid Partition Variable Step Alpha Shapes Algorithm

Zhenxiu Liao,Junxia Meng,Guodong Shi,Jun Liu,Sakander Hayat

doi:10.1155/2021/9919003

Abstract

On the basis of Alpha Shapes boundary extraction algorithm for discrete point set, a grid partition variable step Alpha Shapes algorithm is proposed to deal with the shortcomings of the original Alpha Shapes algorithm in the processing of nonuniform distributed point set and multiconcave point set. Firstly, the grid partition and row-column index table are established for the point set, and the point set of boundary grid partition is quickly extracted. Then, the average distance of the k -nearest neighbors of the point is calculated as the value of α . For the point set of boundary grid partition extracted in the previous step, Alpha Shapes algorithm is used to quickly construct the point set boundary. The proposed algorithm is verified by experiments of simulated point set and measured point set, and it has high execution efficiency. Compared with similar algorithms, the larger the number of point sets is, the more obvious the execution efficiency is.

Highlights

From the traditional electronic total station, handheld satellite positioning collector, to mobile three-dimensional laser radar, modern spatial information acquisition technology has entered the era of massive data at the GB and TB level
Process, and express massive data efficiently has become a new challenge to the related fields such as computer information technology (IT), computer-aided design/manufacturing (CAD/CAM), geographic information (GIS) and remote sensing (RS), and even building information modeling (BIM) [1,2,3,4]. e boundary information of the discrete point set is composed of discrete points representing the original contour features of the measured object
Based on the algorithms proposed in literatures [14, 15], this paper puts forward a grid partition variable step Alpha Shapes (GPVAS) algorithm, which has higher computational efficiency while solving the problems caused by nonuniform distribution of point sets

Summary

Introduction

From the traditional electronic total station, handheld satellite positioning collector, to mobile (vehicle-mounted/airborne) three-dimensional laser radar, modern spatial information acquisition technology has entered the era of massive data at the GB and TB level. E boundary information of the discrete point set is composed of discrete points representing the original contour features of the measured object. It is a basic and important technical work in spatial data processing to quickly and efficiently construct the boundary information from the discrete point set. In the 1980s, Edelsbrunner et al [14] gave a rigorous mathematical definition on the “shape of a set of points” based on two-dimensional plane point set and proposed a point set boundary construction algorithm called Alpha Shapes (AS). Based on rigorous mathematical definition, this algorithm can deal with complex discrete point set boundaries including convex hull, concave points, and holes. AS algorithm to automatically extract the building roof from airborne LiDAR point cloud; Shen et al [17] and Li et al [18] used the improved AS algorithm to extract building contour; Wang et al [19] used the improved algorithm to extract edges from massive point cloud data in mountainous areas; Li and Li [20] used the improved algorithm to reconstruct the 3D surface model from the point cloud data of handicrafts; Sun et al [5] applied the improved algorithm to extract the plot boundary from the trajectory data points collected by the vehicle-mounted satellite navigation receiver of agricultural machinery and finely measured the farmland area; Li et al [21] applied the algorithm to construct the tree crown threedimensional model; Fu et al [22] applied the algorithm to construct a three-dimensional model from jujube tree point cloud

Alpha Shapes Algorithm

Algorithm Overview e main improvements of the GPVAS algorithm are as follows:

Comparative Experiments

Conclusions