A Global Continuous Multi-Scale Terrain Contour Simplification Method Based on the Level Set

Haoyue Qian,Run Wang,Wenjie Zhen,Shunping Zhou,Lin Yang,Zejun Zuo

doi:10.3390/app11093855

Abstract

Multi-scale spatial representation has been widely used in geographic information and online mapping systems. Terrain contour, which provides a reference for understanding and monitoring the Earth’s surface, is an important data category. For the multi-scale representation of contour lines, simplification is a fundamental step in providing different levels of detail for linear features. However, achieving a global continuous multi-scale simplification of contours remains a challenge. Therefore, based on the concept of level set, a novel contour simplification method labeled the continuous changing surface model (CCSM) was proposed in this paper. The CCSM was built by using a non-uniform rational B-spline constrained with characteristics and was then intersected with a set of horizontal planes with progressive height values. The generated intersection lines are considered continuous multi-scale simplified contours. Experiments were conducted on a 1:50,000 real contour dataset to verify the effectiveness of CCSM. Results showed that the changes in the shape of the simplified contours generated by CCSM are more natural and progressive than those generated by two other significant simplification methods. CCSM can also effectively balance local and global structures and has potential applications in obtaining a continuous multi-scale representation of terrain contours.

Highlights

Multi-scale spatial representation has a wide range of applications, such as zooming in/out, and is among the most common operators in geographic information and online mapping systems [1,2,3,4]
To evaluate effectiveness of our proposed method, the simplified contours generated by Douglas–Peucker (DP) algorithm, Wang–Muller (WM) the algorithm, and continuous changing surface model (CCSM)
To detect changes in the shape of the simplified taken as the thethree initial scale (i.e., 1:50,000), the contour scale(including was taken as the contours, simplification methods allwhereas produced

Summary

Introduction

Multi-scale spatial representation has a wide range of applications, such as zooming in/out, and is among the most common operators in geographic information and online mapping systems [1,2,3,4]. Rendering spatial data at different scales improves our understanding and analysis of spatial data, thereby meeting the continuous visual needs of modern map users. A simplification of these contour lines provides different levels of detail for linear features, which is an effective operator for maintaining essential shapes in multi-scale terrain maps [1,8,9]. Contour simplification methods have been investigated for a long time, studies on the continuous multi-scale representation of contour lines still face considerable limitations.

Objectives

Results

Conclusion