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

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.