Multi-scale Automatic Extraction of Terrain Structure Lines Based on Wavelet Analysis

Terrain structure lines (valleys and ridges) are very important for geomorphological characterization, they construct the skeleton of terrain undation and variation, and they are scale-dependent because the ones are more important at a larger geographical scale than their counterparts at a smaller. Wavelet analysis is a new branch of mathematics burgeoning at the end of 80s. It has double meanings simultaneously on profundity of theory and extent of application. Because it has good local character at both time or space and frequency field simultaneously, and sample interval of signal can be adjusted automatically with different frequency components, wavelet analysis method can adapt to different type of relief at the same time, such as mountainous or plain terrain or the both. This paper formulates briefly the basic principle of multiresolution analysis(MRA) on wavelet transform, represents a new method of multi-scale automatic extraction of terrain structure lines from contour data. It employs curvature to describe contour data through curve spline fitting, then decomposes curvature based on the wavelet MRA at multiple scales, thereafter determines the contributive size of curvature by inspecting the wavelet coefficients at different scale and records their corresponding positions exactly at which describes the degree of convexity and concavity. Accordingly, we can get the candidate point sets belong to the structure lines at different scale. Assuming the higher elevation is to the left and the lower is to the right along a contour line, the positive curvature represents the convexity, namely ridges, the negative represents the concavity, namely valleys. Therefore, the point sets belong to valleys or ridges can be sorted out easily from the candidate point sets at different scale. According to the basic rules of relief contour representation, multi-scale valleys and ridges can be determined from the point sets belong to valleys or ridges by identifying ascription of bisector at concave corner or convex corner on adjacent contours. Some practical examples are given to exam the method. Finally, this paper also discusses the efficiency and accuracy of the algorithms, and simply compares it with existing method.