Multi-scale Representation Model for Contour Based on Fourier Series

Automatically building of multi-scale representation model based on the same data source has been the focus in the field of map generalization.This paper extracts characteristic vector of contour based on Fourier series,and provides a model of multi-scale representation of contour.Open contours are mirrored into close contours according to the line including the start and end point,then the close contours are expressed into periodical functions about the length of arc and further Fourier series.Building the matching relationship between Fourier series expanding items and contour map scales based on the crack which formed due to the original curve and the current expanding curve.The model based on Fourier series provided in this paper is a method of reconstructing the curve through adjusting the length of characteristic vector instead of selecting the points and bent on the curve in the traditional methods and can be carried out.It is a progressive scale contour representation.