Wavelet-based line simplification

Over the past decades, wavelet transformations are widely applied to seismic data processing, image processing, sound processing, and so on. In contrast, less attention is paid to wavelet-based simplification of geometrical elements, e.g., iso-contour simplification. This paper is intended to explore wavelet-based line simplification for the purpose of map generalization. Iso-contour simplification is taken into account. After making wavelet transformations of the iso-contour, the wavelet coefficients at certain level are tailored with a threshold. Innovatively, the threshold is evaluated by the extended radical law of Topfer and Pillewizer. Furthermore, the threshold is evaluated differently with the three-level importance of an iso-contour. The multilevel wavelet transformations of the iso-contour are performed, and the wavelet coefficients are thresholded at each level. Through a reverse transformation of tailored wavelet coefficients, a simplified iso-contour is obtained. Without the consideration of relationships between iso-contours, the generalized iso-contour map is a set of simplified iso-contours. The experiment of iso-contour generalization has shown the feasibility of wavelet-based line simplification by tailoring wavelet coefficients with a map scale-derived threshold.