Line Decomposition Based on Critical Points Detection

Abstract

The problem of line simplification is a recurrent problem in cartography. The purpose is to remove irrelevant details while emphasising the main features of the line. Most of the current techniques belong to the spatial domain (least square method, active contour, point selection). However, some techniques applying to the frequency domain (Fourier transform, wavelets) have also been introduced. These latter methods are mostly employed for simplification and compression purposes where information about line features is rarely taken into account, thus limiting their usefulness for cartographic applications. This paper presents the principle of Empirical Mode Decomposition which belongs to the frequency domain. It is used in signal processing to decompose a signal into its different frequencies. The method for line simplification has been studied, showing that line features can be taken into account by introducing a new decomposition method based on the detection of critical points. Results obtained at different levels of detail are discussed. Finally, future directions for work are presented.