Multi-scale curve decomposition based on alpha-shape

Curve Decomposition is widely used in various fields, such as curve simplification, denoising and enhancement. Most of the current techniques belong to the spatial domain (such as least square method, active contour, point selection). However, some techniques applying to the frequency domain (fourier transform, wavelets, et al.) have also been introduced. This paper presents a new frequency method for curve decomposition based on alpha shape. It firstly utilizes the alpha shape to extract the envelope of the curve. And then, the Filtered Medial Axis Transform (FMAT) is used to generate the base layer. By using different alpha values, we can get base layers in different scales. Future directions of this work are presented at the end of this paper.