In cartography curve simplification is a recurrent problem. The purpose is to remove irrelevant details while emphasizing the main features of the curve. Decomposition of curve is preprocessing of curve simplification. 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. 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) generate the base layer. By using different alpha values, we can get base layer in different scales. Future directions for work are presented at the end of this paper.