In this study, we propose a compact shape descriptor, which represents the 2-D shape information by 1-D functions. For this purpose a two-step method is proposed. In the first step, the 2-D shape information is mapped into 1-D moment functions without using a predefined resolution. The mapping is based on the beams, which are originated from a boundary point, connecting that point with the rest of the points on the boundary. At each point, the angle between a pair of beams is taken as a random variable to define the statistics of the topological structure of the boundary. The second order statistics of all the beam angles is used to construct 1-D Beam Angle Statistics (BAS) functions. In the second step, the 1-D functions are further compressed by using Discrete Fourier Transforms applied on the BAS functions of the shape boundary. BAS function is invariant to translation, rotation and scale. It is insensitive to distortions. Experiments are done on the dataset of MPEG 7 Core Experiments Shape-1. It is observed that proposed shape descriptor outperforms the popular MPEG 7 shape descriptors.