This paper presents a novel approach to identify complex shapes based on the Radon transform. We propose an adaptation of Radon transform called $\mathcal R$-transform which is invariant to common geometrical transformations. Moreover, to improve the uniqueness of the approach, a binary shape is projected into the Radon space for different levels of the Chamfer distance transform. The accuracy and the efficiency of the proposed algorithm in the presence of a variety of transformations are evaluated within a shape recognition process.