Structure Integral Transform Versus Radon Transform: A 2D Mathematical Tool for Invariant Shape Recognition

In this paper, we present a novel mathematical tool, Structure Integral Transform (SIT), for invariant shape description and recognition. Different from the Radon Transform (RT), which integrates the shape image function over a 1D line in the image plane, the proposed SIT builds upon two orthogonal integrals over a 2D $K$ -cross dissecting structure spanning across all rotation angles by which the shape regions are bisected in each integral. The proposed SIT brings the following advantages over the RT: 1) it has the extra function of describing the interior structural relationship within the shape which provides a more powerful discriminative ability for shape recognition; 2) the shape regions are dissected by the $K$ -cross in a coarse to fine hierarchical order that can characterize the shape in a better spatial organization scanning from the center to the periphery; and 3) it is easier to build a completely invariant shape descriptor. The experimental results of applying SIT to shape recognition demonstrate its superior performance over the well-known Radon transform, and the well-known shape contexts and the polar harmonic transforms.