Accurate Computation of ART Coefficients for Binary Images

The coefficients of the Angular Radial Transform (ART) are used as MPEG-7 Shape descriptors where the bases functions ART are defined in polar coordinates over a unit disk. Conventional computational methods for computing the ART coefficients are depending on a circular to square mapping which produce two kinds of errors and results in inaccurate set descriptors. This work proposes accurate and efficient method for computing ART coefficients in polar coordinates. The unit disk is divided into a number of non-overlapped circular rings that are divided into circular sectors of the same area. Each sector is represented by one point in its centre. Computation process in the polar domain completely removes both approximation and geometrical errors produced by the conventional methods. Symmetry properties are applied to significantly reduce the computational complexity. Numerical experiments are performed to ensure the efficiency of the proposed method.