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Angular radial transform (ART), which is the region-based shape descriptor of MPEG-7, has desirable properties for representing shape information in a small number of features with no redundancy. However, in order for ART to be useful, especially in limited computing environments, the computational cost of ART must be greatly reduced. In this paper, we derive symmetric/antisymmetric properties from the basis functions of ART and present a fast and efficient method to compute the ART coefficients using these properties. The proposed method significantly reduces the number of sinusoidal operations and multiplications in computing the coefficients of ART. Moreover, the memory requirements needed to store the ART basis functions in lookup tables are only 25% of the conventional method. The experimental results are presented to show the effectiveness of the proposed method.