Generalizations of angular radial transform for 2D and 3D shape retrieval

The angular radial transform (ART) is a moment-based image description method adopted in MPEG-7 as a 2D region-based shape descriptor. This paper proposes generalizations of the ART to describe two-dimensional images and three-dimensional models. First, we propose an 2D extension, called GART, which allows applying ART to images while insuring robustness to all possible rotations and to perspective deformations. Then, we generalize the ART to index 3D models. This new 3D shape descriptor, so called 3D ART, has the same properties that the original transform: robustness to rotation, translation, noise and scaling while keeping a compact size and a good retrieval cost. The size of the descriptor is an essential evaluation parameter on which depends the response time of a content-based retrieval system. For both generalizations, many experiments were made on large databases and have shown, that GART outperforms ART in accuracy at the cost of speed, and that 3D ART outperforms the spherical harmonics shape descriptor (Vranic, D.V., Saupe, D., 2002. Description of 3D-shape using a complex function on the sphere, in: IEEE International Conference on Multimedia and Expo (ICME 2002), Lausanne, Switzerland, 2002, pp. 177-180; Funkhouser, T., Min, P. Kazhdan, M., Chen, J., Halderman, A., Dobkin, D., Jacobs, D., 2003. A search engine for 3D models. ACM Trans. Graphics 22(1), 83-105) in speed at the cost of accuracy. (c) 2005 Elsevier B.V. All rights reserved.