Affine invariant descriptors using principal components analysis

In this paper, we propose new methods for recognizing 2D/3D objects undergoing affine transforms. Robustness with respect to level-of-detail is achieved by selection of points belonging to fixed directions on a circle, i.e., the 2D case, or a sphere, i.e., the 3D case (called the Ray casting selection method in the literature). The proposed descriptors are based on principal component analysis (PCA); each shape is represented by its eigenvalues and the corresponding eigenvectors. The proposed methods allow recognition under an affine transform which is not possible using other methods in the literature, for example, that in [1]. Here we use an asymmetric PCA to achieve invariance under an affine transform. The text was submitted by the author in English. Ahmed El Oirrak. Received the CEUS and 3rd Cycle thesis both in Computer Science from the Faculty of the Sciences, Mohammed V University, Rabat, Morocco, in 1996 and 1999, respectively. He joined Cadi Ayyad University, Marrakech, Morocco, in 1999, first as an assistant professor, and received the Doctorate in signal processing from the Mohammed V University, Rabat, Morocco, in 2001. He is presently an associate professor with the Faculty of the sciences of Marrakech Semlalia. His research interests include image processing, pattern recognition, and their applications. Author of the more than 20 publications.