Abstract Finding efficient features which are invariant under affine transformation is the key to recognizing the images captured at different angles. Affine invariants, such as affine Gaussian descriptors, are derived in this paper. The covariance matrix of the given image is computed at first. Then its eigenvalues and eigenvectors are calculated, by which a set of ellipses with the same center are generated. Finally, affine Gaussian descriptors are derived based on 2dimensional Gaussian function and image compactification theory. Numerical experiments are carried out and the results show that the performance of affine Gaussian descriptors is high.
[1] Gao Wen, Zhao Xilin. Computer Vision: Algorithms and Principles. Beijing, China: Tsinghua University Press, 1998 (in Chinese) (高 文,赵熙霖.计算机视觉——算法与系统原理.北京:清华大学出版社, 1998) [2] Zhou Xinghe. Advanced Geometry. Beijing, China: Science Press, 2003 (in Chinese) (周兴和.高等几何.北京:科学出版社, 2003) [3] Kim W Y, Kim Y S. A RegionBased Shape Descriptor Using Zernike Moments. Signal Processing: Image Communication, 2000, 16(1): 95102 [4] Zhang Dengsheng, Lu Guojun. Enhanced Generic Fourier Descriptors for ObjectBased Image Retrieval // Proc of the IEEE International Conference on Acoustics, Speech and Signal Processing. Orlando, USA, 2002: 36683671 [5] Goshtasby A. Description and Discrimination of Planar Shapes Using Shape Matrices. IEEE Trans on Pattern Analysis and Machine Intelligence, 1985, 7(6): 738743 [6] Liu Yishu. A New Type of Shape Features: Gaussian Descriptors. Journal of Image and Graphics, 2007, 12(3): 482490 (in Chinese) (刘亦书. 一种新的形状特征——高斯描绘子. 中国图象图形学报, 2007, 12(3): 482490) [7] Leu J G. Shape Normalization through Compacting. Pattern Recognition Letters, 1989, 10(4): 243250 [8] Pei S C, Lin C N. Image Normalization for Pattern Recognition. Image and Vision Computing, 1995, 13(10): 711723 [9] Shen Dinggang, Ip H H S. Generalized Affine Invariant Image Normalization. IEEE Trans on Pattern Analysis and Machine Intelligence, 1997, 19(5): 430440 [10] Chen Zhijie. Advanced Algebra and Analytical Geometry. Beijing, China: Advanced Education Press, 2002 (in Chinese) (陈志杰.高等代数与解析几何.北京:高等教育出版社, 2002) [11] Tou J T, Gonzales R C. Pattern Recognition Principles. Reading, USA: AddisonWesley, 1974 [12] Apostol T M. Mathematical Analysis. Reading, USA: AddisonWesley, 1957 [13] Burns J B, Weiss R S, Riseman E M. View Variation of PointSet and LineSegment Features. IEEE Trans on Pattern Analysis and Machine Intelligence, 1993, 15(1): 5168
2007, Vol. 20 
