Quaternion higher-order spectra and their invariants for color image recognition |
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| Affiliation: | 1. College of Mathematics, Jilin University, Changchun, Jilin Province 130012, China;2. Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Science, Changchun 130033, China;1. Centro de Investigaciones en Óptica, Asociación Civil, Loma Del Bosque 115, León, Guanajuato C.P. 37150, México;2. Universidad Autónoma de Zacatecas, Calzada Solidaridad Esquina con Paseo la Bufa S/N, Zacatecas C.P. 98060, México;1. Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun, Jilin 130033, China;2. University of Chinese Academy of Sciences, Beijing 100039, China;1. Department of Computer Science, KU Leuven, Celestijnenlaan 200A, 3001 Leuven, Belgium;2. School of Mathematics and Statistics, University of New South Wales, Sydney, NSW 2052, Australia;1. Department of Mechanical Engineering, Faculty of Engineering, University of Malaya, 50603 Kuala Lumpur, Malaysia;2. Department of Mechanical Engineering, Mohammad Ali Jinnah University, Islamabad, Pakistan;3. Advanced Technovation Ltd., Loughborough Innovation Centre, Loughborough University Science & Enterprise Park (Holywell Park), Loughborough, LE11 3AQ, UK |
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| Abstract: | This paper describes an invariants generation method for color images, which could be a useful tool in color object recognition tasks. First, by using the algebra of quaternions, we introduce the definition of quaternion higher-order spectra (QHOS) in the spatial domain and derive its equivalent form in the frequency domain. Then, QHOS invariants with respect to rotation, translation, and scaling transformations for color images are constructed using the central slice theorem and quaternion bispectral analysis. The feature data are further reduced to a smaller set using quaternion principal component analysis. The proposed method can deal with color images in a holistic manner, and the constructed QHOS invariants are highly immune to background noise. Experimental results show that the extracted QHOS invariants form compact and isolated clusters, and that a simple minimum distance classifier can yield high recognition accuracy. |
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| Keywords: | Color image recognition Quaternion Bispectrum Higher-order spectra invariant Quaternion principal component analysis |
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