Color Image Analysis by Quaternion-Type Moments

In this paper, by using the quaternion algebra, the conventional complex-type moments (CTMs) for gray-scale images are generalized to color images as quaternion-type moments (QTMs) in a holistic manner. We first provide a general formula of QTMs from which we derive a set of quaternion-valued QTM in...

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Published in	Journal of mathematical imaging and vision Vol. 51; no. 1; pp. 124 - 144
Main Authors	Chen, Beijing, Shu, Huazhong, Coatrieux, Gouenou, Chen, Gang, Sun, Xingming, Coatrieux, Jean Louis
Format	Journal Article
Language	English
Published	Boston Springer US 01.01.2015 Springer Verlag
Subjects	Applications of Mathematics Bioengineering Computer Science Engineering Sciences Image Processing and Computer Vision Imaging Life Sciences Mathematical Methods in Physics Signal and Image processing Signal,Image and Speech Processing Color image registration Moment Quaternion Color face recognition Color image Moment invariant INVARIANTS ALGEBRA CLASSIFICATION HYPERCOMPLEX FOURIER-TRANSFORMS TRANSLATION FAST COMPUTATION ZERNIKE MOMENTS VECTOR OBJECT RECOGNITION
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Abstract	In this paper, by using the quaternion algebra, the conventional complex-type moments (CTMs) for gray-scale images are generalized to color images as quaternion-type moments (QTMs) in a holistic manner. We first provide a general formula of QTMs from which we derive a set of quaternion-valued QTM invariants (QTMIs) to image rotation, scale and translation transformations by eliminating the influence of transformation parameters. An efficient computation algorithm is also proposed so as to reduce computational complexity. The performance of the proposed QTMs and QTMIs are evaluated considering several application frameworks ranging from color image reconstruction, face recognition to image registration. We show they achieve better performance than CTMs and CTM invariants (CTMIs). We also discuss the choice of the unit pure quaternion influence with the help of experiments. ( i - j - k ) / 3 appears to be an optimal choice.
AbstractList	In this paper, by using the quaternion algebra, the conventional complex-type moments (CTMs) for gray-scale images are generalized to color images as quaternion-type moments (QTMs) in a holistic manner. We first provide a general formula of QTMs from which we derive a set of quaternion-valued QTM invariants (QTMIs) to image rotation, scale and translation transformations by eliminating the influence of transformation parameters. An efficient computation algorithm is also proposed so as to reduce computational complexity. The performance of the proposed QTMs and QTMIs are evaluated considering several application frameworks ranging from color image reconstruction, face recognition to image registration. We show they achieve better performance than CTMs and CTM invariants (CTMIs). We also discuss the choice of the unit pure quaternion influence with the help of experiments. ( i - j - k ) / 3 appears to be an optimal choice. In this paper, by using the quaternion algebra, the conventional complex-type moments (CTMs) for gray-scale images are generalized to color images as quaternion-type moments (QTMs) in a holistic manner. We first provide a general formula of QTMs from which we derive a set of quaternion-valued QTM invariants (QTMIs) to image rotation, scale and translation transformations by eliminating the influence of transformation parameters. An efficient computation algorithm is also proposed so as to reduce computational complexity. The performance of the proposed QTMs and QTMIs are evaluated considering several application frameworks ranging from color image reconstruction, face recognition to image registration. We show they achieve better performance than CTMs and CTM invariants (CTMIs). We also discuss the choice of the unit pure quaternion influence with the help of experiments. appears to be an optimal choice.
Author	Coatrieux, Gouenou Sun, Xingming Chen, Beijing Coatrieux, Jean Louis Chen, Gang Shu, Huazhong
Author_xml	– sequence: 1 givenname: Beijing surname: Chen fullname: Chen, Beijing organization: School of Computer and Software, Nanjing University of Information Science and Technology, Jiangsu Engineering Center of Network Monitoring, Nanjing University of Information Science and Technology, Institut Mines-Telecom, Telecom Bretagne, INSERM UMR1101 LaTIM – sequence: 2 givenname: Huazhong surname: Shu fullname: Shu, Huazhong email: shu.list@seu.edu.cn organization: Laboratory of Image Science and Technology, Southeast University, Centre de Recherche en Information Biomédicale Sino-Français (CRIBs) – sequence: 3 givenname: Gouenou surname: Coatrieux fullname: Coatrieux, Gouenou organization: Institut Mines-Telecom, Telecom Bretagne, INSERM UMR1101 LaTIM – sequence: 4 givenname: Gang surname: Chen fullname: Chen, Gang organization: Laboratory of Image Science and Technology, Southeast University – sequence: 5 givenname: Xingming surname: Sun fullname: Sun, Xingming organization: School of Computer and Software, Nanjing University of Information Science and Technology, Jiangsu Engineering Center of Network Monitoring, Nanjing University of Information Science and Technology – sequence: 6 givenname: Jean Louis surname: Coatrieux fullname: Coatrieux, Jean Louis organization: Centre de Recherche en Information Biomédicale Sino-Français (CRIBs), INSERM, U1099, Laboratoire Traitement du Signal et de l’Image, Université de Rennes I
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Keywords	Color image registration Moment Quaternion Color face recognition Color image Moment invariant INVARIANTS ALGEBRA CLASSIFICATION HYPERCOMPLEX FOURIER-TRANSFORMS TRANSLATION FAST COMPUTATION ZERNIKE MOMENTS VECTOR OBJECT RECOGNITION
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Snippet	In this paper, by using the quaternion algebra, the conventional complex-type moments (CTMs) for gray-scale images are generalized to color images as...
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SubjectTerms	Applications of Mathematics Bioengineering Computer Science Engineering Sciences Image Processing and Computer Vision Imaging Life Sciences Mathematical Methods in Physics Signal and Image processing Signal,Image and Speech Processing
Title	Color Image Analysis by Quaternion-Type Moments
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