Volume 6 Issue 6
Dec.  2013
Turn off MathJax
Article Contents
GUO Li-qiang, ZHU Ming. Commutative Clifford algebra method for color image processing[J]. Chinese Optics, 2013, 6(6): 885-891. doi: 10.3788/CO.20130606.885
Citation: GUO Li-qiang, ZHU Ming. Commutative Clifford algebra method for color image processing[J]. Chinese Optics, 2013, 6(6): 885-891. doi: 10.3788/CO.20130606.885

Commutative Clifford algebra method for color image processing

  • Received Date: 21 Sep 2013
  • Rev Recd Date: 23 Nov 2013
  • Publish Date: 10 Dec 2013
  • By using the commutative Clifford algebra method to model for a color image, the parallel processing of R, G and B components in the color image can be realized in a holistic manner and the integrating processing for the color image can be implemented. This paper reviews the progress of color image modeling, researches a type of commutative Clifford algebra, namely Cl2com and gives the definitions of the arithmetic operations, unit element, inverse element, conjugation, and the norm for the commutative Clifford algebra. Then, it describes the expression of the color image based on the commutative Clifford algebra and introduces an application example of this method:the edge detection of color image. In comparison with the quaternion-based color image modeling, the proposed method can remove the data redundancy and reduce the computational complexity to the utmost extent. The proposed color image modeling method can be applied in color image processing tasks as a useful tool.

     

  • loading
  • [1] KOSCHAN M,ABIDI M. Digital Color Image Processing[M]. Somerset NJ:John Sons Wiley,Inc.,2009. [2] 李光鑫,吴伟平,胡君. 红外和彩色可见光图像亮度-对比度传递融合算法[J]. 中国光学,2011,4(2):161-168. LI G X,WU W P,HU J. Luminance-contrast transfer based fusion algorithm for infrared and color visible images[J]. Chinese Optics,2011,4(2):161-168.(in Chinese) [3] 朱明,孙继刚,郭立强. 彩色图像四元数矩不变量的研究[J]. 中国光学,2011,4(5):497-502. ZHU M,SUN J G,GUO L Q. Quaternion moment invariant for color image[J]. Chinese Optics,2011,4(5):497-502.(in Chinese) [4] 王墨林,莽思淋,桑爱军,等. 彩色图像三维六边形离散余弦变换编码[J]. 光学 精密工程,2013,21(1):217-223. WANG M L,MANG S L,SANG A J,et al.. Three dimentional hexagonal discrete cosine transform for color image coding[J]. Opt. Precision Eng.,2013,21(1):217-223.(in Chinese) [5] 王宇庆,朱明. 评价彩色图像质量的四元数矩阵最大奇异值方法[J]. 光学 精密工程,2013,21(2):469-478. WANG Y Q,ZHU M. Max singular value method of quaternion matrix for evaluating color image quality[J]. Opt. Precision Eng.,2013,21(2):469-478.(in Chinese) [6] 陈勇,李愿,吕霞付,等. 视觉感知的彩色图像质量积极评价方法[J]. 光学 精密工程,2013,21(3):742-750. CHEN Y,LI Y,LV X F,et al.. Active assessment of color image quality based on visual perception[J]. Opt. Precision Eng.,2013,21(3):742-750.(in Chinese) [7] KANTOR I L,SDODOVNIKOV A S. Hypercomplex Number:An Elementary Introduction to Algebras[M]. NewYork:Springer-Verlag,1989. [8] ELL T A. Hypercomplex spectral transform[D]. Minneapolis:University of Minnesota,1992. [9] SANGWINE S J. Fourier transforms of colour images using quaternion, or hypercomplex numbers[J]. Electronics Lett.,1996,32(1):1979-1980. [10] MOXEY C E,SANGWINE S J,ELL T A. Hypercomplex corelation techniques for vector images[J]. Comput Vis. Image Und.,2007,107:88-96. [11] SHI L,FUNT B. Quaternion color texture segmentation[J]. IEEE. Signal Processing Lett.,2008,15:669-672. [12] YEH M H. Relationships among various 2-D quaternion Fourier transforms[J]. IEEE. Signal Processing Lett.,2008,15:669-672. [13] SUBAKAN O N,VEMURI B C. A Quaternion framework for color image smoothing and segmentation[J]. Int. J. Comput. Vision,2011,91:233-250. [14] GUO L,ZHU M. Quaternion Fourier-Mellin moments for color images[J]. Pattern Recognition,2011,44(2):187-195. [15] CHEN B J,SHU H Z,ZHANG H,et al.. Quaternion Zernike moments and their invariants for color image analysis and object recognition[J]. Signal Processing,2012,92:308-318. [16] BAYRO-CORROCHANO E,SCHEUERMANN G. Geometric Algebra Computing in Engineering and Computer Science[M]. New York:Springer-Verlag,2010. [17] GIRARD P R. Quaternions, Clifford Algebras and Relativistics Physics[M]. New York:Springer-Verag,2007. [18] SCHLEMMER M,HAGEN H,HOTZ I,et al.. Clifford pattern matching for color image edge detection[EB/OL].[2013-01-11].Http://wenku.baidu.com/view/41d9d46ba45177232f60a2fo.html?from=related. [19] 谢维信,曹文明,蒙山. 基于Clifford代数的混合型传感器网络覆盖理论分析[J]. 中国科学E辑:信息科学,2007,37(8):1018-1031. XIE W X,CAO W M,MENG SH. Analysis of hybrid sensor network coverage based on the theory of Clifford Algebras[J]. Science in China E Series:Information Sciences,2007,37(8):1018-1031.(in Chinese) [20] 刘伟.八元数及Clifford代数在数字图像处理中的应用[D]. 广州:华南师范大学,2010. LIU W. Octonion and Clifford algebra in the application of digital image processing[D]. Guangzhou:South China Normal University,2010.(in Chinese) [21] BAYRO-CORROCHANO E J,ARANA-DANIEL N. Clifford support vector machines for classification, regression, and recurrence[J]. IEEE T. Neural Networks,2010,21(11):1731-1746. [22] 刘辉,徐晨,曹文明. 基于Clifford代数的多光谱图像边缘检测[J]. 东南大学学报 (自然科学版),2012,42(2):244-248. LIU H,XU CH,CAO W M. Edge detection of multispectral image based on Clifford algebra[J]. J. Southeast University(Natural Science Edition),2012,42(2):244-248.(in Chinese) [23] 吴涌彬,李兴民. 基于Clifford代数矢量积的掌纹提取方法[J]. 计算机与现代化,2012,5:45-54. WU Y B,LI X M. Palmprint extraction method based on Clifford algebra vector product[J]. Computer Modern Agriculture,2012,5:45-54.(in Chinese) [24] 丁立军,冯浩,华亮. Clifford代数3D人脸姿态矫正方法[J]. 小型微型计算机系统,2013,34(4):906-909. DING L J,FENG H,HUA L. Clifford algebra approach for 3D face pose correction[J]. J. Chinese Computer Systems,2013,34(4):906-909.(in Chinese)
  • 加载中

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索
    Article views(3131) PDF downloads(748) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return