Color & grayscale image representation using multivector

Clifford Algebra (CA) and its significance in a color image representation is discussed in this paper. Multivector in 3D space explains the representation of color & grayscale image following RGB color model. The colors are defined by the color blades in multivector. Gray value of a pixel is determined by grayscale vector in multivector form. Rotor operators are applied on different shades of color to obtain a new shade. Every color used in an image is mapped in Clifford color space. The gray values are also closed in it for respective color. The multivector function representing the image follows this color space. It stores an image either in form of color or gray value. The reduction of computational time for image processing is another concern of this paper. The color blade or grayscale vector represents itself as grade-k vector.

[1]  Giorgio Vassallo,et al.  Clifford Algebra Based Edge Detector for Color Images , 2012, 2012 Sixth International Conference on Complex, Intelligent, and Software Intensive Systems.

[2]  Tony DeRose,et al.  A Coordinate Free Geometry ADT , 1997 .

[3]  Stephen Mann,et al.  Geometric Algebra: A computational framework for geometrical applications Part 1 , 2002, IEEE Computer Graphics and Applications.

[4]  A. Ray,et al.  An Analytical Approach for Sampling the RGB Color Space Considering Physiological Limitations of Human Vision and its Application for Color Image Analysis , 2000 .

[5]  Leo Dorst,et al.  Geometric algebra: A computational framework for geometrical applications ({Part II: Applications}) , 2002 .

[6]  Philippe Carré,et al.  Colour gradient using geometric algebra , 2007, 2007 15th European Signal Processing Conference.

[7]  Stephen Mann,et al.  Geometric Algebra: A Computational Framework for Geometrical Applications (Part 2) , 2002, IEEE Computer Graphics and Applications.

[8]  Stephen J. Sangwine,et al.  Colour image filters based on hypercomplex convolution , 2000 .

[9]  Jesús Angulo,et al.  Geometric algebra colour image representations and derived total orderings for morphological operators - Part I: Colour quaternions , 2010, J. Vis. Commun. Image Represent..

[10]  Peter R. Wilson,et al.  Advancement in color image processing using Geometric Algebra , 2008, 2008 16th European Signal Processing Conference.

[11]  Peter R. Wilson,et al.  Color edge detection hardware based on geometric algebra , 2006 .

[12]  Tiancheng He,et al.  An Algorithm for Removing Facial Makeup Disturbances Based on Clifford Algebras , 2007, 2007 International Conference on Computational Intelligence and Security Workshops (CISW 2007).

[13]  Valeriy Labunets.  Clifford Algebras as Unified Language for Image Processing and Pattern Recognition , 2004 .

[14]  Somasis Roy,et al.  Color Image Representation Using Multivector , 2014, 2014 5th International Conference on Intelligent Systems, Modelling and Simulation.

[15]  Leo Dorst,et al.  Geometric algebra: A computational framework for geometrical applications (Part I: Algebra) , 2002 .