Quaternion Atomic Function Wavelet for Applications in Image Processing

  • E. Ulises Moya-Sánchez
  • Eduardo Bayro-Corrochano
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6419)


Atomic Functions are widely used in different applications in image processing, pattern recognition, computational physics and also in the digital interpretation of signal measurements. The main contribution of this work is to develop a Quaternionic Atomic Function Wavelet as a new quaternionic image wavelet transform. This filter have a real part and three imaginary parts (i,j,k) of the Quaternion Atomic Function, as a result we can extract more information from the image by the three phases (φ,θ, ϕ) of the quaternion representation. The experimental part shows clearly that the phase information of the image is not afected by illumination changes.


Quaternion Algebra Atomic functions Image Processing 2D Phase Information 


  1. 1.
    Kravchenko, V.F., Perez-Meana, H.M., Ponomaryov, V.I.: Adaptive digital processing of multidimensional signals with applications. MOSCOW FIZMATLIT, MOSCOW (2009)Google Scholar
  2. 2.
    Bayro-Corrochano: Geometric Computing for Wavelet Transforms, Robot Vision, Learning, Control and Action. Springer, London (2010)zbMATHGoogle Scholar
  3. 3.
    Bülow, T.: Hypercomplex Spectral Signal Representations for the Processing and Analysis of Images. Christian- Albert, Kiel University, Ph.D Thesis (1999)Google Scholar
  4. 4.
    Jähne, B.: Digital Image Processing. Springer, Germany (2002)CrossRefzbMATHGoogle Scholar
  5. 5.
    Kovesi, P.: Invariant measures of images features from phase information. University of Western Australia, PhD Thesis (1996)Google Scholar
  6. 6.
    Guyaev Yu, V., Kravchenko, V.F.: A New class of WA-Systems of Kravchenko-Rvachev Functions. MOSCOW Doklady Mathematics 75(2), 325–332 (2007)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • E. Ulises Moya-Sánchez
    • 1
  • Eduardo Bayro-Corrochano
    • 1
  1. 1.Electrical and Computer Sciences DepartmentCINVESTAV, Unidad GuadalajaraMexico

Personalised recommendations