Quaternionic Analytic Signal Using Atomic Functions

  • E. Ulises Moya-Sánchez
  • Eduardo Bayro-Corrochano
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7441)


Atomic Functions are widely used in different applications in image processing, pattern recognition, computational physics and also in the digital interpretation of signal measurements. In 1D signals, is usual to compute the phase and the magnitude of a signal using the analytic signal (the signal and its Hilbert transform using complex numbers). However, for high dimensional signals the monogenic signal (the signal and its Riesz transform) has been used to obtain the local phase and orientation with good results. The main aim of this work is to present a new way to make the computation of the Hilbert transform using the atomic function. The computation of the Hilbert transform take relevance when the phase computation is required.


Quaternion Algebra Atomic functions Image Processing 2D Phase Information 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

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

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