Hypercomplex Spectral Signal Representations for the Processing and Analysis of Images

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subtitleAdditional title :
  • Zugl.: Kiel, Univ., Diss, 1999
involved person(s) / institution(s)author :
datePublished :
  • August 1999
size173 Seiten

In the present work hypercomplex spectral methods of the processing and analysis of
images are introduced. The thesis is divided into three main chapters. First the quaternionic
Fourier transform (QFT) for 2D signals is presented and its main properties are
investigated. The QFT is closely related to the 2D Fourier transform and to the 2D
Hartley transform. Similarities and differences of these three transforms are investigated
with special emphasis on the symmetry properties. The Clifford Fourier transform
is presented as nD generalization of the QFT. Secondly the concept of the phase
of a signal is considered. We distinguish the global, the local and the instantaneous phase
of a signal. It is shown how these 1D concepts can be extended to 2D using the QFT.
In order to extend the concept of global phase we introduce the notion of the quaternionic
analytic signal of a real signal. Defining quaternionic Gabor filters leads to the
definition of the local quaternionic phase. The relation between signal structure and
local signal phase, which is well-known in 1D, is extended to 2D using the quaternionic
phase. In the third part two application of the theory are presented. For the image processing
tasks of disparity estimation and texture segmentation there exist approaches
which are based on the (complex) local phase. These methods are extended to the use
of the quaternionic phase. In either case the properties of the complex approaches are
preserved while new features are added by using the quaternionic phase.
Static URLhttps://www.uni-kiel.de/journals/receive/jportal_jparticle_00000190
 
URN:NBNurn:nbn:de:gbv:8:1-zs-00000190-a9
IDNumber of report :
  • TR_9903