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Research Seminar - February 23, 2001
Seminar Announcement
AbstractImage processing and image analysis as linear approach to multidimensional signals is based on a signal theory which is limited by its roots in 1-D signal theory. Thus, the linear access to locally intrinsic N-D structures is hindered. The embedding of signal theory in Clifford algebra enables the development of an adequate theory of multidimensional signals and thus, tools for linearly local image analysis.We will present the way we have recently aimed at producing steerable spherical quadrature filters which have several advantages over traditional approaches. This class of filters generalizes the structure tensor. It contributes a seven-dimensional vector, called structure multivector because it is constituted by elements from |R^3 x H|. We will present the Clifford Fourier transform for N-D signals and the quaternionic Fourier transform for 2-D signals. We will show the possibilities to generalize the Hilbert transform and to compute in that way a generalized analysis signal. We also present a quaternionic Gabor filter which can respond to intrinsic 2-D signals. All these approaches are based on symmetry considerations, which result in new phase concepts. Thus, the phase of the structure multivector is of dimension 7. |
