Signal Processing for Computer Vision
Signal Processing for Computer Vision
Multi-Dimensional Signal Processin Using an Algebraically Extended Signal Representation
AFPAC '97 Proceedings of the International Workshop on Algebraic Frames for the Perception-Action Cycle
Mustererkennung 1997, 19. DAGM-Symposium
Quaternion Gabor Filters for Local Structure Classification
ICPR '98 Proceedings of the 14th International Conference on Pattern Recognition-Volume 1 - Volume 1
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The analytic signal of a real signal is a standard concept in 1D signal processing. However, the definition of an analytic signal for real 2D signals is not possible by a straightforward extension of the 1D definition. There rather occur several different approaches in the literature. We review the main approaches and propose a new definition which is based on the recently introduced quaternionic Fourier transform. The approach most closely related to ours is the one by Hahn [8], which defines the analytic signal, which he calls complex signal, to have a single quadrant spectrum. This approach suffers form the fact that the original real signal is not reconstructible from its complex signal. We show that this drawback is cured by replacing the complex frequency domain by the quaternionic frequency domain defined by the quaternionic Fourier transform. It is shown how the new definition comprises all the older ones. Experimental results demonstrate that the new definition of the analytic signal in 2D is superior to the older approaches.