The Monogenic Scale-Space: A Unifying Approach to Phase-Based Image Processing in Scale-Space

  • Authors:

  • M. Felsberg;G. Sommer

  • Affiliations:

  • Department of Electrical Engineering, Linköping University. mfe@isy.liu.se;Institute of Computer Science and Applied Mathematics, Christian-Albrechts-University of Kiel. gs@ks.informatik.uni-kiel.de

  • Venue:
  • Journal of Mathematical Imaging and Vision
  • Year:
  • 2004

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Abstract

In this paper we address the topics of scale-space and phase-based image processing in a unifying framework. In contrast to the common opinion, the Gaussian kernel is not the unique choice for a linear scale-space. Instead, we chose the Poisson kernel since it is closely related to the monogenic signal, a 2D generalization of the analytic signal, where the Riesz transform replaces the Hilbert transform. The Riesz transform itself yields the flux of the Poisson scale-space and the combination of flux and scale-space, the monogenic scale-space, provides the local features phase-vector and attenuation in scale-space. Under certain assumptions, the latter two again form a monogenic scale-space which gives deeper insight to low-level image processing. In particular, we discuss edge detection by a new approach to phase congruency and its relation to amplitude based methods, reconstruction from local amplitude and local phase, and the evaluation of the local frequency.