Journal of Mathematical Imaging and Vision

, Volume 21, Issue 1, pp 5–26

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

Authors

  • M. Felsberg
    • Department of Electrical EngineeringLinköping University
  • G. Sommer
    • Institute of Computer Science and Applied MathematicsChristian-Albrechts-University of Kiel
Article

DOI: 10.1023/B:JMIV.0000026554.79537.35

Cite this article as:
Felsberg, M. & Sommer, G. Journal of Mathematical Imaging and Vision (2004) 21: 5. doi:10.1023/B:JMIV.0000026554.79537.35

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.

Poisson kernelscale-spacelocal phaseanalytic signalRiesz transformmonogenic signal

Copyright information

© Kluwer Academic Publishers 2004