Riesz-transforms versus derivatives: on the relationship between the boundary tensor and the energy tensor

Authors:
Ullrich Köthe;Michael Felsberg
Affiliations:
Cognitive Systems Group, University of Hamburg;Computer Vision Laboratory, Linköping University
Venue:
Scale-Space'05 Proceedings of the 5th international conference on Scale Space and PDE Methods in Computer Vision
Year:
2005

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Abstract

Traditionally, quadrature filters and derivatives have been considered as alternative approaches to low-level image analysis. In this paper we show that there actually exist close connections: We define the quadrature-based boundary tensor and the derivative-based gradient energy tensor which exhibit very similar behavior. We analyse the reason for this and determine how to minimize the difference. These insights lead to a simple and very efficient integrated feature detection algorithm.