Riesz-Transforms Versus Derivatives: On the Relationship Between the Boundary Tensor and the Energy Tensor

Ullrich Köthe, Michael Felsberg

in: R. Kimmel, N. Sochen, J. Weickert (Eds.): Scale Space and PDE Methods in Computer Vision, Proc. Scale-Space 2005, Lecture Notes in Computer Science 3459, pp. 179-191, Heidelberg: Springer, 2005. (note: this article is © Springer-Verlag)

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.

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