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

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. © Springer-Verlag Berlin Heidelberg 2005.