A generalized discrete scale-space formulation for 2-D and 3-D signals

Authors:
Ji-Young Lim;H. Siegfried Stiehl
Affiliations:
Universität Hamburg, Fachbereich Informatik, Arbeitsbereich Kognitive Systeme, Hamburg, Germany;Universität Hamburg, Fachbereich Informatik, Arbeitsbereich Kognitive Systeme, Hamburg, Germany
Venue:
Scale Space'03 Proceedings of the 4th international conference on Scale space methods in computer vision
Year:
2003

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Abstract

This paper addresses the issue of a higher dimensional discrete scale-space (DSS) formulation. The continuous linear scale-space theory provides a unique framework for visual front-end processes. In practice, a higher dimensional DSS formulation is necessary since higher dimensional discrete signals must be dealt with. In this paper, first we examine the approximation fidelity of the commonly used sampled Gaussian. Second, we propose a generalized DSS formulation for 2-D and 3-D signals. The DSS theory has been presented at first by Lindeberg. While his 1-D DSS formulation is complete, the formulation as related to the extension to higher dimensions has not been fully derived. Furthermore, we investigate the properties of our derived DSS kernels and present the results of a validation study with respect to both smoothing and differentiation performance.