Scale selection for differential operators

Tony Lindeberg

Technical report, Department of Numerical Analysis and Computing Science, Royal Institute of Technology, S-100 44 Stockholm, Sweden, Jan. 1994. (ISRN KTH NA/P--94/05--SE)

Shortened version in Proc. 8th Scandinavian Conference on Image Analysis, (Tromso, Norway), pp. 857--866, May 1993.

Abstract

Although traditional scale-space theory provides a well-founded framework for dealing with image structures at different scales, it does not directly address the problem of how to select appropriate scales for further analysis.

This paper describes a systematic approach for dealing with this problem---a heuristic principle stating that local extrema over scales of different combinations of normalized scale invariant derivatives are likely candidates to correspond to interesting structures. Support is given by theoretical considerations and experiments on real and synthetic data.

The resulting methodology lends itself naturally to two-stage algorithms; feature detection at coarse scales followed by feature localization at finer scales. Experiments on blob detection, junction detection and edge detection demonstrate that the proposed method gives intuitively reasonable results.

Keywords: scale, scale-space, scale selection, normalized derivative, differentiald invariant, feature detection, feature localization, blob detection, junction detection, edge detection multi-scale representation

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Note! Only a shortened version is available here (please contact your library or ask a secretary at our department for the printed long version of this report.

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Shortened version: (PDF 0.5Mb)

Related work: (Application to junction detection) (Application to shape from texture) (More general scale selection principle) (Scale selection for edge detection and ridge detection) (Review paper on methods for automatic scale selection) (Review paper on principles for automatic scale selection) (Earlier related work on scale selection for blob detection) (Monograph on scale-space theory)