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Recognition by symmetry derivatives and the generalized structure tensor
Halmstad University, School of Information Science, Computer and Electrical Engineering (IDE), Halmstad Embedded and Intelligent Systems Research (EIS).ORCID iD: 0000-0002-4929-1262
TietoEnator AB, Storg. 3, 58223 Linköping, Sweden.
Halmstad University, School of Information Science, Computer and Electrical Engineering (IDE), Halmstad Embedded and Intelligent Systems Research (EIS).
2004 (English)In: IEEE Transaction on Pattern Analysis and Machine Intelligence, ISSN 0162-8828, E-ISSN 1939-3539, Vol. 26, no 12, p. 1590-1605Article in journal (Refereed) Published
Abstract [en]

We suggest a set of complex differential operators that can be used to produce and filter dense orientation (tensor) fields for feature extraction, matching, and pattern recognition. We present results on the invariance properties of these operators, that we call symmetry derivatives. These show that, in contrast to ordinary derivatives, all orders of symmetry derivatives of Gaussians yield a remarkable invariance: they are obtained by replacing the original differential polynomial with the same polynomial, but using ordinary coordinates x and y corresponding to partial derivatives. Moreover, the symmetry derivatives of Gaussians are closed under the convolution operator and they are invariant to the Fourier transform. The equivalent of the structure tensor, representing and extracting orientations of curve patterns, had previously been shown to hold in harmonic coordinates in a nearly identical manner. As a result, positions, orientations, and certainties of intricate patterns, e.g., spirals, crosses, parabolic shapes, can be modeled by use of symmetry derivatives of Gaussians with greater analytical precision as well as computational efficiency. Since Gaussians and their derivatives are utilized extensively in image processing, the revealed properties have practical consequences for local orientation based feature extraction. The usefulness of these results is demonstrated by two applications:

  1. tracking cross markers in long image sequences from vehicle crash tests and
  2. alignment of noisy fingerprints.
Place, publisher, year, edition, pages
Los Alamitos, USA: IEEE Computer Society, 2004. Vol. 26, no 12, p. 1590-1605
Keywords [en]
Fourier transforms, Gaussian processes, Feature extraction, Image matching, Image sequences, Tensors
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:hh:diva-237DOI: 10.1109/TPAMI.2004.126ISI: 000224388700005PubMedID: 15573820Scopus ID: 2-s2.0-9244242591Local ID: 2082/532OAI: oai:DiVA.org:hh-237DiVA, id: diva2:237415
Note

©2004 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.

Available from: 2006-11-24 Created: 2006-11-24 Last updated: 2018-03-23Bibliographically approved

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Bigun, JosefNilsson, Kenneth

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