Orientation fields filtering by derivates of a Gaussian

Authors:
Josef Bigun;Tomas Bigun;Kenneth Nilsson
Affiliations:
Halmstad University, Halmstad, Sweden;TietoEnator ArosTech, Linkping, Sweden;Halmstad University, Halmstad, Sweden
Venue:
SCIA'03 Proceedings of the 13th Scandinavian conference on Image analysis
Year:
2003

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Abstract

We suggest a set of complex differential operators, symmetry derivatives, that can be used for matching and pattern recognition. We present results on the invariance properties of these. These show that 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 scalars. Moreover, these functions are closed under convolution and they are invariant to the Fourier transform. The revealed properties have practical consequences for local orientation based feature extraction. This is shown by two applications: i) tracking markers in vehicle tests ii) alignment of fingerprints.