On the potential of Hermann Weyl's discrepancy norm for texture analysis

Authors Bernhard Moser
Tomáš Kazmar
Peter Haslinger
Editors M. Masoud Mohammadian
Title On the potential of Hermann Weyl's discrepancy norm for texture analysis
Booktitle Proceedings of the International Conference on Computational Intelligence for Modelling, Control and Automation (CIMCA 2008)
Type in proceedings
Publisher IEEE Computer Society
ISBN 1-4244-3329-0
Month December
Year 2008
Pages 187-191
SCCH ID# 835

The paper focuses on similarity-based texture classification and analysis techniques. A novel similarity measure is introduced in this context that takes also structural spatial information of the intensity distribution of the textured image into account which turns out to be advantageous compared to standard concepts as for example pixel-by-pixel based similarity measures like cross-correlation or statistics based measures like the Bhattacharyya coefficient. The introduced measure relies on the evaluation of partial sums and can be computed in linear time based on integral images. It is a crucial property of this measure that for integrable (non-periodic) functions it can be proven that the auto-correlation based on this measure shows monotonicity with respect to the amount of spatial shift. In this paper experimental studies with regular textures demonstrate the usefulness of applying this measure to the problem of texture classification and analysis, further its well-behavior regarding noise is outlined.