Texture classification with SVM based on Hermann Weyl’s discrepancy norm

Autoren Bernhard Moser
Peter Haslinger
Tomáš Kazmar
TitelTexture classification with SVM based on Hermann Weyl’s discrepancy norm
BuchtitelProceedings of the 9th International Conference on Quality Control by Artificial Vision (QCAV'09)
Typin Konferenzband
SeitenID 115

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 measures based on information theoretical concepts that rely on the evaluation of histograms. Examples of such measures include mutual information, Kullback-Leibler distance and the Jensen-R´enyi divergence measure. The introduced measure relies on the evaluation of partial sums which goes back to Hermann Weyl’s concept of discrepancy. It provides a measure for assessing to which extent a given distribution of pseudo-random numbers deviates from a uniform distribution. It is a crucial property of this discrepancy concept that it is a norm in the geometric sense. Furthermore, for arbitrary 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 translational shift. It is this monotonicity property that makes this discrepancy concept appealing for high-frequent or chaotic structured textures. Moreover, this discrepancy concept can be computed in linear time based on integral images. In this paper the construction of a kernel based on this discrepancy norm is presented and discussed in the context of texture classification and analysis by employing support vector machines (SVM). Experimental studies with regular textures demonstrate the usefulness of the proposed approach.