| 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. |