On the Potential of Hermann Weyl´s Discrepancy Norm for Texture Analysis

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.