A Similarity Measure for Image and Volumetric Data Based on Hermann Weyl´s Discrepancy

The paper focuses on similarity measures for translationally misaligned image and volumetric patterns. For measures based on standard concepts such as cross-correlation, L_p-norm, and mutual information, monotonicity with respect to the extent of misalignment cannot be guaranteed. In this paper, we introduce a novel distance measure based on Hermann Weyl´s discrepancy concept that relies on the evaluation of partial sums. In contrast to standard concepts, in this case, monotonicity, positive-definiteness, and a homogenously linear upper bound with respect to the extent of misalignment can be proven. We show that this monotonicity property is not influenced by the image´s frequencies or other characteristics, which makes this new similarity measure useful for similarity-based registration, tracking, and segmentation.