A similarity measure for image and volumetric data based on Hermann Weyl's discrepancy

• Bernhard Moser

The paper focuses on similarity measures for translationally misaligned image and volumetric patterns. It turns out that for measures based on standard concepts like cross-correlation, Lp-norm and mutual information monotonicity with respect to the extent of misalignment can not be guarantueed. In this paper a novel distance measure based on Hermann Weyl's discrepancy concept is introduced which 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. It is shown that this monotonicity property is not influenced by the image's frequencies or other characteristics which makes this new similarity measure predestinated for similarity-based registration, tracking and segmentation.