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...

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Bibliographic Details
Published in:IEEE transactions on pattern analysis and machine intelligence 2011-11, Vol.33 (11), p.2321-2329
Main Author: Moser, B. A.
Format: Article
Language:English
Subjects:
Application software
Applied sciences
Artificial intelligence
Autocorrelation
Computer science
control theory
systems
discrepancy norm
Exact sciences and technology
Fluctuations
Frequency measurement
image processing
Image segmentation
Image texture analysis
Intelligence
Measurement standards
Misalignment
Mutual information
normalized cross correlation
Pattern analysis
Pattern recognition. Digital image processing. Computational geometry
Programming languages
registration
Segmentation
Similarity
similarity measure
Similarity of images
Software
Tracking
Upper bound
Volume measurement
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Summary: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.
ISSN:0162-8828
1939-3539
2160-9292
DOI:10.1109/TPAMI.2009.50