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Storath, M.* ; Weinmann, A.

Fast median filtering for phase or orientation data.

IEEE Trans. Pattern Anal. Mach. Intell. 40, 639-652 (2018)
Postprint DOI
Open Access Green
Median filtering is among the most utilized tools for smoothing real-valued data, as it is robust, edge-preserving, value-preserving, and yet can be computed efficiently. For data living on the unit circle, such as phase data or orientation data, a filter with similar properties is desirable. For these data, there is no unique means to define a median; so we discuss various possibilities. The arc distance median turns out to be the only variant which leads to robust, edge-preserving and value-preserving smoothing. However, there are no efficient algorithms for filtering based on the arc distance median. Here, we propose fast algorithms for filtering of signals and images with values on the unit circle based on the arc distance median. For non-quantized data, we develop an algorithm that scales linearly with the filter size. The runtime of our reference implementation is only moderately higher than the Matlab implementation of the classical median filter for real-valued data. For quantized data, we obtain an algorithm of constant complexity w.r.t. the filter size. We demonstrate the performance of our algorithms for real life data sets: phase images from interferometric synthetic aperture radar, planar flow fields from optical flow, and time series of wind directions.
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Publication type Article: Journal article
Document type Scientific Article
Corresponding Author
Keywords Median Filter ; Circle-median ; Phase Data ; Orientation Data ; Circle-valued Data ; Manifold-valued Data; Total Variation Regularization; Directional-data; Constant-time; Signals; Circle
ISSN (print) / ISBN 0162-8828
e-ISSN 1939-3539
Journal IEEE Transactions on Pattern Analysis and Machine Intelligence
Quellenangaben Volume: 40, Issue: 3, Pages: 639-652 Article Number: , Supplement: ,
Publisher Institute of Electrical and Electronics Engineers (IEEE)
Publishing Place Los Alamitos
Non-patent literature Publications
Reviewing status Peer reviewed
Institute(s) Institute of Computational Biology (ICB)