Fast median filtering for phase or orientation data

• Verfasst von: Storath, Martin [VerfasserIn]
• Verfasst von: Weinmann, Andreas [VerfasserIn]
• Titel: Fast median filtering for phase or orientation data
• Verf.angabe: Martin Storath, Andreas Weinmann
• E-Jahr: 2018
• Jahr: March 2018
• Umfang: 14 S.
• Fussnoten: Gesehen am 21.04.2020
• Titel Quelle: Enthalten in: Institute of Electrical and Electronics EngineersIEEE transactions on pattern analysis and machine intelligence
• Ort Quelle: New York, NY : IEEE, 1979
• Jahr Quelle: 2018
• Band/Heft Quelle: 40(2018), 3, Seite 639-652
• ISSN Quelle: 1939-3539
• DOI: doi:10.1109/TPAMI.2017.2692779
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: adaptive filters
• Sach-SW: arc distance median
• Sach-SW: circle-median
• Sach-SW: circle-valued data
• Sach-SW: Complexity theory
• Sach-SW: fast median filtering
• Sach-SW: filter size
• Sach-SW: Image edge detection
• Sach-SW: manifold-valued data
• Sach-SW: MATLAB
• Sach-SW: Median filter
• Sach-SW: median filtering
• Sach-SW: median filters
• Sach-SW: nonquantized data
• Sach-SW: Optical interferometry
• Sach-SW: orientation data
• Sach-SW: phase data
• Sach-SW: phase images
• Sach-SW: Robustness
• Sach-SW: Runtime
• Sach-SW: Smoothing methods
• K10plus-PPN: 1695253116

Abstract

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.