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Fast Median Filtering for Phase or Orientation Data.

Martin Storath, Andreas Weinmann

    IEEE Transactions on Pattern Analysis and Machine Intelligence
    |April 20, 2017
    PubMed
    Summary
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    This study introduces fast algorithms for median filtering of circular data, improving upon existing methods. The new techniques offer efficient, robust, and edge-preserving smoothing for various data types.

    Area of Science:

    • Signal Processing
    • Image Analysis
    • Data Smoothing

    Background:

    • Median filtering is a standard technique for smoothing real-valued data due to its robustness and efficiency.
    • Data on the unit circle (e.g., phase, orientation) require specialized filtering methods.
    • Existing methods for circular data lack efficient algorithms for robust smoothing.

    Purpose of the Study:

    • To develop fast algorithms for filtering signals and images with values on the unit circle using the arc distance median.
    • To provide efficient, edge-preserving, and value-preserving smoothing for circular data.

    Main Methods:

    • Developed fast algorithms for arc distance median filtering of non-quantized and quantized circular data.
    • Algorithm for non-quantized data scales linearly with filter size.

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  • Algorithm for quantized data achieves constant complexity with respect to filter size.

    • Main Results:

    • Proposed algorithms demonstrate efficient performance comparable to classical median filters for real-valued data.
    • Achieved linear time complexity for non-quantized data and constant time complexity for quantized data.
    • Validated algorithms on real-world datasets including SAR phase images, optical flow fields, and wind direction time series.

    Conclusions:

    • The developed algorithms provide efficient and effective solutions for median filtering of circular data.
    • These methods preserve important data characteristics like edges and values.
    • The algorithms are applicable to diverse scientific and engineering fields involving circular data analysis.