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A novel method for image edge extraction based on the Hausdorff derivative

Author

Listed:
  • Qiu, Lin
  • Lin, Ji
  • Chen, Wen
  • Wang, Fajie
  • Hua, Qingsong

Abstract

Image edge extraction based on the differential equations is an important branch of image processing. This paper makes the first attempt to employ the Hausdorff derivative gradient method (HDHM) to extract the image edge. In terms of the visual quality of details, contours, edge integrity, and continuity, the original images and noisy images were extracted by using an appropriate fractal dimension. Numerical results indicate that the HDGM outperforms the Sobel operator, Canny algorithm and traditional gradient method. Moreover, it can be confirmed that the proposed method with multiple values is effective for some images on which the gray value in different parts is quite different. This work extends the Hausdorff derivative to a new field and provides an effective methodology for image edge extraction.

Suggested Citation

  • Qiu, Lin & Lin, Ji & Chen, Wen & Wang, Fajie & Hua, Qingsong, 2020. "A novel method for image edge extraction based on the Hausdorff derivative," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    • Handle: RePEc:eee:phsmap:v:540:y:2020:i:c:s0378437119317674
    DOI: 10.1016/j.physa.2019.123137
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    References listed on IDEAS

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    1. Chen, Wen & Liang, Yingjie, 2017. "New methodologies in fractional and fractal derivatives modeling," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 72-77.
    2. Weberszpil, J. & Lazo, Matheus Jatkoske & Helayël-Neto, J.A., 2015. "On a connection between a class of q-deformed algebras and the Hausdorff derivative in a medium with fractal metric," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 436(C), pages 399-404.
    3. Balankin, Alexander S. & Bory-Reyes, Juan & Shapiro, Michael, 2016. "Towards a physics on fractals: Differential vector calculus in three-dimensional continuum with fractal metric," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 444(C), pages 345-359.
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