, Volume 102, Issue 1, pp 247–261 | Cite as

Comparative analysis on landsat image enhancement using fractional and integral differential operators

  • Xianxian Luo
  • Taisheng Zeng
  • Wei Zeng
  • Jianlong HuangEmail author


In this paper, Landsat image enhancement based on the fractional and integral differential methods is compared. Enhancement techniques used in remote sensing are based on the traditional integral order differential mask operators, such as Sobel, Prewitt and Laplacian operators. Other techniques involve the fractional calculus and general masks using Grünwald-Letnikov with eight directions. Notably, it is crucial to perform fractional filtering of I weight (intensity or brightness) in color space of (hue, saturation, intensity or brightness) according to the filtering rule. We study the quantitative analysis of enhancement performance via the gray-scale histogram and information entropy. Finally, we demonstrated that fractional differential operator is capable of enhanced performance superior to that of the integral differential operators. The optimal fractional order for image enhancement of Landsat Thematic Mapper is 1.15, 1.4, and 0.6 based on the (3 × 3), (5 × 5), and (7 × 7) masks, respectively.


Remote sensing Image enhancement Fractional calculus Integral operators 

Mathematics Subject Classification

26A33 62H35 94A17 31A10 



The work was supported by Department of Quanzhou Science and Technology (No. 2016N057), The authors also gratefully acknowledge the support of K.C. Wong Education and DAAD (No. 91551268). The authors also acknowledge the support by Fujian Provincial Key Laboratory of Data-Intensive Computing, Fujian University Laboratory of Intelligent Computing and Information Processing, and Fujian Provincial Big Data Research Institute of Intelligent Manufacturing.


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Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2019

Authors and Affiliations

  • Xianxian Luo
    • 1
  • Taisheng Zeng
    • 1
  • Wei Zeng
    • 1
  • Jianlong Huang
    • 1
    Email author
  1. 1.Faculty of Mathematics and Computer ScienceQuanzhou Normal UniversityQuanzhouChina

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