Skip to main content

The Fractional Harris-Laplace Feature Detector

  • Conference paper
  • First Online:
Scale Space and Variational Methods in Computer Vision (SSVM 2019)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 11603))

Abstract

Fractional calculus is an extension of integer-order differentiation and integration which explains many natural physical processes. New applications of the fractional calculus are in constant development. The current paper introduces fractional differentiation to feature detection in digital images. The Harris-Laplace feature detector is adapted to use the non-local properties of the fractional derivative to include more information about image pixel perturbations when quantifying features. Using fractional derivatives in the Harris-Laplace detector leads to higher repeatability when detecting features in grayscale images. Applications of this development are suggested.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Baleanu, D., Diethelm, K., Scalas, E., Trujillo, J.J.: Fractional Calculus: Models and Numerical Methods. World Scientific, Singapore (2012)

    Book  Google Scholar 

  2. Bradski, G.: The OpenCV library. Dr. Dobb’s J. Softw. Tools 25, 120–126 (2000)

    Google Scholar 

  3. ElAraby, W.S., Median, A.H., Ashour, M.A., Farag, I., Nassef, M.: Fractional canny edge detection for biomedical applications. In: 28th International Conference on Microelectronics (ICM), pp. 265–268. IEEE (2016)

    Google Scholar 

  4. Harris, C., Stephens, M.: A combined corner and edge detector. In: Fourth Alvey Vision Conference, vol. 15, pp. 147–151 (1988)

    Google Scholar 

  5. Liu, Y.: Remote sensing image enhancement based on fractional differential. In: International Conference on Computational and Information Sciences (ICCIS), pp. 881–884. IEEE (2010)

    Google Scholar 

  6. Lowe, D.G.: Distinctive image features from scale-invariant keypoints. Int. J. Comput. Vis. 60(2), 91–110 (2004)

    Article  Google Scholar 

  7. Mathieu, B., Melchior, P., Oustaloup, A., Ceyral, C.: Fractional differentiation for edge detection. Signal Process. 83(11), 2421–2432 (2003)

    Article  Google Scholar 

  8. Mikolajczyk, K., Schmid, C.: Scale & affine invariant interest point detectors. Int. J. Comput. Vis. 60(1), 63–86 (2004)

    Article  Google Scholar 

  9. Oldham, K., Spanier, J.: The Fractional Calculus: Theory and Applications of Differentiation and Integration to Arbitrary Order, vol. 111. Academic Press Inc., New York (1974)

    MATH  Google Scholar 

  10. Ortigueira, M.D., Machado, J.T.: What is a fractional derivative? J. Comput. Phys. 293, 4–13 (2015)

    Article  MathSciNet  Google Scholar 

  11. Ortigueira, M.D.: Riesz potential operators and inverses via fractional centred derivatives. Int. J. Math. Math. Sci. 2006, 12 (2006)

    Article  MathSciNet  Google Scholar 

  12. Pu, Y., Wang, W., Zhou, J., Wang, Y., Jia, H.: Fractional differential approach to detecting textural features of digital image and its fractional differential filter implementation. Sci. China Ser. F: Inf. Sci. 51(9), 1319–1339 (2008)

    MathSciNet  MATH  Google Scholar 

  13. Schmid, C., Mohr, R., Bauckhage, C.: Evaluation of interest point detectors. Int. J. Comput. Vis. 37(2), 151–172 (2000)

    Article  Google Scholar 

  14. Weickert, J.: Anisotropic Diffusion in Image Processing, vol. 1. Teubner, Stuttgart (1998)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Matthew Adams .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Adams, M. (2019). The Fractional Harris-Laplace Feature Detector. In: Lellmann, J., Burger, M., Modersitzki, J. (eds) Scale Space and Variational Methods in Computer Vision. SSVM 2019. Lecture Notes in Computer Science(), vol 11603. Springer, Cham. https://doi.org/10.1007/978-3-030-22368-7_1

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-22368-7_1

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-22367-0

  • Online ISBN: 978-3-030-22368-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics