Nothing Special   »   [go: up one dir, main page]

Skip to main content

Derivative Half Gaussian Kernels and Shock Filter

  • Conference paper
  • First Online:
Advanced Concepts for Intelligent Vision Systems (ACIVS 2018)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 11182))

  • 1226 Accesses

Abstract

Shock filter represents an important family in the field of nonlinear Partial Differential Equations (PDEs) models for image restoration and enhancement. Commonly, the smoothed second order derivative of the image assists this type of method in the deblurring mechanism. This paper presents the advantages to insert information issued of oriented half Gaussian kernels in a shock filter process. Edge directions assist to preserve contours whereas the gradient direction allow to enhance and deblur images. For this purpose, the two edge directions are extracted by the oriented half kernels, preserving and enhancing well corner points and object contours as well as small objects. The proposed approach is compared to 7 other PDE techniques, presenting its robustness and reliability, without creating a grainy effect around edges.

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

Access this chapter

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Similar content being viewed by others

References

  1. Abdulrahman, H., Magnier, B., Montesinos, P.: Oriented asymmetric kernels for corner detection. In: IEEE EUSIPCO, pp. 778–782 (2017)

    Google Scholar 

  2. Aubert, G., Kornprobst, P.: Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations, vol. 147. Springer, New York (2006).https://doi.org/10.1007/978-0-387-44588-5

  3. Alvarez, L., Mazorra, L.: Signal and image restoration using shock filters and anisotropic diffusion. SIAM J. Numer. Anal. 31(2), 590–605 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  4. Bettahar, S., Lambert, P., Stambouli, A.B.: Anisotropic color image denoising and sharpening. In: IEEE ICIP, pp. 2669–2673 (2014)

    Google Scholar 

  5. Fu, S., Ruan, Q., Wang, W., Chen, J.: Region-based shock-diffusion equation for adaptive image enhancement. In: Huang, D.S., Li, K., Irwin, G.W. (eds.) Advances in Machine Vision, Image Processing, and Pattern Analysis. Lecture Notes in Control and Information Sciences, vol. 345, pp. 387–395. Springer, Heidelberg (2006). https://doi.org/10.1007/978-3-540-37258-5_133

    Chapter  Google Scholar 

  6. Gilboa, G., Sochen, N.A., Zeevi, Y.Y.: Regularized shock filters and complex diffusion. In: Heyden, A., Sparr, G., Nielsen, M., Johansen, P. (eds.) ECCV 2002. LNCS, vol. 2350, pp. 399–413. Springer, Heidelberg (2002). https://doi.org/10.1007/3-540-47969-4_27

    Chapter  Google Scholar 

  7. Guichard, F., Moisan, L., Morel, J.-M.: A review of PDE models in image processing and image analysis. J. Phys. IV 12(1), 137–154 (2002)

    Google Scholar 

  8. Kornprobst, P., Deriche, R., Aubert, G.: Image coupling, restoration and enhancement via PDE’s. In: IEEE ICIP, pp. 458–46 (1997)

    Google Scholar 

  9. Ludusan, C., Lavialle, O., Terebes, R., Borda, M.: Morphological sharpening and denoising using a novel shock filter model. In: Elmoataz, A., Lezoray, O., Nouboud, F., Mammass, D., Meunier, J. (eds.) ICISP 2010. LNCS, vol. 6134, pp. 19–27. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-13681-8_3

    Chapter  Google Scholar 

  10. Magnier, B.: An objective evaluation of edge detection methods based on oriented half kernels. In: Mansouri, A., El Moataz, A., Nouboud, F., Mammass, D. (eds.) ICISP 2018. LNCS, vol. 10884, pp. 80–89. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-94211-7_10

    Chapter  Google Scholar 

  11. Magnier, B.: Matlab code of “Edge detection methods based on oriented half kernels”. https://fr.mathworks.com/matlabcentral/fileexchange/66853-edge-detection-methods-based-on-oriented-half-kernels?s_tid=srchtitle

  12. Magnier, B., Montesinos, P., Diep, D.: Texture removal by pixel classification using a rotating filter. In: IEEE ICASSP, pp. 1097–1100 (2011)

    Google Scholar 

  13. Magnier, B., Montesinos, P.: Evolution of image regularization with PDEs toward a new anisotropic smoothing based on half kernels. In: IS&T/SPIE Electrical Imaging, International Society for Optics and Photonics, p. 86550M (2013)

    Google Scholar 

  14. Montesinos, P., Magnier, B.: A new perceptual edge detector in color images. In: Blanc-Talon, J., Bone, D., Philips, W., Popescu, D., Scheunders, P. (eds.) ACIVS 2010. LNCS, vol. 6474, pp. 209–220. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-17688-3_21

    Chapter  Google Scholar 

  15. Montesinos, P., Magnier, B.: Des filtres anisotropes causaux pour une diffusion non contrôlées. In: GRETSI (2017)

    Google Scholar 

  16. Osher, S., Rudin, L.I.: Feature-oriented image enhancement using shock filters. SIAM J. Numer. Anal. 27(4), 919–940 (1990). ISSN 0036–1429

    Article  MATH  Google Scholar 

  17. Perona, P., Malik, J.: Scale-space and edge detection using anisotropic diffusion. IEEE TPAMI 12, 629–639 (1990)

    Article  Google Scholar 

  18. Püspöki, Z., Martin, S., Sage, D., Unser, M.: Transforms and operators for directional bioimage analysis: a survey. In: De Vos, W., Munck, S., Timmermans, J.P. (eds.) Focus on Bio-Image Informatics, vol. 219, pp. 69–93. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-28549-8_3

    Chapter  Google Scholar 

  19. Tschumperlé, D., Deriche, R.: Diffusion PDE’s on vector-valued images: local approach and geometric viewpoint. IEEE Signal Process. Mag. 19(5), 16–25 (2002)

    Article  MATH  Google Scholar 

  20. Venkatrayappa, D., Montesinos, P., Diep, D., Magnier, B.: A novel image descriptor based on anisotropic filtering. In: Azzopardi, G., Petkov, N. (eds.) CAIP 2015. LNCS, vol. 9256, pp. 161–173. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-23192-1_14

    Chapter  Google Scholar 

  21. Wang, Z., Bovik, A., Sheikh, H., Simoncelli, E.: Image quality assessment: from error visibility to structural similarity. IEEE TIP 13(4), 600–612 (2004)

    Google Scholar 

  22. Weickert, J.: Coherence-enhancing shock filters. In: Michaelis, B., Krell, G. (eds.) DAGM 2003. LNCS, vol. 2781, pp. 1–8. Springer, Heidelberg (2003). https://doi.org/10.1007/978-3-540-45243-0_1

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Baptiste Magnier .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Magnier, B., Noblet, V., Voisin, A., Legouestre, D. (2018). Derivative Half Gaussian Kernels and Shock Filter. In: Blanc-Talon, J., Helbert, D., Philips, W., Popescu, D., Scheunders, P. (eds) Advanced Concepts for Intelligent Vision Systems. ACIVS 2018. Lecture Notes in Computer Science(), vol 11182. Springer, Cham. https://doi.org/10.1007/978-3-030-01449-0_49

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-01449-0_49

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-01448-3

  • Online ISBN: 978-3-030-01449-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics