Oriented Half Gaussian Kernels and Anisotropic Diffusion

Baptiste Magnier, Philippe Montesinos

Abstract

Nonlinear PDEs (partial differential equations) offer a convenient formal framework for image regularization and are at the origin of several efficient algorithms. In this paper, we present a new approach which is based (i) on a set of half Gaussian kernel filters, and (ii) a nonlinear anisotropic PDE diffusion. On one hand, half Gaussian kernels provide oriented filters whose flexibility enables to detect edges with great accuracy. On the other hand, a nonlinear anisotropic diffusion scheme offers a means to smooth images while preserving fine structures or details, e.g. lines, corners and junctions. Based on the calculus of the gradient magnitude and two diffusion directions, we construct a diffusion control function able to achieve precise image regularization. Some quantified experimental results compared to existing PDEs approaches and a discussion about the parameterizing of the method are presented.

References

  1. Alvarez, L., Lions, P.-L., and Morel, J.-M. (1992). Image selective smoothing and edge detection by nonlinear diffusion, ii. SIAM J. of Num. Anal., 29(3):845-866.
  2. Aubert, G. and Kornprobst, P. (2006). Mathematical problems in image processing: partial differential equations and the calculus of variations (second edition), volume 147. Springer-Verlag.
  3. Canny, F. (1986). A computational approach to edge detection. IEEE TPAMI, 8(6):679-698.
  4. Caselles, V. and Morel, J. (1998). Introduction to the special issue on partial differential equations and geometrydriven diffusion in image processing and analysis. IEEE TIP, 7(3):269-273.
  5. Catté, F., Lions, P., Morel, J., and Coll, T. (1992). Image selective smoothing and edge detection by nonlinear diffusion. SIAM J. of Num. Anal., pages 182-193.
  6. Deriche, R. (1992). Recursively implementing the gaussian and its derivatives. In ICIP, pages 263-267.
  7. Freeman, W. T. and Adelson, E. H. (1991). The design and use of steerable filters. IEEE TPAMI, 13:891-906.
  8. Jacob, M. and Unser, M. (2004). Design of steerable filters for feature detection using canny-like criteria. IEEE TPAMI, 26(8):1007-1019.
  9. Koenderink, J. (1984). The structure of images. Biological Cybernetics, 50(5):363-370.
  10. Kornprobst, P., Deriche, R., and Aubert, G. (1997). Nonlinear operators in image restoration. In ICVPR, pages 325-331.
  11. Magnier, B., Huanyu, X., Montesinos, P., et al. (2013a). Half gaussian kernels based shock filter for image deblurring and regularization. In VISAPP, volume 1, pages 51-60.
  12. Magnier, B. and Montesinos, P. (2013). Evolution of image regularization with pdes toward a new anisotropic smoothing based on half kernels. In IS&T/SPIE Electronic Imaging, pages 86550M-86550M. International Society for Optics and Photonics.
  13. Magnier, B., Montesinos, P., and Diep, D. (2011a). Fast Anisotropic Edge Detection Using Gamma Correction in Color Images. In IEEE 7th ISPA, pages 212-217.
  14. Magnier, B., Montesinos, P., and Diep, D. (2011b). Texture Removal in Color Images by Anisotropic Diffusion. In VISAPP, pages 40-50.
  15. Magnier, B., Montesinos, P., and Diep, D. (2012). A new region-based pde for perceptual image restoration. In VISAPP, pages 56-65.
  16. Magnier, B., Montesinos, P., Diep, D., et al. (2013b). Perceptual color image smoothing via a new region-based pde scheme. Electronic Letters on Computer Vision and Image Analysis 12 (1), 1:17-32.
  17. Michelet, F., Da Costa, J.-P., Lavialle, O., Berthoumieu, Y., Baylou, P., and Germain, C. (2007). Estimating local multiple orientations. Sig. Proc., 87(7):1655-1669.
  18. Montesinos, P. and Magnier, B. (2010). A New Perceptual Edge Detector in Color Images. In ACIVS, volume 2, pages 209-220.
  19. Mühlich, M., Friedrich, D., and Aach, T. (2012). Design and implementation of multisteerable matched filters. TPAMI, 34(2):279-291.
  20. Perona, P. (1992). Steerable-scalable kernels for edge detection and junction analysis. IMAVIS, 10(10):663-672.
  21. Perona, P. and Malik, J. (1990). Scale-space and edge detection using anisotropic diffusion. IEEE TPAMI, 12:629-639.
  22. Simoncelli, E. and Farid, H. (1996). Steerable wedge filters for local orientation analysis. IEEE TIP, 5(9):1377- 1382.
  23. Tschumperlé, D. (2006). Fast anisotropic smoothing of multi-valued images using curvature-preserving PDE's. IJCV, 68(1):65-82.
  24. Tschumperlé, D. and Deriche, R. (2005). Vector-valued image regularization with pdes: A common framework for different applications. IEEE TPAMI, pages 506- 517.
  25. Wang, Z., Bovik, A., Sheikh, H., and Simoncelli, E. (2004). Image quality assessment: From error visibility to structural similarity. IEEE TIP, 13(4):600-612.
  26. Weickert, J. (1999). Coherence-enhancing diffusion filtering. IJCV, 31(2):111-127.
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Paper Citation


in Harvard Style

Magnier B. and Montesinos P. (2014). Oriented Half Gaussian Kernels and Anisotropic Diffusion . In Proceedings of the 9th International Conference on Computer Vision Theory and Applications - Volume 1: VISAPP, (VISIGRAPP 2014) ISBN 978-989-758-003-1, pages 73-81. DOI: 10.5220/0004679500730081


in Bibtex Style

@conference{visapp14,
author={Baptiste Magnier and Philippe Montesinos},
title={Oriented Half Gaussian Kernels and Anisotropic Diffusion},
booktitle={Proceedings of the 9th International Conference on Computer Vision Theory and Applications - Volume 1: VISAPP, (VISIGRAPP 2014)},
year={2014},
pages={73-81},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0004679500730081},
isbn={978-989-758-003-1},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 9th International Conference on Computer Vision Theory and Applications - Volume 1: VISAPP, (VISIGRAPP 2014)
TI - Oriented Half Gaussian Kernels and Anisotropic Diffusion
SN - 978-989-758-003-1
AU - Magnier B.
AU - Montesinos P.
PY - 2014
SP - 73
EP - 81
DO - 10.5220/0004679500730081