ANALYTICAL APPROXIMATIONS FOR NONLINEAR DIFFUSION TIME IN MULTISCALE EDGE ENHANCEMENT

C. Platero, J. Sanguino, M. C. Tobar, J. M. Poncela, G. Asensio

2009

Abstract

The image simplification, noise elimination and edge enhancement steps are all fundamental to segmentation tasks. These processing techniques usually require the tuning of their control parameters; a procedure known to be incompatible with automatic segmentation. The aim of this paper is to adopt a procedure, based on nonlinear diffusion, that is capable of auto tuning by means of analytical expressions that relate diffusion times to the gradient module. The numerical method and experimental results are shown in 1D, 2D and 3D.

References

  1. Andreu, F., Caselles, V., Daz, J., and Mazn, J. (2002). Some qualitative properties for the total variation flow. Journal of Functional Analysis, 188:516-547.
  2. Buades, A., Coll, B., and Morel, J. M. (2005). A review of image denoising algorithms with a new one. Multiscale Modeling & Simulation, 4:490-530.
  3. Catte, F., Lions, P. L., Morel, J. M., and Coll, T. (1992). Image selective smoothing and edge detection by nonlinear diffusion. SIAM Journal on Applied Mathematics, 29(1):182-193.
  4. Keeling, S. L. and Stollberger, R. (2002). Nonlinear anisotropic diffusion filters for wide range edge sharpening. Inverse Problems, 18:175-190.
  5. Kichenassamy, S. (1997). The perona-malik paradox. SIAM Journal on Applied Mathematics, 57(5):1328-1342.
  6. Perona, P. and Malik, J. (1990). Scale-space and edge detection using anisotropic diffusion. IEEE Transaction on pattern analysis and machine intelligence, 12(7):629- 639.
  7. Platero, C., Poncela, J. M., Gonzalez, P., Tobar, M. C., Sanguino, J., Asensio, G., and Santos, E. (2008). Liver segmentation for hepatic lesions detection and characterisation. Biomedical Imaging: From Nano to Macro, 2008.ISBI 2008.5th IEEE International Symposium on, pages 13-16.
  8. Steidl, G., Weickert, J., Brox, T., Mrzek, P., and Welk, M. (2004). On the equivalence of soft wavelet shrinkage, total variation diffusion, total variation regularitation, and sides. SIAM Journal on Applied Mathematics, 42(2):686-713.
  9. Teboul, S., Blanc-Feraud, L., Aubert, G., and Barlaud, M. (1998). Variational approach for edge-preserving regularization using couple pdes. IEEE Trasanctions on Image Processing, 7:387-397.
  10. Tsurkov, V. I. (2000). An analytical model of edge protection under noise suppression by anisotropic diffusion. Journal of Computer and Systems Sciences International, 39(3):437-440.
  11. Weickert, J. and Benhamouda, B. (1997). A semidiscrete nonlinear scale-space theory and its relation to the perona-malik paradox. Advances in Computer Vision, pages 1-10.
  12. Weickert, J., ter Haar Romeny, B., and Viergever, M. A. (1998). Efficient and reliable schemes for nonlinear diffusion filtering. IEEE Trasanctions on Image Processing, 7(3):398-410.
  13. Welk, M., Steidl, G., and Weickert, J. (2008). Locally analytic schemes: A link between diffusion filtering and wavelet shrinkage. Applied and Computational Harmonic Analysis, 24(2):195-224.
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Paper Citation


in Harvard Style

Platero C., Sanguino J., C. Tobar M., M. Poncela J. and Asensio G. (2009). ANALYTICAL APPROXIMATIONS FOR NONLINEAR DIFFUSION TIME IN MULTISCALE EDGE ENHANCEMENT . In Proceedings of the Fourth International Conference on Computer Vision Theory and Applications - Volume 1: VISAPP, (VISIGRAPP 2009) ISBN 978-989-8111-69-2, pages 78-81. DOI: 10.5220/0001789200780081


in Bibtex Style

@conference{visapp09,
author={C. Platero and J. Sanguino and M. C. Tobar and J. M. Poncela and G. Asensio},
title={ANALYTICAL APPROXIMATIONS FOR NONLINEAR DIFFUSION TIME IN MULTISCALE EDGE ENHANCEMENT},
booktitle={Proceedings of the Fourth International Conference on Computer Vision Theory and Applications - Volume 1: VISAPP, (VISIGRAPP 2009)},
year={2009},
pages={78-81},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0001789200780081},
isbn={978-989-8111-69-2},
}


in EndNote Style

TY - CONF
JO - Proceedings of the Fourth International Conference on Computer Vision Theory and Applications - Volume 1: VISAPP, (VISIGRAPP 2009)
TI - ANALYTICAL APPROXIMATIONS FOR NONLINEAR DIFFUSION TIME IN MULTISCALE EDGE ENHANCEMENT
SN - 978-989-8111-69-2
AU - Platero C.
AU - Sanguino J.
AU - C. Tobar M.
AU - M. Poncela J.
AU - Asensio G.
PY - 2009
SP - 78
EP - 81
DO - 10.5220/0001789200780081