Using Channel Representations in Regularization Terms - A Case Study on Image Diffusion

Christian Heinemann, Freddie Åström, George Baravdish, Kai Krajsek, Michael Felsberg, Hanno Scharr

2014

Abstract

In this work we propose a novel non-linear diffusion filtering approach for images based on their channel representation. To derive the diffusion update scheme we formulate a novel energy functional using a soft-histogram representation of image pixel neighborhoods obtained from the channel encoding. The resulting Euler-Lagrange equation yields a non-linear robust diffusion scheme with additional weighting terms stemming from the channel representation which steer the diffusion process. We apply this novel energy formulation to image reconstruction problems, showing good performance in the presence of mixtures of Gaussian and impulse-like noise, e.g. missing data. In denoising experiments of common scalar-valued images our approach performs competitive compared to other diffusion schemes as well as state-of-the-art denoising methods for the considered noise types.

References

  1. Black, M., Sapiro, G., Marimont, D., and Heeger, D. (1998). Robust anisotropic diffusion. TIP, pages 421- 432.
  2. Buades, A. and Coll, B. (2005). A non-local algorithm for image denoising. In CVPR, pages 60-65.
  3. Buades, A., Coll, B., and Morel, J.-M. (2011). Non-Local Means Denoising. Image Processing On Line, 2011.
  4. Burgeth, B., Didas, S., Florack, L., and Weickert, J. (2007). A generic approach to diffusion filtering of matrixfields. Computing, 81:179-197.
  5. Dabov, K., Foi, A., Katkovnik, V., and Egiazarian, K. (2006). Image denoising with block-matching and 3d filtering. In Electronic Imaging'06, Proc. SPIE 6064.
  6. Felsberg, M., Forssén, P.-E., and Scharr, H. (2006). Channel smoothing: Efficient robust smoothing of low-level signal features. PAMI, 28(2):209-222.
  7. Goh, A., Lenglet, C., Thompson, P. M., and Vidal, R. (2011). A nonparametric riemannian framework for processing high angular resolution diffusion images and its applications to odf-based morphometry. NeuroImage, 56(3):1181 - 1201.
  8. Gonzalez, R. C. and Woods, R. E. (2008). Digital Image Processing - 3d edition. Pearson International Edition.
  9. Granlund, G. H. (2000). An associative perception-action structure using a localized space variant information representation. In Proceedings of AFPAC.
  10. Kimmel, R., Malladi, R., and Sochen, N. A. (1998). Image processing via the Beltrami operator. In ACCV LNCS, pages 574-581.
  11. Krajsek, K., Menzel, M., Zwanger, M., and Scharr, H. (2008). Riemannian anisotropic diffusion for tensor valued images. In ECCV, LNCS, pages 326-339.
  12. Martin, D., Fowlkes, C., Tal, D., and Malik, J. (2001). A database of human segmented natural images and its application to evaluating segmentation algorithms and measuring ecological statistics. In ICCV. 416-423.
  13. Perona, P. and Malik, J. (1990). Scale-space and edge detection using anisotropic diffusion. PAMI, 12:629-639.
  14. Roth, S. and Black, M. J. (2005). Fields of experts: A framework for learning image priors. In CVPR. 860- 867.
  15. Scharr, H. (2006). Diffusion-like reconstruction schemes from linear data models. In Pattern Recognition LNCS, volume 4174, pages 51-60, Berlin. Springer.
  16. Scherzer, O. and Weickert, J. (1998). Relations between regularization and diffusion filtering. Journal of Mathematical Imaging and Vision, 12:43-63.
  17. Tomasi, C. and Manduchi, R. (1998). Bilateral filtering for gray and color images. In ICCV, pages 839-846.
  18. Tschumperlé, D. and Deriche, R. (2005). Vector-valued image regularization with pdes: A common framework for different applications. PAMI, 27(4):506-517.
  19. 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.
  20. Weickert, J. (1998). Anisotropic Diffusion In Image Processing. ECMI Series, Teubner-Verlag, Stuttgart.
  21. Zhu, S. C. and Mumford, D. (1997). Prior learning and gibbs reaction-diffusion. PAMI, 19:1236-1250.
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Paper Citation


in Harvard Style

Heinemann C., Åström F., Baravdish G., Krajsek K., Felsberg M. and Scharr H. (2014). Using Channel Representations in Regularization Terms - A Case Study on Image 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 48-55. DOI: 10.5220/0004667500480055


in Bibtex Style

@conference{visapp14,
author={Christian Heinemann and Freddie Åström and George Baravdish and Kai Krajsek and Michael Felsberg and Hanno Scharr},
title={Using Channel Representations in Regularization Terms - A Case Study on Image Diffusion},
booktitle={Proceedings of the 9th International Conference on Computer Vision Theory and Applications - Volume 1: VISAPP, (VISIGRAPP 2014)},
year={2014},
pages={48-55},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0004667500480055},
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 - Using Channel Representations in Regularization Terms - A Case Study on Image Diffusion
SN - 978-989-758-003-1
AU - Heinemann C.
AU - Åström F.
AU - Baravdish G.
AU - Krajsek K.
AU - Felsberg M.
AU - Scharr H.
PY - 2014
SP - 48
EP - 55
DO - 10.5220/0004667500480055