Towards Morphological Image Regularization Using the Counter-Harmonic Mean
The introduction of nonlinear filters which approximate flat dilation and erosion is an issue that has been studied during the past years. In the literature, we can find works which involve the definition of robust morphological-like filters from well-known operators such as the Counter-Harmonic Mean (CHM). The main goal of this paper is to provide the reader with a morphological CHM-based regularization which simultaneously preserve both the structural information in areas of the image with high gradient and the morphological effect in the areas with low gradient. With this purpose, we introduce a suitable mathematical framework and then deal with the variational formulation which is derived from it. Practical aspects of the implementation are discussed and some results are provided to illustrate the behaviour of our approach.
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- 1.Angulo, J.: Generalised morphological image diffusion. Submitted to Computer Vision and Image UnderstandingGoogle Scholar
- 4.van den Boomgaard, R., Dorst, L.: The morphological equivalent of gaussian scale-space. In: Proc. of Gaussian Scale-Space Theory, pp. 203–220 (1997)Google Scholar
- 5.Bullen, P.S.: Handbook of Means and their Inequalities, 2nd edn. Springer (1987)Google Scholar
- 7.Darbon, J.: Total variation minimization with l 1 data fidelity as a contrast invariant filter. In: 4th International Symposium on Image and Signal Processing (ISPA), pp. 221–226 (2005)Google Scholar
- 8.Forsyth, A.R.: Calculus of Variations. Dover Publishing (1960)Google Scholar
- 9.Gelfand, I.M., Fomin, S.V.: Calculus of Variations. Dover Publishing (2000)Google Scholar
- 10.González, R.C., Woods, R.E.: Digital Image Processing. Addison-Wesley, Boston (1992)Google Scholar
- 15.Serra, J.: Image Analysis and Mathematical Morphology, vol. II: Theoretical Advances. Academic Press, London (1988)Google Scholar
- 16.Soille, P.: Morphological Image Analysis. Springer (1999)Google Scholar
- 17.van Vliet, L.J.: Robust local max-min filters by normalized power-weighted filtering. In: Proc. IEEE International Conference of Pattern Recognition, vol. 17, pp. 696–699 (2004)Google Scholar