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. © 2013 Springer-Verlag.