Pseudo-morphological Image Diffusion Using the Counter-Harmonic Paradigm

Abstract : Relationships between linear and morphological scale-spaces have been considered by various previous works. The aim of this paper is to study how to generalize the diffusion-based approaches in order to introduce nonlinear filters which effects mimic morphological dilation and erosion. A methodology based on the counter-harmonic mean is adopted here. Details of numerical implementation are discussed and results are provided to illustrate the behaviour of various studied cases: isotropic, nonlinear and coherence-enhanced diffusion. We also rediscover the classical link between Gaussian scale-space and dilation/erosion scale-spaces based on quadratic structuring functions.