Generalised morphological image diffusion

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 generalise the diffusion-based approaches in order to introduce nonlinear filters whose effects mimic the asymmetric behaviour of morphological dilation and erosion, as well as other evolved morphological filters. A methodology based on the counter-harmonic mean is adopted here. Details of numerical implementation are discussed and results are provided to illustrate the various studied cases: isotropic, nonlinear and coherence-enhancing diffusion. We also found a new way to derive the classical link between Gaussian scale-space and dilation/erosion scale-spaces based on quadratic structuring functions. We have included some preliminary applications of the generalised morphological diffusion to solve image processing problems such as denoising and image enhancement in the case of asymmetric bright/dark image properties.
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Nonlinear Analysis: Theory, Methods and Applications, Elsevier, 2016, 134, 〈10.1016/j.na.2015.12.015〉
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Jesus Angulo. Generalised morphological image diffusion. Nonlinear Analysis: Theory, Methods and Applications, Elsevier, 2016, 134, 〈10.1016/j.na.2015.12.015〉. 〈hal-00789162v4〉

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