Levellings based on spatially adaptive scale spaces using local image features

The authors propose here to overcome lacks of robustness against noise and adaptability to image features for which classical morphological operators suffer from. For doing this, they propose to deal with partial differential equations (PDEs) for generalised Cauchy problems, and they show that the proposed PDEs are equivalent to impose both robustness and adaptability to structuring functions of the corresponding sup-inf operators. This allows them to introduce spatially adaptability in levellings, and it turns out that the proposed approach constitutes a PDE formulation and a generalisation of a larger class of levellings, the so-called extended levellings, for which one of them are characterised by quasi-flat zones. They show the efficiency of the proposed approach on synthetic, grey, and colour images with different types of noises.