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Journal Articles Computers & Mathematics with Applications Year : 2023

Fast and stable schemes for non-linear osmosis filtering

Abstract

We consider a non-linear variant of the transport-diffusion osmosis model for solving a variety of imaging problems such as shadow/soft-light removal and compact data representation. The non-linear behaviour is encoded in terms of a general scalar function g with suitable properties, which allows to balance the diffusion intensity on the different regions of the image while preventing smoothing artefacts. For the proposed model, conservation properties (intensity and non-negativity) are proved and a variational interpretation is showed for specific choices of g. Upon suitable spatial discretisation, both an explicit and a semi-implicit iterative scheme are considered, for which convergence restrictions and unconditional sta- bility are proved, respectively. To validate the proposed modelling and the computational speed of the numerical schemes considered, we report several results and comparisons for the problem of shadow/light-spot removal and compact data representation, showing that artefact-free and computationally efficient results are obtained in comparison to standard linear and anisotropic models, and state-of-the art approaches.

Dates and versions

hal-04294091 , version 1 (19-11-2023)

Identifiers

Cite

Luca Calatroni, S. Morigi, S. Parisotto, G.A. Recupero. Fast and stable schemes for non-linear osmosis filtering. Computers & Mathematics with Applications, 2023, 133, pp.30-47. ⟨10.1016/j.camwa.2022.12.015⟩. ⟨hal-04294091⟩
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