Fast and stable schemes for non-linear osmosis filtering

TL;DR

This paper introduces a non-linear osmosis filtering model for image processing that balances diffusion to prevent artifacts, proves its properties, and demonstrates its efficiency and effectiveness in shadow removal and data representation tasks.

Contribution

It develops a novel non-linear osmosis model with stability proofs and efficient schemes, improving image processing quality and speed over existing linear and anisotropic methods.

Findings

Artefact-free shadow and light spot removal

Unconditional stability of the proposed schemes

Superior computational efficiency and quality compared to standard models

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 stability 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.