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Anisotropic drift-diffusion PDEs

In this project, we focus on a non-symmetric drift-diffusion equation, called osmosis for its analogies with the physical process, introduced by Weickert and collaborators in 2013. Compared to standard plain diffusion models, the osmosis model considers an additional drift term, making the process asymmetric and allowing non-constant steady-states.

Firstly, we propose an efficient numerical implementation of the osmosis equation, based on alternate directions and operator splitting techniques. We study their scale-space properties and show their efficiency in processing large Cultural Heritage images.

Secondly, the idea of using directional gradients for imaging applications is used for the generalisation of the osmosis equation to its anisotropic counter-part, which accommodate suitable directional information: this modification turns out to be useful to correct for the well-known blurring artefacts that the original osmosis model introduces when applied to the removal of (contant) shadow in images. Thus, anisotropic osmosis is applied to the shadow removal problem, where the directional interpolation on the shadow boundaries is based on the spectral decomposition of a refined Tensor Voting approach.

Numerical analysis

Shadow Removal

CH Applications

CH Applications

Journal Articles

Parisotto, Simone; Calatroni, Luca; Bugeau, Aurélie; Papadakis, Nicolas; Schönlieb, Carola-Bibiane: Variational Osmosis for Non-linear Image Fusion. In: IEEE Transactions on Image Processing, 2020. (Type: Journal Article | Abstract | Links)
Parisotto, Simone; Calatroni, Luca; Caliari, Marco; Schönlieb, Carola-Bibiane; Weickert, Joachim: Anisotropic osmosis filtering for shadow removal in images. In: Inverse Problems, 35 (5), 2019. (Type: Journal Article | Abstract | Links)


Parisotto, Simone; Calatroni, Luca; Daffara, Claudia: Digital Cultural Heritage Imaging via Osmosis Filtering. In: Mansouri, Alamin; Moataz, Abderrahim El; Nouboud, Fathallah; Mammass, Driss (Ed.): ICISP 2018: Image and Signal Processing, Lecture Notes in Computer Science, pp. 407-415, Springer, 2018. (Type: Inproceedings | Abstract | Links)
Parisotto, Simone; Calatroni, Luca; Daffara, Claudia: Mathematical osmosis imaging for multi-modal and multi-spectral applications in Cultural Heritage conservation. In: Image Processing for Art Investigation, Ghent, 2018. (Type: Inproceedings | Abstract | Links)
Calatroni, Luca; Estatico, Claudio; Garibaldi, Nicola; Parisotto, Simone: Alternating Direction Implicit (ADI) schemes for a PDE-based image osmosis model. In: Journal of Physics: Conference Series, IOP publishing, 2017. (Type: Inproceedings | Abstract | Links)

PhD Theses

Parisotto, Simone: Anisotropic variational models and PDEs for inverse imaging problems. University of Cambridge, 2019. (Type: PhD Thesis | Abstract | Links)