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Finding Optimal Smoothnessnoperators for Inpainting with Bi-level Optimization


Tomasson,  Jon Arnar
International Max Planck Research School, MPI for Informatics, Max Planck Society;

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Tomasson, J. A. (2017). Finding Optimal Smoothnessnoperators for Inpainting with Bi-level Optimization. Master Thesis, Universität des Saarlandes, Saarbrücken.

Cite as: https://hdl.handle.net/21.11116/0000-0000-7641-2
Inpainting and image denoising are two problems in image processing that can be formulated as rather similar partial differential equations or PDE. In this work the effects of higher order smoothness constraints on the results of denoising and inpaintingvwere looked at. Methods from bi-level optimization were used in order to learn optimal smoothness constraints. The differences between the optimal smoothness constraints for the two problems were looked at both for a linear model and a more complex non-linear model. The results for the linear model were that inpainting favoured first order smoothness. For denoising on the other hand all of the different orders of smoothness made up a comparable part of the optimal smoothness constraint. Even with this difference the overall effect on the quality of the results was similar for both problems. For the non-linear model it was much more difficult to find a good smoothness constraint for the inpainting problem than for the denoising problem and the learned smoothness constraints looked very different.