Connecting image inpainting with denoising in the homogeneous diffusion setting
While local methods for image denoising and inpainting may use similar concepts, their connections have hardly been investigated so far. The goal of this work is to establish links between the two by focusing on the most foundational scenario on both sides – the homogeneous diffusion setting. To thi...
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| Published in | Advances in continuous and discrete models Vol. 2025; no. 1; p. 74 |
|---|---|
| Main Authors | , , , , |
| Format | Journal Article |
| Language | English |
| Published |
Cham
Springer International Publishing
28.03.2025
Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
| ISSN | 2731-4235 1687-1839 2731-4235 1687-1847 |
| DOI | 10.1186/s13662-025-03935-7 |
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| Abstract | While local methods for image denoising and inpainting may use similar concepts, their connections have hardly been investigated so far. The goal of this work is to establish links between the two by focusing on the most foundational scenario on both sides – the homogeneous diffusion setting. To this end, we study a denoising by inpainting (DbI) framework. It averages multiple inpainting results from different noisy subsets. We derive equivalence results between DbI on shifted regular grids and homogeneous diffusion filtering in 1D via an explicit relation between the density and the diffusion time. We also provide an empirical extension to the 2D case. We present experiments that confirm our theory and suggest that it can also be generalized to diffusions with nonhomogeneous data or nonhomogeneous diffusivities. More generally, our work demonstrates that the hardly explored idea of data adaptivity deserves more attention – it can be as powerful as some popular models with operator adaptivity. |
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| AbstractList | While local methods for image denoising and inpainting may use similar concepts, their connections have hardly been investigated so far. The goal of this work is to establish links between the two by focusing on the most foundational scenario on both sides – the homogeneous diffusion setting. To this end, we study a denoising by inpainting (DbI) framework. It averages multiple inpainting results from different noisy subsets. We derive equivalence results between DbI on shifted regular grids and homogeneous diffusion filtering in 1D via an explicit relation between the density and the diffusion time. We also provide an empirical extension to the 2D case. We present experiments that confirm our theory and suggest that it can also be generalized to diffusions with nonhomogeneous data or nonhomogeneous diffusivities. More generally, our work demonstrates that the hardly explored idea of data adaptivity deserves more attention – it can be as powerful as some popular models with operator adaptivity. While local methods for image denoising and inpainting may use similar concepts, their connections have hardly been investigated so far. The goal of this work is to establish links between the two by focusing on the most foundational scenario on both sides - the homogeneous diffusion setting. To this end, we study a denoising by inpainting (DbI) framework. It averages multiple inpainting results from different noisy subsets. We derive equivalence results between DbI on shifted regular grids and homogeneous diffusion filtering in 1D via an explicit relation between the density and the diffusion time. We also provide an empirical extension to the 2D case. We present experiments that confirm our theory and suggest that it can also be generalized to diffusions with nonhomogeneous data or nonhomogeneous diffusivities. More generally, our work demonstrates that the hardly explored idea of data adaptivity deserves more attention - it can be as powerful as some popular models with operator adaptivity.While local methods for image denoising and inpainting may use similar concepts, their connections have hardly been investigated so far. The goal of this work is to establish links between the two by focusing on the most foundational scenario on both sides - the homogeneous diffusion setting. To this end, we study a denoising by inpainting (DbI) framework. It averages multiple inpainting results from different noisy subsets. We derive equivalence results between DbI on shifted regular grids and homogeneous diffusion filtering in 1D via an explicit relation between the density and the diffusion time. We also provide an empirical extension to the 2D case. We present experiments that confirm our theory and suggest that it can also be generalized to diffusions with nonhomogeneous data or nonhomogeneous diffusivities. More generally, our work demonstrates that the hardly explored idea of data adaptivity deserves more attention - it can be as powerful as some popular models with operator adaptivity. |
| ArticleNumber | 74 |
| Author | Adam, Robin Dirk Chizhov, Vassillen Peter, Pascal Gaa, Daniel Weickert, Joachim |
| Author_xml | – sequence: 1 givenname: Daniel orcidid: 0009-0009-8102-0487 surname: Gaa fullname: Gaa, Daniel email: gaa@mia.uni-saarland.de organization: Mathematical Image Analysis Group, Faculty of Mathematics and Computer Science, Saarland University – sequence: 2 givenname: Vassillen surname: Chizhov fullname: Chizhov, Vassillen organization: Mathematical Image Analysis Group, Faculty of Mathematics and Computer Science, Saarland University – sequence: 3 givenname: Pascal surname: Peter fullname: Peter, Pascal organization: Mathematical Image Analysis Group, Faculty of Mathematics and Computer Science, Saarland University – sequence: 4 givenname: Joachim surname: Weickert fullname: Weickert, Joachim organization: Mathematical Image Analysis Group, Faculty of Mathematics and Computer Science, Saarland University – sequence: 5 givenname: Robin Dirk surname: Adam fullname: Adam, Robin Dirk organization: Mathematical Image Analysis Group, Faculty of Mathematics and Computer Science, Saarland University |
| BackLink | https://www.ncbi.nlm.nih.gov/pubmed/40162338$$D View this record in MEDLINE/PubMed |
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| Keywords | 68U10 Inpainting Partial differential equations 94A08 Diffusion Sampling 65D18 Denoising |
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| SubjectTerms | Analysis Difference and Functional Equations Diffusion Functional Analysis Mathematics Mathematics and Statistics Noise reduction Ordinary Differential Equations Partial Differential Equations |
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| Title | Connecting image inpainting with denoising in the homogeneous diffusion setting |
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