Image Reconstruction from an Elastically Distorted Scan
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916652804734976 |
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| author | Lopez, Adrian Mahadevan, L. |
| author_facet | Lopez, Adrian Mahadevan, L. |
| contents | We consider the problem of inverting the artifacts associated with scanning a page from an open book, i.e. "xeroxing." The process typically leads to a non-uniform combination of distortion, blurring and darkening owing to the fact that the page is bound to a stiff spine that causes the sheet of paper to be bent inhomogeneously. Complementing purely data-driven approaches, we use knowledge about the geometry and elasticity of the curved sheet to pose and solve a minimal physically consistent inverse problem to reconstruct the image. Our results rely on 3 dimensionless parameters, all of which can be measured for a scanner, and show that we can improve on the data-driven approaches. More broadly, our results might serve as a "textbook" example and a tutorial of how knowledge of generative mechanisms can speed up the solution of inverse problems. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_11584 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Image Reconstruction from an Elastically Distorted Scan Lopez, Adrian Mahadevan, L. Image and Video Processing Soft Condensed Matter We consider the problem of inverting the artifacts associated with scanning a page from an open book, i.e. "xeroxing." The process typically leads to a non-uniform combination of distortion, blurring and darkening owing to the fact that the page is bound to a stiff spine that causes the sheet of paper to be bent inhomogeneously. Complementing purely data-driven approaches, we use knowledge about the geometry and elasticity of the curved sheet to pose and solve a minimal physically consistent inverse problem to reconstruct the image. Our results rely on 3 dimensionless parameters, all of which can be measured for a scanner, and show that we can improve on the data-driven approaches. More broadly, our results might serve as a "textbook" example and a tutorial of how knowledge of generative mechanisms can speed up the solution of inverse problems. |
| title | Image Reconstruction from an Elastically Distorted Scan |
| topic | Image and Video Processing Soft Condensed Matter |
| url | https://arxiv.org/abs/2503.11584 |