Perspective Shape-from-Shading Problem: A Unified Convergence Result for Several Non-Lambertian Models
Shape-from-Shading represents the problem of computing the three-dimensional shape of a surface given a single gray-value image of it as input. In a recent paper, we showed that the introduction of an attenuation factor in the brightness equations related to various perspective Shape-from-Shading mo...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-02-01
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| Series: | Journal of Imaging |
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| Online Access: | https://www.mdpi.com/2313-433X/8/2/36 |
| _version_ | 1797479015562346496 |
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| author | Silvia Tozza |
| author_facet | Silvia Tozza |
| author_sort | Silvia Tozza |
| collection | DOAJ |
| description | Shape-from-Shading represents the problem of computing the three-dimensional shape of a surface given a single gray-value image of it as input. In a recent paper, we showed that the introduction of an attenuation factor in the brightness equations related to various perspective Shape-from-Shading models allows us to ensure the well-posedness of the corresponding differential problems. Here, we propose a unified convergence result of a numerical scheme for several non-Lambertian reflectance models. This result is interesting since it can be easily extended to other non-Lambertian models in a unified and, therefore, powerful framework. |
| first_indexed | 2024-03-09T21:39:51Z |
| format | Article |
| id | doaj.art-12d36be21c454048ada27e5cc7854faa |
| institution | Directory Open Access Journal |
| issn | 2313-433X |
| language | English |
| last_indexed | 2024-03-09T21:39:51Z |
| publishDate | 2022-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Journal of Imaging |
| spelling | doaj.art-12d36be21c454048ada27e5cc7854faa2023-11-23T20:33:18ZengMDPI AGJournal of Imaging2313-433X2022-02-01823610.3390/jimaging8020036Perspective Shape-from-Shading Problem: A Unified Convergence Result for Several Non-Lambertian ModelsSilvia Tozza0Department of Mathematics, Alma Mater Studiorum—Università di Bologna, Piazza di Porta San Donato 5, 40126 Bologna, ItalyShape-from-Shading represents the problem of computing the three-dimensional shape of a surface given a single gray-value image of it as input. In a recent paper, we showed that the introduction of an attenuation factor in the brightness equations related to various perspective Shape-from-Shading models allows us to ensure the well-posedness of the corresponding differential problems. Here, we propose a unified convergence result of a numerical scheme for several non-Lambertian reflectance models. This result is interesting since it can be easily extended to other non-Lambertian models in a unified and, therefore, powerful framework.https://www.mdpi.com/2313-433X/8/2/36Shape-from-Shadingperspective projectionconvergence resultnon-Lambertian modelsstationary Hamilton–Jacobi equations |
| spellingShingle | Silvia Tozza Perspective Shape-from-Shading Problem: A Unified Convergence Result for Several Non-Lambertian Models Journal of Imaging Shape-from-Shading perspective projection convergence result non-Lambertian models stationary Hamilton–Jacobi equations |
| title | Perspective Shape-from-Shading Problem: A Unified Convergence Result for Several Non-Lambertian Models |
| title_full | Perspective Shape-from-Shading Problem: A Unified Convergence Result for Several Non-Lambertian Models |
| title_fullStr | Perspective Shape-from-Shading Problem: A Unified Convergence Result for Several Non-Lambertian Models |
| title_full_unstemmed | Perspective Shape-from-Shading Problem: A Unified Convergence Result for Several Non-Lambertian Models |
| title_short | Perspective Shape-from-Shading Problem: A Unified Convergence Result for Several Non-Lambertian Models |
| title_sort | perspective shape from shading problem a unified convergence result for several non lambertian models |
| topic | Shape-from-Shading perspective projection convergence result non-Lambertian models stationary Hamilton–Jacobi equations |
| url | https://www.mdpi.com/2313-433X/8/2/36 |
| work_keys_str_mv | AT silviatozza perspectiveshapefromshadingproblemaunifiedconvergenceresultforseveralnonlambertianmodels |