{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,20]],"date-time":"2026-05-20T10:26:43Z","timestamp":1779272803698,"version":"3.51.4"},"reference-count":31,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2025,6,13]],"date-time":"2025-06-13T00:00:00Z","timestamp":1749772800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"EFOP-3.6.2-16-2017-00015","award":["TKP2021-NKTA"],"award-info":[{"award-number":["TKP2021-NKTA"]}]},{"name":"EFOP-3.6.2-16-2017-00015","award":["C1774095"],"award-info":[{"award-number":["C1774095"]}]},{"name":"TKP2021-NKTA-34","award":["TKP2021-NKTA"],"award-info":[{"award-number":["TKP2021-NKTA"]}]},{"name":"TKP2021-NKTA-34","award":["C1774095"],"award-info":[{"award-number":["C1774095"]}]},{"name":"Innovation Fund of Hungary","award":["TKP2021-NKTA"],"award-info":[{"award-number":["TKP2021-NKTA"]}]},{"name":"Innovation Fund of Hungary","award":["C1774095"],"award-info":[{"award-number":["C1774095"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Imaging"],"abstract":"<jats:p>The synthesis of realistic fog in images is critical for applications such as autonomous navigation, augmented reality, and visual effects. Traditional methods based on Koschmieder\u2019s law or GAN-based image translation typically assume homogeneous fog distributions and rely on oversimplified scattering models, limiting their physical realism. In this paper, we propose a physics-driven approach to fog synthesis by discretizing the Radiative Transfer Equation (RTE). Our method models spatially inhomogeneous fog and anisotropic multi-scattering, enabling the generation of structurally consistent and perceptually plausible fog effects. To evaluate performance, we construct a dataset of real-world foggy, cloudy, and sunny images and compare our results against both Koschmieder-based and GAN-based baselines. Experimental results show that our method achieves a lower Fr\u00e9chet Inception Distance (\u221210% vs. Koschmieder, \u221242% vs. CycleGAN) and a higher Pearson correlation (+4% and +21%, respectively), highlighting its superiority in both feature space and structural fidelity. These findings highlight the potential of RTE-based fog synthesis for physically consistent image augmentation under challenging visibility conditions. However, the method\u2019s practical deployment may be constrained by high memory requirements due to tensor-based computations, which must be addressed for large-scale or real-time applications.<\/jats:p>","DOI":"10.3390\/jimaging11060196","type":"journal-article","created":{"date-parts":[[2025,6,13]],"date-time":"2025-06-13T09:51:24Z","timestamp":1749808284000},"page":"196","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Generation of Synthetic Non-Homogeneous Fog by Discretized Radiative Transfer Equation"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0009-0001-1203-6890","authenticated-orcid":false,"given":"Marcell","family":"Beregi-Kovacs","sequence":"first","affiliation":[{"name":"Faculty of Informatics, University of Debrecen, 4028 Debrecen, Hungary"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4405-2040","authenticated-orcid":false,"given":"Balazs","family":"Harangi","sequence":"additional","affiliation":[{"name":"Faculty of Informatics, University of Debrecen, 4028 Debrecen, Hungary"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1718-9770","authenticated-orcid":false,"given":"Andras","family":"Hajdu","sequence":"additional","affiliation":[{"name":"Faculty of Informatics, University of Debrecen, 4028 Debrecen, Hungary"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0907-6821","authenticated-orcid":false,"given":"Gyorgy","family":"Gat","sequence":"additional","affiliation":[{"name":"Institute of Mathematics, University of Debrecen, 4028 Debrecen, Hungary"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,6,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"110313","DOI":"10.1016\/j.jcp.2021.110313","article-title":"Deterministic radiative transfer equation solver on unstructured tetrahedral meshes: Efficient assembly and preconditioning","volume":"437","author":"Jolivet","year":"2021","journal-title":"J. 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