{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,24]],"date-time":"2025-11-24T09:33:38Z","timestamp":1763976818718,"version":"3.45.0"},"reference-count":55,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2025,11,23]],"date-time":"2025-11-23T00:00:00Z","timestamp":1763856000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61971306"],"award-info":[{"award-number":["61971306"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Information"],"abstract":"<jats:p>As an economical and effective method to enhance the resolution of remote sensing images (RSIs), remote sensing image super-resolution (RSISR) has been widely studied. However, the existing methods lack the utilization of prior information in RSIs, which leads to unsatisfactory detail representation in the reconstructed images. To address this, in this paper, we propose a digital surface model (DSM) and fractal-guided multi-directional super resolution network (DFMDN), which utilizes additional explicit priors from DSM to facilitate the reconstruction of realistic high-frequency details. Meanwhile, to more accurately identify relationships between objects in RSIs, we design a multi-directional feature extraction module: multi-directional residual-in-residual dense blocks (MDRRDB), which captures the variation from different viewing angles. Finally, to guide and constrain the network to generate reconstructed images with textures that align more closely with natural patterns, we develop a fractal mapping algorithm (FMA) and a related loss function. Our method demonstrates significant improvements in both quantitative metrics and visual quality compared to existing approaches on various datasets.<\/jats:p>","DOI":"10.3390\/info16121020","type":"journal-article","created":{"date-parts":[[2025,11,24]],"date-time":"2025-11-24T09:02:07Z","timestamp":1763974927000},"page":"1020","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Digital Surface Model and Fractal-Guided Multi-Directional Network for Remote Sensing Image Super-Resolution"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4793-3161","authenticated-orcid":false,"given":"Sumei","family":"Li","sequence":"first","affiliation":[{"name":"School of Electrical and Information Engineering, Tianjin University, Tianjin 300072, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0009-6674-9712","authenticated-orcid":false,"given":"Jiang","family":"He","sequence":"additional","affiliation":[{"name":"School of Electrical and Information Engineering, Tianjin University, Tianjin 300072, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bo","family":"Zhao","sequence":"additional","affiliation":[{"name":"Research Center of Big Data Technology, Nanhu Laboratory, Jiaxing 314000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,11,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1111\/j.1467-8306.1979.tb01235.x","article-title":"The office of naval research and geography","volume":"69","author":"Pruitt","year":"1979","journal-title":"Ann. Assoc. Am. Geogr."},{"key":"ref_2","unstructured":"Lillesand, T., Kiefer, R.W., and Chipman, J. (2015). Remote Sensing and Image Interpretation, John Wiley & Sons."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"369","DOI":"10.1126\/science.227.4685.369","article-title":"African land-cover classification using satellite data","volume":"227","author":"Tucker","year":"1985","journal-title":"Science"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1016\/j.isprsjprs.2005.02.002","article-title":"Satellite remote sensing of earthquake, volcano, flood, landslide and coastal inundation hazards","volume":"59","author":"Tralli","year":"2005","journal-title":"ISPRS J. Photogramm. Remote Sens."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1171","DOI":"10.14358\/PERS.72.10.1171","article-title":"Landsat","volume":"72","author":"Williams","year":"2006","journal-title":"Photogramm. Eng. Remote Sens."},{"key":"ref_6","unstructured":"Schowengerdt, R.A. (2006). Remote Sensing: Models and Methods for Image Processing, Elsevier."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Nakazawa, S., and Iwasaki, A. (2014, January 13\u201318). Super-resolution imaging using remote sensing platform. Proceedings of the 2014 IEEE Geoscience and Remote Sensing Symposium, Quebec City, QC, Canada.","DOI":"10.1109\/IGARSS.2014.6946851"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Vishnukumar, S., and Wilscy, M. (2016, January 18\u201319). Super-resolution for remote sensing images using content adaptive detail enhanced self examples. Proceedings of the 2016 International Conference on Circuit, Power and Computing Technologies (ICCPCT), Nagercoil, India.","DOI":"10.1109\/ICCPCT.2016.7530375"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1016\/S1566-2535(01)00036-7","article-title":"A new look at IHS-like image fusion methods","volume":"2","author":"Tu","year":"2001","journal-title":"Inf. Fusion"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"2565","DOI":"10.1109\/TGRS.2014.2361734","article-title":"A critical comparison among pansharpening algorithms","volume":"53","author":"Vivone","year":"2014","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1291","DOI":"10.1109\/TGRS.2004.825593","article-title":"Fusion of multispectral and panchromatic images using improved IHS and PCA mergers based on wavelet decomposition","volume":"42","author":"Saleta","year":"2004","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Masi, G., Cozzolino, D., Verdoliva, L., and Scarpa, G. (2016). Pansharpening by convolutional neural networks. Remote Sens., 8.","DOI":"10.3390\/rs8070594"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"883","DOI":"10.5194\/isprs-archives-XLI-B3-883-2016","article-title":"Single-image super resolution for multispectral remote sensing data using convolutional neural networks","volume":"41","author":"Liebel","year":"2016","journal-title":"Int. Arch. Photogramm. Remote Sens. Spat. Inf. Sci."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"6792","DOI":"10.1109\/TGRS.2018.2843525","article-title":"A new deep generative network for unsupervised remote sensing single-image super-resolution","volume":"56","author":"Haut","year":"2018","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1432","DOI":"10.1109\/LGRS.2019.2899576","article-title":"Remote sensing single-image superresolution based on a deep compendium model","volume":"16","author":"Haut","year":"2019","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_16","first-page":"5000905","article-title":"Remote sensing image super-resolution via multiscale enhancement network","volume":"20","author":"Wang","year":"2023","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"5183","DOI":"10.1109\/TGRS.2020.3009918","article-title":"Remote sensing image super-resolution via mixed high-order attention network","volume":"59","author":"Zhang","year":"2021","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"He, D., and Zhong, Y. (2023). Deep hierarchical pyramid network with high-frequency-aware differential architecture for super-resolution mapping. IEEE Trans. Geosci. Remote Sens., 61.","DOI":"10.1109\/TGRS.2023.3243927"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Huan, H., Li, P., Zou, N., Wang, C., and Xu, D. (2021). End-to-End Super-Resolution for Remote-Sensing Images Using an Improved Multi-Scale Residual Network. Remote Sens., 13.","DOI":"10.3390\/rs13040666"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"5799","DOI":"10.1109\/TGRS.2019.2902431","article-title":"Edge-enhanced GAN for remote sensing image super resolution","volume":"57","author":"Jiang","year":"2019","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_21","first-page":"5402114","article-title":"Local-Global Context-Aware Generative Dual-Region Adversarial Networks for Remote Sensing Scene Image Super-Resolution","volume":"62","author":"Li","year":"2024","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_22","first-page":"5633314","article-title":"RS-Mamba for Large Remote Sensing Image Dense Prediction","volume":"62","author":"Zhao","year":"2024","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"5401410","DOI":"10.1109\/TGRS.2021.3069889","article-title":"Hybrid-scale self-similarity exploitation for remote sensing image super-resolution","volume":"60","author":"Lei","year":"2022","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1109\/TPAMI.2015.2439281","article-title":"Image super-resolution using deep convolutional networks","volume":"38","author":"Dong","year":"2016","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_25","unstructured":"Kim, J., Lee, J.K., and Lee, K.M. (July, January 26). Accurate image super-resolution using very deep convolutional networks. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, Las Vegas, NV, USA."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Lim, B., Son, S., Kim, H., Nah, S., and Lee, K.M. (2017, January 21\u201326). Enhanced deep residual networks for single image super-resolution. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, Workshops, Honolulu, HI, USA.","DOI":"10.1109\/CVPRW.2017.151"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Ledig, C., Theis, L., Husz\u00e1r, F., Caballero, J., Cunningham, A., Acosta, A., Aitken, A., Tejani, A., Totz, J., and Wang, Z. (2017, January 21\u201326). Photo-realistic single image super-resolution using a generative adversarial network. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, Honolulu, HI, USA.","DOI":"10.1109\/CVPR.2017.19"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Wang, X., Yu, K., Wu, S., Gu, J., Liu, Y., Dong, C., Qiao, Y., and Change Loy, C. (2019, January 20\u201322). ESRGAN: Enhanced super-resolution generative adversarial networks. Proceedings of the European Conference on Computer Vision Workshops, Munich, Germany.","DOI":"10.1007\/978-3-030-11021-5_5"},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Zhang, Y., Li, K., Li, K., Wang, L., Zhong, B., and Fu, Y. (2018, January 8\u201314). Image super-resolution using very deep residual channel attention networks. Proceedings of the European Conference on Computer Vision, Munich, Germany.","DOI":"10.1007\/978-3-030-01234-2_18"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Dai, T., Cai, J., Zhang, Y., Xia, S.T., and Zhang, L. (2019, January 16\u201320). Second-order attention network for single image super-resolution. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, Long Beach, CA, USA.","DOI":"10.1109\/CVPR.2019.01132"},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Liang, J., Cao, J., Sun, G., Zhang, K., Van Gool, L., and Timofte, R. (2021, January 11\u201317). SwinIR: Image restoration using Swin transformer. Proceedings of the IEEE\/CVF International Conference on Computer Vision Workshops, Virtual.","DOI":"10.1109\/ICCVW54120.2021.00210"},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Liu, C., Yang, H., Fu, J., and Qian, X. (2022, January 18\u201324). Learning trajectory-aware transformer for video super-resolution. Proceedings of the IEEE\/CVF Conference on Computer Vision and Pattern Recognition, New Orleans, LA, USA.","DOI":"10.1109\/CVPR52688.2022.00560"},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Chen, X., Wang, X., Zhou, J., and Dong, C. (2023, January 18\u201322). Activating more pixels in image super-resolution transformer. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, Vancouver, BC, Canada.","DOI":"10.1109\/CVPR52729.2023.02142"},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Yekeben, Y., Cheng, S., and Du, A. (2024). CGFTNet: Content-Guided Frequency Domain Transform Network for Face Super-Resolution. Information, 15.","DOI":"10.3390\/info15120765"},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Yao, X., Pan, Y., and Wang, J. (2024). An omnidirectional image super-resolution method based on enhanced SwinIR. Information, 15.","DOI":"10.3390\/info15050248"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"1243","DOI":"10.1109\/LGRS.2017.2704122","article-title":"Super-resolution for RSIs via local\u2013global combined network","volume":"14","author":"Lei","year":"2017","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Lu, T., Wang, J., Zhang, Y., Wang, Z., and Jiang, J. (2019). Satellite image super-resolution via multi-scale residual deep neural network. Remote Sens., 11.","DOI":"10.3390\/rs11131588"},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Ma, C., Rao, Y., Cheng, Y., Chen, C., Lu, J., and Zhou, J. (2020, January 14\u201319). Structure-preserving super resolution with gradient guidance. Proceedings of the IEEE\/CVF Conference on Computer Vision and Pattern Recognition, Seattle, WA, USA.","DOI":"10.1109\/CVPR42600.2020.00779"},{"key":"ref_39","first-page":"5634514","article-title":"Hyper-Laplacian Prior for Remote Sensing Image Super-Resolution","volume":"62","author":"Zhao","year":"2024","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"5624715","DOI":"10.1109\/TGRS.2022.3180068","article-title":"Multiattention Generative Adversarial Network for Remote Sensing Image Super-Resolution","volume":"60","author":"Jia","year":"2022","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_41","first-page":"5601117","article-title":"RRSGAN: Reference-Based Super-Resolution for Remote Sensing Image","volume":"60","author":"Dong","year":"2022","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"5607221","DOI":"10.1109\/TGRS.2024.3359095","article-title":"RGTGAN: Reference-Based Gradient-Assisted Texture-Enhancement GAN for Remote Sensing Super-Resolution","volume":"62","author":"Tu","year":"2024","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_43","first-page":"5400822","article-title":"Single remote sensing image super-resolution via a generative adversarial network with stratified dense sampling and chain training","volume":"62","author":"Meng","year":"2023","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_44","doi-asserted-by":"crossref","unstructured":"Cannon, J.W., Floyd, W.J., and Parry, W.R. (2000). Crystal growth, biological cell growth, and geometry. Pattern Formation in Biology: Vision, and Dynamics, World Scientific.","DOI":"10.1142\/9789812817723_0004"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"1150","DOI":"10.1109\/ICCV.1999.790410","article-title":"Object recognition from local scale-invariant features","volume":"Volume 2","author":"Lowe","year":"1999","journal-title":"Proceedings of the Seventh IEEE International Conference on Computer Vision"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"1560","DOI":"10.1109\/TIP.2003.818038","article-title":"Fractal image denoising","volume":"12","author":"Ghazel","year":"2003","journal-title":"IEEE Trans. Image Process."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"3782","DOI":"10.1109\/TIP.2018.2826139","article-title":"Single-Image Super-Resolution Based on Rational Fractal Interpolation","volume":"27","author":"Zhang","year":"2018","journal-title":"IEEE Trans. Image Process."},{"key":"ref_48","doi-asserted-by":"crossref","unstructured":"Hua, Z., Zhang, H., and Li, J. (2019). Image Super Resolution Using Fractal Coding and Residual Network. Complexity, 2019.","DOI":"10.1155\/2019\/9419107"},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1016\/j.cag.2023.04.007","article-title":"Image super-resolution with multi-scale fractal residual attention network","volume":"113","author":"Song","year":"2023","journal-title":"Comput. Graph."},{"key":"ref_50","first-page":"293","article-title":"The ISPRS benchmark on urban object classification and 3D building reconstruction","volume":"I-3","author":"Rottensteiner","year":"2012","journal-title":"ISPRS Ann. Photogramm. Remote Sens. Spat. Inf. Sci."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"196","DOI":"10.1016\/j.isprsjprs.2022.06.008","article-title":"UNetFormer: A UNet-like transformer for efficient semantic segmentation of remote sensing urban scene imagery","volume":"190","author":"Wang","year":"2022","journal-title":"ISPRS J. Photogramm. Remote Sens."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"600","DOI":"10.1109\/TIP.2003.819861","article-title":"Image quality assessment: From error visibility to structural similarity","volume":"13","author":"Zhou","year":"2004","journal-title":"IEEE Trans. Image Process."},{"key":"ref_53","unstructured":"Kingma, D.P., and Ba, J. (2014). Adam: A method for stochastic optimization. arXiv."},{"key":"ref_54","first-page":"1","article-title":"Contextual transformation network for lightweight remote-sensing image super-resolution","volume":"60","author":"Wang","year":"2022","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"738","DOI":"10.1109\/TIP.2023.3349004","article-title":"TTST: A top-k token selective transformer for remote sensing image super-resolution","volume":"33","author":"Xiao","year":"2024","journal-title":"IEEE Trans. Image Process."}],"container-title":["Information"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2078-2489\/16\/12\/1020\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,11,24]],"date-time":"2025-11-24T09:28:45Z","timestamp":1763976525000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2078-2489\/16\/12\/1020"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,11,23]]},"references-count":55,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2025,12]]}},"alternative-id":["info16121020"],"URL":"https:\/\/doi.org\/10.3390\/info16121020","relation":{},"ISSN":["2078-2489"],"issn-type":[{"type":"electronic","value":"2078-2489"}],"subject":[],"published":{"date-parts":[[2025,11,23]]}}}