{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,8]],"date-time":"2026-09-08T05:10:14Z","timestamp":1788844214497,"version":"build-2803163510"},"reference-count":49,"publisher":"MDPI AG","issue":"17","license":[{"start":{"date-parts":[[2026,8,31]],"date-time":"2026-08-31T00:00:00Z","timestamp":1788134400000},"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":["52308447"],"award-info":[{"award-number":["52308447"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"award":["52308447"],"award-info":[{"award-number":["52308447"]}],"id":[{"id":"https:\/\/ror.org\/01h0zpd94","id-type":"ROR","asserted-by":"publisher"}]},{"name":"Jiangsu Province Youth Science and Technology Talent Lifting Project","award":["JSTJ-2024-089"],"award-info":[{"award-number":["JSTJ-2024-089"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Structural cracks that develop within semi-rigid asphalt pavement structures may remain concealed beneath the pavement surface, making their opening widths, depths, and morphologies difficult to determine nondestructively. Although ground-penetrating radar (GPR) can localize subsurface reflective cracks, the hyperbolic anomalies in a B-scan, a two-dimensional cross-sectional radar profile obtained from sequential measurements along a survey line, do not directly represent the actual geometrical dimensions of the cracks. To solve this problem, this paper proposes a geometrical dimension detection and morphological inversion (GDMI) method, called the GPR-GDMI. The GPR-GDMI comprises two independently trained networks: GPR-GCDNet for geometrical dimensions detection and GPR-CMIGAN for morphology inversion. GPR-GCDNet utilizes trapezoidal boxes to represent crack dimensions in B-scan, enhanced by directional crack attention (DCA) for hyperbolic pattern extraction, a SetTrap Head for trapezoidal proposal generation, and multi-scale feature fusion for improved receptive field and coverage. GPR-CMIGAN is an unsupervised framework consisting of two independently designed U-Net generators and discriminators, with Gaussian noise injected to prevent mode collapse. The crack-dimension-constrained cycle-consistency loss incorporates GPR-GCDNet\u2019s detected dimensions as physical constraints in the inversion, while Wasserstein loss mitigates over-constraints and improves stability during training. On the test set, GPR-GCDNet achieved an AP of 0.84, an F1-score of 0.89, and an mIoU of 0.74 under an IoU threshold of 0.5. GPR-CMIGAN achieved a performance on MS-SSIM, LPIPS, and FID of 0.9984, 0.0566, and 2.3145, respectively. Ablation studies confirm the contribution of each component. By quantitative experiments, GPR-GDMI achieves accurate detection of crack geometrical dimensions and morphological inversion based on field-collected GPR data.<\/jats:p>","DOI":"10.3390\/s26175527","type":"journal-article","created":{"date-parts":[[2026,9,1]],"date-time":"2026-09-01T03:19:26Z","timestamp":1788232766000},"page":"5527","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["GPR-GDMI: A Geometrical Dimension Detection and Morphological Inversion Method of Structural Cracks in Semi-Rigid Asphalt Pavements with Ground Penetrating Radar"],"prefix":"10.3390","volume":"26","author":[{"given":"Haochuan","family":"Zhou","sequence":"first","affiliation":[{"name":"School of Transportation, Southeast University, Tianjin 300461, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Fanwen","family":"Meng","sequence":"additional","affiliation":[{"name":"Tianjin Port Engineering Institute Co., Ltd. of CCCC First Harbor Engineering Co., Ltd., Tianjin 300461, China"},{"name":"CCCC First Harbor Engineering Co., Ltd., Tianjin 300461, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jiaqi","family":"Li","sequence":"additional","affiliation":[{"name":"School of Transportation, Southeast University, Tianjin 300461, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Weiguang","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Transportation, Southeast University, Tianjin 300461, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6894-3521","authenticated-orcid":false,"given":"Zheng","family":"Tong","sequence":"additional","affiliation":[{"name":"School of Transportation, Southeast University, Tianjin 300461, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,8,31]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Baek, J., and Al-Qadi, I.L. (2008, January 15\u201318). Finite element modeling of reflective cracking under moving vehicular loading: Investigation of the mechanism of reflective cracking in hot-mix asphalt overlays reinforced with interlayer systems. Proceedings of the Airfield and Highway Pavements 2008: Efficient Pavements Supporting Transportation\u2019s Future, Bellevue, WA, USA.","DOI":"10.1061\/41005(329)7"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"198","DOI":"10.1080\/10298436.2014.937809","article-title":"Temperature modelling in pavements: The effect of long- and short-wave radiation","volume":"16","author":"Mammeri","year":"2015","journal-title":"Int. J. Pavement Eng."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1016\/j.sigpro.2016.05.016","article-title":"An overview of ground-penetrating radar signal processing techniques for road inspections","volume":"132","author":"Benedetto","year":"2017","journal-title":"Signal Process."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"726","DOI":"10.4236\/ijg.2017.85040","article-title":"Depth estimates of buried utility systems using the GPR method: Studies at the IAG\/USP Geophysics Test Site","volume":"8","author":"Poluha","year":"2017","journal-title":"Int. J. Geosci."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1007\/s11220-005-0004-1","article-title":"Radius estimation for cylindrical objects detected by ground penetrating radar","volume":"6","author":"Shihab","year":"2005","journal-title":"Subsurf. Sens. Technol. Appl."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1620","DOI":"10.1016\/j.cageo.2009.01.003","article-title":"A new method to simultaneously estimate the radius of a cylindrical object and the wave propagation velocity from GPR data","volume":"35","author":"Ristic","year":"2009","journal-title":"Comput. Geosci."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"104118","DOI":"10.1016\/j.jappgeo.2020.104118","article-title":"Automated detection of cracks in roads using ground penetrating radar","volume":"179","author":"Li","year":"2020","journal-title":"J. Appl. Geophys."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"102293","DOI":"10.1016\/j.ndteint.2020.102293","article-title":"An experimental and numerical approach to combine ground penetrating radar and computational modeling for the identification of early cracking in cement concrete pavements","volume":"115","author":"Rasol","year":"2020","journal-title":"NDT E Int."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Guo, S., Xu, Z., Li, X., and Zhu, P. (2022). Detection and characterization of cracks in highway pavement with the amplitude variation of GPR diffracted waves: Insights from forward modeling and field data. Remote Sens., 14.","DOI":"10.3390\/rs14040976"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Guo, S., Yu, M., Xu, Z., Yue, G., Cai, W., and Tian, P. (2025). Study on the attribute characteristics of road cracks detected by ground-penetrating radar. Sensors, 25.","DOI":"10.3390\/s25030595"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"141124","DOI":"10.1016\/j.conbuildmat.2025.141124","article-title":"Confidence level-based size estimation of internal crack using multi-trace ground penetrating radar","volume":"474","author":"Zhang","year":"2025","journal-title":"Constr. Build. Mater."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Bernatek-Jakiel, A., and Kondracka, M. (2019). Detection of soil pipes using ground penetrating radar. Remote Sens., 11.","DOI":"10.3390\/rs11161864"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Li, Z., Zeng, Z., Xiong, H., Lu, Q., An, B., Yan, J., Li, R., Xia, L., Wang, H., and Liu, K. (2023). Study on rapid inversion of soil water content from ground-penetrating radar data based on deep learning. Remote Sens., 15.","DOI":"10.3390\/rs15071906"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1016\/j.jappgeo.2013.04.006","article-title":"Clay content evaluation in soils through GPR signal processing","volume":"97","author":"Tosti","year":"2013","journal-title":"J. Appl. Geophys."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Wu, K., Desesquelles, H., Cockenpot, R., Guyard, L., Cuisiniez, V., and Lambot, S. (2022). Ground-penetrating radar full-wave inversion for soil moisture mapping in trench-hill potato fields for precise irrigation. Remote Sens., 14.","DOI":"10.3390\/rs14236046"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1016\/j.autcon.2018.08.014","article-title":"Improved characterization of underground structure defects from two-stage Bayesian inversion using crosshole GPR data","volume":"95","author":"Qin","year":"2018","journal-title":"Autom. Constr."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"466","DOI":"10.1109\/LGRS.2020.2976146","article-title":"Multiparameter full-waveform inversion of 3-D on-ground GPR with a modified total variation regularization scheme","volume":"18","author":"Wang","year":"2021","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"5935918","DOI":"10.1109\/TGRS.2024.3500588","article-title":"A synergistic GPR approach of back projection algorithm and full-wave inversion for reconstruction in unknown multilayered environments","volume":"62","author":"Xu","year":"2024","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"B401","DOI":"10.1137\/120877854","article-title":"Full waveform inversion and the truncated Newton method","volume":"35","author":"Brossier","year":"2013","journal-title":"SIAM J. Sci. Comput."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Zhang, M., Wang, C., Wan, T., Li, W., Li, X., and Shen, F. (2024, January 20\u201323). Underground pipeline depth localization based on stepped frequency continuous wave GPR. Proceedings of the 2024 IEEE International Instrumentation and Measurement Technology Conference (I2MTC), Glasgow, UK.","DOI":"10.1109\/I2MTC60896.2024.10560657"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"104443","DOI":"10.1016\/j.jconhyd.2024.104443","article-title":"Time-lapse dielectric properties monitoring of the flow cell during DNAPL contamination and remediation processes by full-waveform inversion of GPR data using particle swarm optimization: A laboratory study","volume":"267","author":"Kaplanvural","year":"2024","journal-title":"J. Contam. Hydrol."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Wang, S., Gong, X., and Han, L. (2024). Monte Carlo full-waveform inversion of cross-hole ground-penetrating radar data based on improved residual network. Remote Sens., 16.","DOI":"10.3390\/rs16020243"},{"key":"ref_23","first-page":"3500405","article-title":"Enhanced ground-penetrating radar inversion with closed-loop convolutional neural networks","volume":"22","author":"Huang","year":"2025","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"108265","DOI":"10.1016\/j.aap.2025.108265","article-title":"Enhancing autonomous driving safety in real lane-changing scenarios under friction variability: A friction-adaptive shield reinforcement learning framework","volume":"223","author":"Fang","year":"2025","journal-title":"Accid. Anal. Prev."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"105333","DOI":"10.1016\/j.jappgeo.2024.105333","article-title":"GPR-TransUNet: An improved TransUNet based on self-attention mechanism for ground penetrating radar inversion","volume":"222","author":"Ge","year":"2024","journal-title":"J. Appl. Geophys."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"139081","DOI":"10.1016\/j.conbuildmat.2024.139081","article-title":"Identification and 3D reconstruction of semi-rigid base loose distress from GPR B-scan using generative adversarial network","volume":"455","author":"Zhang","year":"2024","journal-title":"Constr. Build. Mater."},{"key":"ref_27","first-page":"30","article-title":"Crash severity prediction and interpretation for road determinants based on a hybrid method","volume":"17","author":"Cheng","year":"2025","journal-title":"J. Transp. Saf. Secur."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"5918214","DOI":"10.1109\/TGRS.2024.3410277","article-title":"Wavelet-GAN: A GPR noise and clutter removal method based on small real datasets","volume":"62","author":"Ge","year":"2024","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"e2022JB025493","DOI":"10.1029\/2022JB025493","article-title":"FWIGAN: Full-waveform inversion via a physics-informed generative adversarial network","volume":"128","author":"Yang","year":"2023","journal-title":"J. Geophys. Res. Solid Earth"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"499","DOI":"10.1007\/s11770-021-0913-3","article-title":"Seismic velocity inversion based on CNN-LSTM fusion deep neural network","volume":"18","author":"Cao","year":"2021","journal-title":"Appl. Geophys."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Qin, Y., Jiang, Z., Tian, Y., Jiang, Y., Zhao, G., Yan, J., Li, Z., Cui, Z., Zhao, Z., and Huang, L. (2024). Deep learning\u2013based inverse analysis of GPR data for landslide hazards. Front. Earth Sci., 11.","DOI":"10.3389\/feart.2023.1340484"},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Zhang, D., Wang, Z., Qin, H., Geng, T., and Pan, S. (2023). GAN-based inversion of crosshole GPR data to characterize subsurface structures. Remote Sens., 15.","DOI":"10.3390\/rs15143650"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"4505113","DOI":"10.1109\/TGRS.2024.3388480","article-title":"Application of subset full-waveform inversion to multi-offset surface ground-penetrating radar data","volume":"62","author":"Qin","year":"2024","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"5105016","DOI":"10.1109\/TGRS.2023.3275306","article-title":"3DInvNet: A deep learning-based 3D ground-penetrating radar data inversion","volume":"61","author":"Dai","year":"2023","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_35","unstructured":"Bochkovskiy, A., Wang, C.-Y., and Liao, H.-Y.M. (2020). YOLOv4: Optimal speed and accuracy of object detection. arXiv."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"He, K., Zhang, X., Ren, S., and Sun, J. (2016, January 27\u201330). Deep residual learning for image recognition. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, Las Vegas, NV, USA.","DOI":"10.1109\/CVPR.2016.90"},{"key":"ref_37","unstructured":"Ge, Z., Liu, S., Wang, F., Li, Z., and Sun, J. (2021). YOLOX: Exceeding YOLO series in 2021. arXiv."},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Zand, M., Etemad, A., and Greenspan, M. (2022, January 23\u201327). ObjectBox: From centers to boxes for anchor-free object detection. Proceedings of the European Conference on Computer Vision\u2014ECCV 2022, Tel Aviv, Israel.","DOI":"10.1007\/978-3-031-20080-9_23"},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Carion, N., Massa, F., Synnaeve, G., Usunier, N., Kirillov, A., and Zagoruyko, S. (2020, January 23\u201328). End-to-end object detection with transformers. Proceedings of the European Conference on Computer Vision\u2014ECCV 2020, Glasgow, UK.","DOI":"10.1007\/978-3-030-58452-8_13"},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Zhu, J.-Y., Park, T., Isola, P., and Efros, A.A. (2017, January 22\u201329). Unpaired image-to-image translation using cycle-consistent adversarial networks. Proceedings of the IEEE International Conference on Computer Vision, Venice, Italy.","DOI":"10.1109\/ICCV.2017.244"},{"key":"ref_41","unstructured":"Salimans, T., Goodfellow, I., Zaremba, W., Cheung, V., Radford, A., and Chen, X. (2016). Improved techniques for training GANs. Advances in Neural Information Processing Systems 29, Curran Associates."},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Tsiligkaridis, T., and Tsiligkaridis, A. (2023, January 18\u201323). Diverse Gaussian noise consistency regularization for robustness and uncertainty calibration. Proceedings of the 2023 International Joint Conference on Neural Networks (IJCNN), Gold Coast, Australia.","DOI":"10.1109\/IJCNN54540.2023.10191763"},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Karras, T., Laine, S., and Aila, T. (2019, January 15\u201320). A style-based generator architecture for generative adversarial networks. Proceedings of the IEEE\/CVF Conference on Computer Vision and Pattern Recognition, Long Beach, CA, USA.","DOI":"10.1109\/CVPR.2019.00453"},{"key":"ref_44","doi-asserted-by":"crossref","unstructured":"Qin, D., Leichner, C.H., Delakis, M., Fornoni, M., Luo, S., Yang, F., Wang, W., Banbury, C., Ye, C., and Akin, B. (October, January 29). MobileNetV4: Universal models for the mobile ecosystem. Proceedings of the European Conference on Computer Vision\u2014ECCV 2024, Milan, Italy.","DOI":"10.1007\/978-3-031-73661-2_5"},{"key":"ref_45","unstructured":"Tan, M., and Le, Q.V. (2019, January 9\u201315). EfficientNet: Rethinking model scaling for convolutional neural networks. Proceedings of the 36th International Conference on Machine Learning, Long Beach, CA, USA."},{"key":"ref_46","doi-asserted-by":"crossref","unstructured":"Zhang, X., Zhou, X., Lin, M., and Sun, J. (2018, January 18\u201323). ShuffleNet: An extremely efficient convolutional neural network for mobile devices. Proceedings of the IEEE\/CVF Conference on Computer Vision and Pattern Recognition, Salt Lake City, UT, USA.","DOI":"10.1109\/CVPR.2018.00716"},{"key":"ref_47","doi-asserted-by":"crossref","unstructured":"Wu, M., Liu, Q., and Ouyang, S. (2025). Two-stage GPR image inversion method based on multi-scale dilated convolution and hybrid attention gate. Remote Sens., 17.","DOI":"10.3390\/rs17020322"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"106140","DOI":"10.1016\/j.autcon.2025.106140","article-title":"Multi-scale GAN-driven GPR data inversion for monitoring urban road substructure","volume":"174","author":"Hou","year":"2025","journal-title":"Autom. Constr."},{"key":"ref_49","first-page":"5101309","article-title":"Ground-penetrating radar inversion via steady-state diffusion processes","volume":"63","author":"Huang","year":"2025","journal-title":"IEEE Trans. Geosci. Remote Sens."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/26\/17\/5527\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,9,8]],"date-time":"2026-09-08T04:24:48Z","timestamp":1788841488000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/26\/17\/5527"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,8,31]]},"references-count":49,"journal-issue":{"issue":"17","published-online":{"date-parts":[[2026,9]]}},"alternative-id":["s26175527"],"URL":"https:\/\/doi.org\/10.3390\/s26175527","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,8,31]]}}}