{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,24]],"date-time":"2026-08-24T22:43:25Z","timestamp":1787611405104,"version":"build-2736575974"},"reference-count":41,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2021,4,16]],"date-time":"2021-04-16T00:00:00Z","timestamp":1618531200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The segmentation of power lines (PLs) from aerial images is a crucial task for the safe navigation of unmanned aerial vehicles (UAVs) operating at low altitudes. Despite the advances in deep learning-based approaches for PL segmentation, these models are still vulnerable to the class imbalance present in the data. The PLs occupy only a minimal portion (1\u20135%) of the aerial images as compared to the background region (95\u201399%). Generally, this class imbalance problem is addressed via the use of PL-specific detectors in conjunction with the popular class balanced cross entropy (BBCE) loss function. However, these PL-specific detectors do not work outside their application areas and a BBCE loss requires hyperparameter tuning for class-wise weights, which is not trivial. Moreover, the BBCE loss results in low dice scores and precision values and thus, fails to achieve an optimal trade-off between dice scores, model accuracy, and precision\u2013recall values. In this work, we propose a generalized focal loss function based on the Matthews correlation coefficient (MCC) or the Phi coefficient to address the class imbalance problem in PL segmentation while utilizing a generic deep segmentation architecture. We evaluate our loss function by improving the vanilla U-Net model with an additional convolutional auxiliary classifier head (ACU-Net) for better learning and faster model convergence. The evaluation of two PL datasets, namely the Mendeley Power Line Dataset and the Power Line Dataset of Urban Scenes (PLDU), where PLs occupy around 1% and 2% of the aerial images area, respectively, reveal that our proposed loss function outperforms the popular BBCE loss by 16% in PL dice scores on both the datasets, 19% in precision and false detection rate (FDR) values for the Mendeley PL dataset and 15% in precision and FDR values for the PLDU with a minor degradation in the accuracy and recall values. Moreover, our proposed ACU-Net outperforms the baseline vanilla U-Net for the characteristic evaluation parameters in the range of 1\u201310% for both the PL datasets. Thus, our proposed loss function with ACU-Net achieves an optimal trade-off for the characteristic evaluation parameters without any bells and whistles. Our code is available at Github.<\/jats:p>","DOI":"10.3390\/s21082803","type":"journal-article","created":{"date-parts":[[2021,4,19]],"date-time":"2021-04-19T06:35:53Z","timestamp":1618814153000},"page":"2803","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":39,"title":["A Novel Focal Phi Loss for Power Line Segmentation with Auxiliary Classifier U-Net"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5860-944X","authenticated-orcid":false,"given":"Rabeea","family":"Jaffari","sequence":"first","affiliation":[{"name":"Department of Computer and Information Sciences, Universiti Teknologi PETRONAS (UTP), Seri Iskandar 32610, Malaysia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6617-8149","authenticated-orcid":false,"given":"Manzoor Ahmed","family":"Hashmani","sequence":"additional","affiliation":[{"name":"Department of Computer and Information Sciences, Universiti Teknologi PETRONAS (UTP), Seri Iskandar 32610, Malaysia"},{"name":"High Performance Cloud Computing Centre (HPC3), Universiti Teknologi PETRONAS (UTP), Seri Iskandar 32610, Malaysia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9466-2018","authenticated-orcid":false,"given":"Constantino Carlos","family":"Reyes-Aldasoro","sequence":"additional","affiliation":[{"name":"giCentre, Department of Computer Science, University of London, London EC1V 0HB, UK"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2021,4,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"677","DOI":"10.1007\/s00138-009-0206-y","article-title":"Towards automatic power line detection for a UAV surveillance system using pulse coupled neural filter and an improved Hough transform","volume":"21","author":"Li","year":"2010","journal-title":"Mach. Vis. Appl."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"9945","DOI":"10.1109\/ACCESS.2019.2891123","article-title":"Insulator detection in aerial images for transmission line inspection using single shot multibox detector","volume":"7","author":"Miao","year":"2019","journal-title":"IEEE Access"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"387","DOI":"10.1109\/LGRS.2007.895714","article-title":"Automatic extraction of power lines from aerial images","volume":"4","author":"Yan","year":"2007","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Zhang, H., Yang, W., Yu, H., Zhang, H., and Xia, G.-S. (2019). Detecting power lines in UAV images with convolutional features and structured constraints. Remote Sens., 11.","DOI":"10.3390\/rs11111342"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Zhou, G., Yuan, J., Yen, I.-L., and Bastani, F. (2016, January 25\u201328). Robust real-time UAV based power line detection and tracking. Proceedings of the 2016 IEEE International Conference on Image Processing (ICIP), Phoenix, AZ, USA.","DOI":"10.1109\/ICIP.2016.7532456"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"113895","DOI":"10.1016\/j.eswa.2020.113895","article-title":"Weakly supervised power line detection algorithm using a recursive noisy label update with refined broken line segments","volume":"165","author":"Choi","year":"2021","journal-title":"Expert Syst. Appl."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Madaan, R., Maturana, D., and Scherer, S. (2017, January 24\u201328). Wire detection using synthetic data and dilated convolutional networks for unmanned aerial vehicles. Proceedings of the 2017 IEEE\/RSJ International Conference on Intelligent Robots and Systems (IROS), Vancouver, BC, Canada.","DOI":"10.1109\/IROS.2017.8206190"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Choi, H., Koo, G., Kim, B.J., and Kim, S.W. (2019, January 2\u20134). Real-time Power Line Detection Network using Visible Light and Infrared Images. Proceedings of the 2019 International Conference on Image and Vision Computing New Zealand (IVCNZ), Dunedin, New Zealand.","DOI":"10.1109\/IVCNZ48456.2019.8961002"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1016\/j.neunet.2018.07.011","article-title":"A systematic study of the class imbalance problem in convolutional neural networks","volume":"106","author":"Buda","year":"2018","journal-title":"Neural Netw."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"427","DOI":"10.1016\/j.neunet.2007.12.031","article-title":"Training neural network classifiers for medical decision making: The effects of imbalanced datasets on classification performance","volume":"21","author":"Mazurowski","year":"2008","journal-title":"Neural Netw."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1186\/s40537-019-0192-5","article-title":"Survey on deep learning with class imbalance","volume":"6","author":"Johnson","year":"2019","journal-title":"J. Big Data"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Nguyen, V.N., Jenssen, R., and Roverso, D. (2019). Ls-net: Fast single-shot line-segment detector. arXiv.","DOI":"10.1007\/s00138-020-01138-6"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1635","DOI":"10.1109\/LGRS.2019.2903217","article-title":"Attentional information fusion networks for cross-scene power line detection","volume":"16","author":"Li","year":"2019","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"4688","DOI":"10.1007\/s10489-020-01746-9","article-title":"Fast and accurate cable detection using CNN","volume":"50","author":"Dai","year":"2020","journal-title":"Appl. Intell."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"2241","DOI":"10.1109\/TAES.2018.2883879","article-title":"Power line recognition from aerial images with deep learning","volume":"55","author":"Yetgin","year":"2018","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_16","unstructured":"Abdelfattah, R., Wang, X., and Wang, S. (December, January 30). TTPLA: An Aerial-Image Dataset for Detection and Segmentation of Transmission Towers and Power Lines. Proceedings of the Asian Conference on Computer Vision, Kyoto, Japan."},{"key":"ref_17","unstructured":"Tang, Y. (2013). Deep learning using linear support vector machines. arXiv."},{"key":"ref_18","unstructured":"Lee, C.-Y., Xie, S., Gallagher, P., Zhang, Z., and Tu, Z. (2015). Deeply-supervised nets. Artif. Intell. Stat., 562\u2013570."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Milletari, F., Navab, N., and Ahmadi, S.-A. (2016, January 25\u201328). V-net: Fully convolutional neural networks for volumetric medical image segmentation. Proceedings of the 2016 Fourth International Conference on 3D Vision (3DV), Stanford, CA, USA.","DOI":"10.1109\/3DV.2016.79"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Salehi, S.S.M., Erdogmus, D., and Gholipour, A. (2017, January 10). Tversky loss function for image segmentation using 3D fully convolutional deep networks. Proceedings of the International Workshop on Machine Learning in Medical Imaging, Quebec City, QC, Canada.","DOI":"10.1007\/978-3-319-67389-9_44"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Abraham, N., and Khan, N.M. (2019, January 8\u201311). A novel focal tversky loss function with improved attention u-net for lesion segmentation. Proceedings of the 2019 IEEE 16th International Symposium on Biomedical Imaging (ISBI 2019), Venice, Italy.","DOI":"10.1109\/ISBI.2019.8759329"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"167939","DOI":"10.1109\/ACCESS.2020.3020475","article-title":"An Improved Dice Loss for Pneumothorax Segmentation by Mining the Information of Negative Areas","volume":"8","author":"Wang","year":"2020","journal-title":"IEEE Access"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Sudre, C.H., Li, W., Vercauteren, T., Ourselin, S., and Cardoso, M.J. (2017). Generalised dice overlap as a deep learning loss function for highly unbalanced segmentations. Deep Learning in Medical Image Analysis and Multimodal Learning for Clinical Decision Support, Springer.","DOI":"10.1007\/978-3-319-67558-9_28"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Berman, M., Triki, A.R., and Blaschko, M.B. (2018, January 18\u201323). The lov\u00e1sz-softmax loss: A tractable surrogate for the optimization of the intersection-over-union measure in neural networks. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), Salt Lake City, UT, USA.","DOI":"10.1109\/CVPR.2018.00464"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Ronneberger, O., Fischer, P., and Brox, T. (2015, January 5\u20139). U-net: Convolutional networks for biomedical image segmentation. Proceedings of the International Conference on Medical Image Computing and Computer-Assisted Intervention (MICCAI), Munich, Germany.","DOI":"10.1007\/978-3-319-24574-4_28"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Abhishek, K., and Hamarneh, G. (2020). Matthews Correlation Coefficient Loss for Deep Convolutional Networks: Application to Skin Lesion Segmentation. arXiv.","DOI":"10.1109\/ISBI48211.2021.9433782"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Jadon, S. (2020, January 27\u201329). A survey of loss functions for semantic segmentation. Proceedings of the 2020 IEEE Conference on Computational Intelligence in Bioinformatics and Computational Biology (CIBCB), Via del Mar, Chile.","DOI":"10.1109\/CIBCB48159.2020.9277638"},{"key":"ref_28","unstructured":"Yi-de, M., Qing, L., and Zhi-Bai, Q. (2004, January 20\u201322). Automated image segmentation using improved PCNN model based on cross-entropy. Proceedings of the 2004 International Symposium on Intelligent Multimedia, Video and Speech Processing (ISIMP), Hong Kong, China."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Xie, S., and Tu, Z. (2015, January 7\u201313). Holistically-nested edge detection. Proceedings of the IEEE International Conference on Computer Vision (ICCV), Santiago, Chile.","DOI":"10.1109\/ICCV.2015.164"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Lin, T.-Y., Goyal, P., Girshick, R., He, K., and Doll\u00e1r, P. (2017, January 22\u201329). Focal loss for dense object detection. Proceedings of the IEEE International Conference on Computer Vision (ICCV), Venice, Italy.","DOI":"10.1109\/ICCV.2017.324"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1607","DOI":"10.1093\/bioinformatics\/btm158","article-title":"Weighted rank aggregation of cluster validation measures: A monte carlo cross-entropy approach","volume":"23","author":"Pihur","year":"2007","journal-title":"Bioinformatics"},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Ghafoorian, M., Nugteren, C., Baka, N., Booij, O., and Hofmann, M. (2018, January 8\u201314). EL-GAN: Embedding loss driven generative adversarial networks for lane detection. Proceedings of the European Conference on Computer Vision (ECCV), Munich, Germany.","DOI":"10.1007\/978-3-030-11009-3_15"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"24","DOI":"10.1016\/j.compmedimag.2019.04.005","article-title":"Combo loss: Handling input and output imbalance in multi-organ segmentation","volume":"75","author":"Taghanaki","year":"2019","journal-title":"Comput. Med Imaging Graph."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Rezatofighi, H., Tsoi, N., Gwak, J., Sadeghian, A., Reid, I., and Savarese, S. (2019, January 16\u201320). Generalized intersection over union: A metric and a loss for bounding box regression. Proceedings of the IEEE\/CVF Conference on Computer Vision and Pattern Recognition (CVPR), Long Beach, CA, USA.","DOI":"10.1109\/CVPR.2019.00075"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"442","DOI":"10.1016\/0005-2795(75)90109-9","article-title":"Comparison of the predicted and observed secondary structure of T4 phage lysozyme","volume":"405","author":"Matthews","year":"1975","journal-title":"Biochim. Biophys. Acta Protein Struct."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1016\/j.patrec.2020.03.030","article-title":"On the performance of Matthews correlation coefficient (MCC) for imbalanced dataset","volume":"136","author":"Zhu","year":"2020","journal-title":"Pattern Recognit. Lett."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"302","DOI":"10.1007\/s11263-018-1140-0","article-title":"Semantic understanding of scenes through the ade20k dataset","volume":"127","author":"Zhou","year":"2019","journal-title":"Int. J. Comput. Vis."},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Zhou, B., Zhao, H., Puig, X., Fidler, S., Barriuso, A., and Torralba, A. (2017, January 21\u201326). Scene parsing through ade20k dataset. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), Honolulu, Hawaii, USA.","DOI":"10.1109\/CVPR.2017.544"},{"key":"ref_39","unstructured":"Yetgin, \u00d6.E.G., and Gerek, \u00d6.N. (2019). Ground Truth of Powerline Dataset (Infrared-IR and Visible Light-VL), Mendeley Ltd.. [9th ed.]. Available online: http:\/\/dx.doi.org\/10.17632\/twxp8xccsw.9."},{"key":"ref_40","unstructured":"Zhang, W.Y.H., Yu, H., Zhang, H., and Xia, G. (2020, December 17). Powerline Dataset for Urban Scenes (PLDU). Available online: https:\/\/drive.google.com\/drive\/folders\/1XjoWvHm2I8Y4RVi9gEd93ZP-KryjJlm."},{"key":"ref_41","unstructured":"Contributors, M. (2021, January 20). MMSegmentation, an Open Source Semantic Segmentation Toolbox. Available online: https:\/\/github.com\/open-mmlab\/mmsegmentation."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/8\/2803\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T05:48:42Z","timestamp":1760161722000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/8\/2803"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,4,16]]},"references-count":41,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2021,4]]}},"alternative-id":["s21082803"],"URL":"https:\/\/doi.org\/10.3390\/s21082803","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,4,16]]}}}