{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,24]],"date-time":"2026-04-24T14:47:45Z","timestamp":1777042065795,"version":"3.51.4"},"reference-count":48,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2026,4,16]],"date-time":"2026-04-16T00:00:00Z","timestamp":1776297600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Information"],"abstract":"<jats:p>Arctic sea ice is a critical indicator of global climate dynamics, directly influencing maritime navigation, polar biodiversity, and offshore engineering safety. The precise mapping of diverse ice types, such as frazil ice, slush, melt ponds, and open water, is essential for environmental monitoring; however, it remains a formidable challenge in satellite remote sensing. These difficulties arise from low-contrast imagery, overlapping spectral signatures, and the subtle textural nuances characteristic of polar regions. Traditional entropy-based thresholding techniques often falter when segmenting these complex scenes, as they typically rely on Gaussian distribution assumptions that do not align with the stochastic nature of Arctic data. To address these limitations, this paper presents a novel unsupervised segmentation framework based on symmetric cross-entropy (SCE). Unlike standard directional measures, SCE provides a more robust objective function for multi-level thresholding by simultaneously maximizing intra-class cohesion and minimizing inter-class ambiguity. The proposed method uses an optimized search strategy to identify intensity levels that best delineate complex Arctic features. We conducted an extensive entropy-based comparative study that benchmarked SCE against 25 state-of-the-art entropy measures, including Shannon, Kapur, R\u00e9nyi, Tsallis, and Masi entropies. Our experimental results demonstrate that the SCE method: (i) achieves superior accuracy by consistently outperforming established models in segmentation precision and boundary definition; (ii) provides visual clarity by producing segments with significantly reduced noise, making them ideal for identifying small-scale melt ponds and slush zones; and (iii) demonstrates computational robustness by providing stable threshold values even in datasets with non-Gaussian class distributions and poor illumination. Ultimately, these improvements deliver high-quality ice feature data that enhance risk assessment, operational planning, and predictive modeling. This research marks a major step forward in Arctic sea studies and introduces a valuable new tool for wider image processing and computer vision communities.<\/jats:p>","DOI":"10.3390\/info17040373","type":"journal-article","created":{"date-parts":[[2026,4,16]],"date-time":"2026-04-16T11:35:42Z","timestamp":1776339342000},"page":"373","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Symmetric Cross-Entropy: A Novel Multi-Level Thresholding Method and Comprehensive Study of Entropy for High-Precision Arctic Ecosystem Segmentation"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7982-5202","authenticated-orcid":false,"given":"Thaweesak","family":"Trongtirakul","sequence":"first","affiliation":[{"name":"Department of Electrical Power Engineering, Rajamangala University of Technology Phra Nakhon, Bangkok 10300, Thailand"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4601-4507","authenticated-orcid":false,"given":"Sos S.","family":"Agaian","sequence":"additional","affiliation":[{"name":"Graduate Center, City University of New York, New York, NY 10016, USA"}]},{"given":"Sheli Sinha","family":"Chauhuri","sequence":"additional","affiliation":[{"name":"Department of Electronics and Telecommunication Engineering, Jadavpur University, Kolkata 700032, India"}]},{"given":"Khalifa","family":"Djemal","sequence":"additional","affiliation":[{"name":"lnformatique, BIoinformatique et Syst\u00e8mes Complexes (IBISC) Laboratory, University of Evry Paris-Saclay, 91020 Evry, France"}]},{"given":"Amir A.","family":"Feiz","sequence":"additional","affiliation":[{"name":"Laboratoire de M\u00e9canique et d\u2019Energ\u00e9tique d\u2019Evry (LMEE), University of Evry Paris-Saclay, 91020 Evry, France"}]}],"member":"1968","published-online":{"date-parts":[[2026,4,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Andersson, T., Agocs, F., Hosking, S., P\u00e9rez-Ortiz, M., Paige, B., Russell, C., Elliott, A., Law, S., Wilkinson, J., and Askenov, Y. (2020, January 1). Deep Learning for Monthly Arctic Sea Ice Concentration Prediction. Proceedings of the EGU General Assembly Conference Abstracts, Online.","DOI":"10.5194\/egusphere-egu2020-15481"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"3976","DOI":"10.1111\/gcb.14289","article-title":"Toward understanding the contribution of waterbodies to the methane emissions of a permafrost landscape on a regional scale-A case study from the Mackenzie Delta, Canada","volume":"24","author":"Kohnert","year":"2018","journal-title":"Glob. Change Biol."},{"key":"ref_3","unstructured":"Jiang, Z., Von Ness, K., Loisel, J., and Wang, Z. (2019). ArcticNet: A Deep Learning Solution to Classify Arctic Wetlands. arXiv."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"973","DOI":"10.1109\/JOE.2023.3245759","article-title":"Method for Remote Sensing Oil Spill Applications Over Thermal and Polarimetric Imagery","volume":"48","author":"Trongtirakul","year":"2023","journal-title":"IEEE J. Ocean. Eng."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Kumar, A., Jain, M., and Dev, S. (2023, January 16\u201321). Generative Augmentation for Sky\/Cloud Image Segmentation. Proceedings of the IGARSS 2023\u20142023 IEEE International Geoscience and Remote Sensing Symposium, Pasadena, CA, USA.","DOI":"10.1109\/IGARSS52108.2023.10283005"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Liu, M. (2022, January 28\u201330). Momentum Contrast Learning for Aerial Image Segmentation and Precision Agriculture Analysis. Proceedings of the 2022 International Conference on Image Processing, Computer Vision and Machine Learning (ICICML), Xi\u2019an, China.","DOI":"10.1109\/ICICML57342.2022.10009891"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"20889","DOI":"10.1109\/ACCESS.2022.3152744","article-title":"3D Urban Buildings Extraction Based on Airborne LiDAR and Photogrammetric Point Cloud Fusion According to U-Net Deep Learning Model Segmentation","volume":"10","author":"Zhang","year":"2022","journal-title":"IEEE Access"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"4572","DOI":"10.3390\/rs13224572","article-title":"Semi-Automated Semantic Segmentation of Arctic Shorelines Using Very High-Resolution Airborne Imagery, Spectral Indices and Weakly Supervised Machine Learning Approaches","volume":"13","author":"Baur","year":"2021","journal-title":"Remote Sens."},{"key":"ref_9","unstructured":"Doherty, P.H., Matthes, J.T., French, J.R., Duffy, J.A., Hood, B.K., Kane, D.L., Fisher, J.A.D., Pomeroy, J.W., Hinzman, L.D., and Stieglitz, M. (2014, January 1). Arctic-COLORS (Coastal Land Ocean Interactions in the Arctic)\u2014A NASA field campaign scoping study to examine land-ocean interactions in the Arctic. Proceedings of the AGU Fall Meeting Abstracts, San Francisco, CA, USA."},{"key":"ref_10","unstructured":"National Academies of Sciences, Engineering, and Medicine, Division on Earth and Life Studies, Board on Science and Technology for Sustainable Development, and Committee on the Decadal Survey for Earth Science and Applications from Space (2018). Thriving on Our Changing Planet: A Decadal Strategy for Earth Observation from Space, National Academies Press. [Illustrated ed.]."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1016\/j.margeo.2018.07.007","article-title":"Temporal and spatial variability in coastline response to declining sea-ice in northwest Alaska","volume":"404","author":"Farquharson","year":"2018","journal-title":"Mar. Geol."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1016\/0034-4257(94)90041-8","article-title":"The spatial and temporal effect of cloud cover on the acquisition of high quality landsat imagery in the European Arctic sector","volume":"50","author":"Marshall","year":"1994","journal-title":"Remote Sens. Environ."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"9380","DOI":"10.1109\/JSTARS.2025.3553623","article-title":"High Resolution Sea Ice Concentration Using a Sentinel-1 U-Net Ice-Water Classifier","volume":"18","author":"Rusin","year":"2025","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Jiang, M., Xu, L., and Clausi, D.A. (2022). Sea Ice\u2013Water Classification of RADARSAT-2 Imagery Based on Residual Neural Networks (ResNet) with Regional Pooling. Remote Sens., 14.","DOI":"10.3390\/rs14133025"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Chen, J., and Huang, W. (2025, January 16\u201319). GNSS-R Based Sea Ice Classification Using Track Normalized Observables. Proceedings of the OCEANS 2025 Brest, Brest, France.","DOI":"10.1109\/OCEANS58557.2025.11104660"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Yan, Q., and Huang, W. (2019). Sea Ice Remote Sensing Using GNSS-R: A Review. Remote Sens., 11.","DOI":"10.3390\/rs11212565"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Li, W., Karkamkar, V., Liu, Y., Amin, S., Janowicz, K., and Witharana, C. (2022, January 1). Real-Time GeoAI for High-Resolution Mapping and Segmentation of Arctic Permafrost Features: The Case of Ice-Wedge Polygons. Proceedings of the Proceedings of the 5th ACM SIGSPATIAL International Workshop on AI for Geographic Knowledge Discovery, Seattle, WA, USA.","DOI":"10.1145\/3557918.3565869"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Oulefki, A., Amira, A., Kurugollu, F., Trongtirakul, T., Agaian, S., Mohammed, M.K., and Alshoweky, M. (2024, January 27\u201330). Enhancing Intubation Accuracy: Advanced Tracheal Segmentation Techniques In Video Endoscopy. Proceedings of the 2024 IEEE International Conference on Image Processing (ICIP), Abu Dhabi, United Arab Emirates.","DOI":"10.1109\/ICIP51287.2024.10648237"},{"key":"ref_19","first-page":"7","article-title":"Image Segmentation Using Entropy: A Review","volume":"2","author":"Kaur","year":"2013","journal-title":"Int. J. Emerg. Sci. Eng."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"194","DOI":"10.1016\/j.kjs.2023.05.004","article-title":"On Shannon entropy and its applications","volume":"50","author":"Saraiva","year":"2023","journal-title":"Kuwait J. Sci."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"7110","DOI":"10.3934\/mbe.2021353","article-title":"Kapur\u2019s Entropy for Multilevel Thresholding Image Segmentation Based on Moth-Flame Optimization","volume":"18","author":"Wenqi","year":"2021","journal-title":"Math. Biosci. Eng."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Fuentes, J., and Gon\u00e7alves, J. (2022). R\u00e9nyi Entropy in Statistical Mechanics. Entropy, 24.","DOI":"10.3390\/e24081080"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Alomani, G., and Kayid, M. (2023). Further Properties of Tsallis Entropy and Its Application. Entropy, 25.","DOI":"10.3390\/e25020199"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Jia, H., Peng, X., Song, W., Oliva, D., Lang, C., and Li, Y. (2019). Masi Entropy for Satellite Color Image Segmentation Using Tournament-Based L\u00e9vy Multiverse Optimization Algorithm. Remote Sens., 11.","DOI":"10.3390\/rs11080942"},{"key":"ref_25","unstructured":"Kumar, N., Dixit, A., and Vijay, V. (2025). Entropy measures and their applications: A comprehensive review. arXiv."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"3647","DOI":"10.1007\/s11831-024-10093-8","article-title":"A Comprehensive survey of multi-level thresholding segmentation methods for image processing","volume":"31","author":"Amiriebrahimabadi","year":"2024","journal-title":"Arch. Comput. Methods Eng."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"146","DOI":"10.1117\/1.1631315","article-title":"Survey over image thresholding techniques and quantitative performance evaluation","volume":"13","author":"Sezgin","year":"2004","journal-title":"J. Electron. Imaging"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Binney, J. (2025). Entropy: A Very Short Introduction, Oxford University Press.","DOI":"10.1093\/actrade\/9780198901488.001.0001"},{"key":"ref_29","unstructured":"Kolmogorov, A.N. (1933). Foundations of the Theory of Probability, Julius Springer."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"S155","DOI":"10.1016\/j.ajodo.2015.03.002","article-title":"A century of influence: Part 1. Orthodontic pioneers","volume":"147","author":"Burke","year":"2015","journal-title":"Am. J. Orthod. Dentofac. Orthop."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Li, M., and Vit\u00e1nyi, P. (2019). Introduction to Kolmogorov Complexity and Its Applications, Springer.","DOI":"10.1007\/978-3-030-11298-1"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"323","DOI":"10.1016\/j.ins.2012.07.049","article-title":"Local Shannon entropy measure with statistical tests for image randomness","volume":"222","author":"Wu","year":"2013","journal-title":"Inf. Sci."},{"key":"ref_33","unstructured":"Agaian, S. (1999). Visual Morphology (Electronic Imaging \u201999), SPIE."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Benbelkacem, S., Oulefki, A., Agaian, S., Zenati-Henda, N., Trongtirakul, T., Aouam, D., Masmoudi, M., and Zemmouri, M. (2022). COVI3D: Automatic COVID-19 CT Image-Based Classification and Visualization Platform Utilizing Virtual and Augmented Reality Technologies. Diagnostics, 12.","DOI":"10.3390\/diagnostics12030649"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"210","DOI":"10.1016\/0146-664X(81)90038-1","article-title":"Entropic thresholding, a new approach","volume":"16","author":"Pun","year":"1981","journal-title":"Comput. Graph. Image Process."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1016\/0734-189X(85)90125-2","article-title":"A new method for gray-level picture thresholding using the entropy of the histogram","volume":"29","author":"Kapur","year":"1985","journal-title":"Comput. Vis. Graph. Image Process."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1016\/S0031-3203(96)00065-9","article-title":"Threshold selection using Renyi\u2019s entropy","volume":"30","author":"Sahoo","year":"1997","journal-title":"Pattern Recognit."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"174","DOI":"10.3390\/e14020174","article-title":"Special Issue: Tsallis Entropy","volume":"14","author":"Anastasiadis","year":"2012","journal-title":"Entropy"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"479","DOI":"10.1007\/BF01016429","article-title":"Possible Generalization of Boltzmann-Gibbs Statistics","volume":"52","author":"Tsallis","year":"1988","journal-title":"J. Stat. Phys."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1016\/j.physleta.2005.01.094","article-title":"A Step Beyond Tsallis and R\u00e9nyi Entropies","volume":"338","author":"Masi","year":"2005","journal-title":"Phys. Lett. A"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"2931","DOI":"10.1016\/j.sigpro.2012.05.025","article-title":"Tsallis entropy and the long-range correlation in image thresholding","volume":"92","author":"Lin","year":"2012","journal-title":"Signal Process."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"8776","DOI":"10.1109\/JSTARS.2022.3213192","article-title":"MeltPondNet: A Swin Transformer U-Net for Detection of Melt Ponds on Arctic Sea Ice","volume":"15","author":"Sudakow","year":"2022","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Salas-Robles, J.E., Biot-Monterde, V., and Antonino-Daviu, J.A. (2024). Current and Stray Flux Combined Analysis for Sparking Detection in DC Motors\/Generators Using Shannon Entropy. Entropy, 26.","DOI":"10.3390\/e26090744"},{"key":"ref_44","doi-asserted-by":"crossref","unstructured":"Zhang, K., He, M., Dong, L., and Ou, C. (2024). The Application of Tsallis Entropy Based Self-Adaptive Algorithm for Multi-Threshold Image Segmentation. Entropy, 26.","DOI":"10.20944\/preprints202408.0511.v1"},{"key":"ref_45","doi-asserted-by":"crossref","unstructured":"Nomura, R., and Yagi, H. (2024). Optimum Achievable Rates in Two Random Number Generation Problems with f-Divergences Using Smooth R\u00e9nyi Entropy. Entropy, 26.","DOI":"10.3390\/e26090766"},{"key":"ref_46","doi-asserted-by":"crossref","unstructured":"Ayunts, H., Grigoryan, A., and Agaian, S. (2024). Novel Entropy for Enhanced Thermal Imaging and Uncertainty Quantification. Entropy, 26.","DOI":"10.3390\/e26050374"},{"key":"ref_47","doi-asserted-by":"crossref","unstructured":"Ayunts, H., Agaian, S., and Grigoryan, A.M. (2026). Solar Photovoltaic System Fault Classification via Hierarchical Deep Learning with Imbalanced Multi-Class Thermal Dataset. Energies, 19.","DOI":"10.3390\/en19020462"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"107747","DOI":"10.1016\/j.patcog.2020.107747","article-title":"Automatic COVID-19 lung infected region segmentation and measurement using CT-scans images","volume":"114","author":"Oulefki","year":"2021","journal-title":"Pattern Recognit."}],"container-title":["Information"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2078-2489\/17\/4\/373\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,24]],"date-time":"2026-04-24T12:46:37Z","timestamp":1777034797000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2078-2489\/17\/4\/373"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,4,16]]},"references-count":48,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2026,4]]}},"alternative-id":["info17040373"],"URL":"https:\/\/doi.org\/10.3390\/info17040373","relation":{},"ISSN":["2078-2489"],"issn-type":[{"value":"2078-2489","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,4,16]]}}}