{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,21]],"date-time":"2026-10-21T16:47:12Z","timestamp":1792601232519,"version":"4.5.0"},"reference-count":24,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2026,6,12]],"date-time":"2026-06-12T00:00:00Z","timestamp":1781222400000},"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":"crossref","award":["62405131"],"award-info":[{"award-number":["62405131"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"award":["62405131"],"award-info":[{"award-number":["62405131"]}],"id":[{"id":"https:\/\/ror.org\/01h0zpd94","id-type":"ROR","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Head-mounted eye-tracking systems play a critical role in virtual reality, human\u2013computer interaction, and clinical applications, yet achieving both high angular accuracy and precise 3D gaze position estimation with low-cost hardware remains challenging. This paper proposes a lightweight, training-free geometric 3D gaze tracking framework for binocular 3D gaze tracking using consumer-grade hardware, which leverages stereo geometric triangulation and a simplified physiological eye model to achieve robust 3D gaze estimation, requiring only standard infrared cameras and dichroic mirrors without additional specialized hardware. The method was evaluated in controlled indoor conditions with 30 participants, where it achieved an angular error ranging from 1.1\u00b0 to 2.82\u00b0 and a 3D gaze position error below 13.24 mm. Compared to two state-of-the-art academic non-deep-learning methods, the proposed framework delivers competitive angular accuracy while significantly reducing 3D position error, outperforming the baselines by 34% to 56% in depth estimation precision. These results demonstrates that the proposed geometric framework is a practical and effective solution for high-precision 3D gaze tracking on low-cost hardware, suitable for both research and consumer applications.<\/jats:p>","DOI":"10.3390\/s26123741","type":"journal-article","created":{"date-parts":[[2026,6,12]],"date-time":"2026-06-12T06:53:10Z","timestamp":1781247190000},"page":"3741","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Lightweight Geometric Framework for High-Precision 3D Gaze Tracking Based on Infrared Image Processing"],"prefix":"10.3390","volume":"26","author":[{"ORCID":"https:\/\/orcid.org\/0009-0000-9444-9500","authenticated-orcid":false,"given":"Jiawei","family":"Shen","sequence":"first","affiliation":[{"name":"School of Electronic Science and Engineering, Nanjing University, Nanjing 210023, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Pengxiang","family":"Dong","sequence":"additional","affiliation":[{"name":"School of Electronic Science and Engineering, Nanjing University, Nanjing 210023, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Beichen","family":"Hu","sequence":"additional","affiliation":[{"name":"School of Electronic Science and Engineering, Nanjing University, Nanjing 210023, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yuanqing","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Electronic Science and Engineering, Nanjing University, Nanjing 210023, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,6,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"478","DOI":"10.1109\/TPAMI.2009.30","article-title":"In the eye of the beholder: A survey of models for eyes and gaze","volume":"32","author":"Hansen","year":"2010","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1007\/s11263-017-1014-x","article-title":"Auto-calibrated gaze estimation using human gaze patterns","volume":"124","author":"Alnajar","year":"2017","journal-title":"Int. J. Comput. Vis."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"4553","DOI":"10.1038\/s41467-020-18360-5","article-title":"Accelerating eye movement research via accurate and affordable smartphone eye tracking","volume":"11","author":"Valliappan","year":"2020","journal-title":"Nat. Commun."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Krafka, K., Khosla, A., Kellnhofer, P., Kannan, H., Bhandarkar, S., Matusik, W., and Torralba, A. (2016, January 27\u201330). Eye tracking for everyone. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, Las Vegas, NV, USA.","DOI":"10.1109\/CVPR.2016.239"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"13292","DOI":"10.1109\/TMC.2024.3425928","article-title":"Real-time gaze tracking via head-eye cues on head mounted devices","volume":"23","author":"Li","year":"2024","journal-title":"IEEE Trans. Mob. Comput."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Lee, K.F., Chen, Y.L., Yu, C.W., Chin, K.Y., and Wu, C.H. (2020). Gaze tracking and point estimation using low-cost head-mounted devices. Sensors, 20.","DOI":"10.3390\/s20071917"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Chen, L., Li, Y., Bai, X., Wang, X., Hu, Y., and Song, M. (2022, January 17\u201321). Real-time gaze tracking with head-eye coordination for head-mounted displays. Proceedings of the 2022 IEEE International Symposium on Mixed and Augmented Reality, Singapore.","DOI":"10.1109\/ISMAR55827.2022.00022"},{"key":"ref_8","unstructured":"Kagemoto, T., and Takemura, K. (November, January 29). Event-based pupil tracking using bright and dark pupil effect. Proceedings of the Adjunct Proceedings of the 36th Annual ACM Symposium on User Interface Software and Technology, San Francisco, CA, USA."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"768","DOI":"10.1109\/TIP.2019.2934352","article-title":"Arc-support line segments revisited: An efficient high-quality ellipse detection","volume":"29","author":"Lu","year":"2020","journal-title":"IEEE Trans. Image Process."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Lu, C., Chakravarthula, P., Liu, K., Chen, H., and Li, R. (2022, January 17\u201321). Neural 3D gaze: 3D pupil localization and gaze tracking based on anatomical eye model and neural refraction correction. Proceedings of the 2022 IEEE International Symposium on Mixed and Augmented reality (ISMAR), Vancouver, BC, Canada.","DOI":"10.1109\/ISMAR55827.2022.00053"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"8055","DOI":"10.1007\/s00371-023-03222-0","article-title":"Pupil localization algorithm based on lightweight convolutional neural network","volume":"40","author":"Xiong","year":"2024","journal-title":"Vis. Comput."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1642","DOI":"10.1049\/ipr2.13056","article-title":"FSKT-GE: Feature maps similarity knowledge transfer for low-resolution gaze estimation","volume":"18","author":"Yan","year":"2024","journal-title":"IET Image Process."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"37766","DOI":"10.1038\/s41598-025-19617-z","article-title":"Optimizing MobileNetV3 for multimodal eye gaze and emotion recognition via advanced pruning and quantisation techniques","volume":"15","author":"Habib","year":"2025","journal-title":"Sci. Rep."},{"key":"ref_14","unstructured":"Gao, M., Wang, R., Wang, Y., Li, C., and Li, Z. (2025, January 22\u201327). Evaluation of eye-tracking capabilities in Apple Vision Pro for training in hybrid ventricular septal defect procedures. Proceedings of the Medical Imaging 2025: Image-Guided Procedures, Robotic Interventions, and Modeling, San Diego, CA, USA."},{"key":"ref_15","unstructured":"HTC Corporation (2026, June 02). VIVE Focus Vision Technical Specifications. Available online: https:\/\/www.vive.com\/us\/product\/vive-focus-vision\/specs."},{"key":"ref_16","unstructured":"Microsoft Corporation (2026, June 02). Windows Studio Effects: Gaze Tracking Technical Specifications. Available online: https:\/\/learn.microsoft.com\/en-us\/windows\/apps\/develop\/input\/gaze-interactions."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"722","DOI":"10.1109\/TPAMI.2008.300","article-title":"LSD: A fast line segment detector with a false detection control","volume":"32","author":"Gioi","year":"2010","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"3855","DOI":"10.1364\/OE.405600","article-title":"Binocular vision calibration method for long-wavelength infrared camera and a visible-spectrum camera with different resolutions","volume":"29","author":"Li","year":"2021","journal-title":"Opt. Express"},{"key":"ref_19","unstructured":"(2026, June 02). CASIA-IrisV4. Available online: https:\/\/hycasia.github.io\/dataset\/casia-irisv4\/."},{"key":"ref_20","unstructured":"Timm, F., and Barth, E. (2011, January 17\u201321). Accurate eye centre localisation by means of gradients. Proceedings of the International Conference on Computer Vision Theory and Applications (VISAPP), Lisbon, Portugal."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"108307","DOI":"10.1016\/j.jneumeth.2019.05.016","article-title":"DeepVOG: Open-source pupil segmentation and gaze estimation in neuroscience using deep learning","volume":"324","author":"Yiu","year":"2019","journal-title":"J. Neurosci. Methods"},{"key":"ref_22","unstructured":"SensoMotoric Instruments (2010). World\u2019s First: 500Hz Binocular Remote Eye Tracker\u2014SMI RED500, SensoMotoric Instruments."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"53","DOI":"10.3758\/s13428-023-02150-0","article-title":"Noise estimation for head-mounted 3D binocular eye tracking using Pupil Core eye-tracking goggles","volume":"56","author":"Velisar","year":"2024","journal-title":"Behav. Res."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"18","DOI":"10.3758\/s13428-022-01958-6","article-title":"Generating accurate 3D gaze vectors using synchronized eye tracking and motion capture","volume":"56","author":"Stone","year":"2024","journal-title":"Behav. Res."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/26\/12\/3741\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,6,14]],"date-time":"2026-06-14T04:12:19Z","timestamp":1781410339000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/26\/12\/3741"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,6,12]]},"references-count":24,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2026,6]]}},"alternative-id":["s26123741"],"URL":"https:\/\/doi.org\/10.3390\/s26123741","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,6,12]]}}}