{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,10]],"date-time":"2026-01-10T10:58:49Z","timestamp":1768042729718,"version":"3.49.0"},"reference-count":37,"publisher":"MDPI AG","issue":"22","license":[{"start":{"date-parts":[[2021,11,16]],"date-time":"2021-11-16T00:00:00Z","timestamp":1637020800000},"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>This paper presents a novel dense optical-flow algorithm to solve the monocular simultaneous localisation and mapping (SLAM) problem for ground or aerial robots. Dense optical flow can effectively provide the ego-motion of the vehicle while enabling collision avoidance with the potential obstacles. Existing research has not fully utilised the uncertainty of the optical flow\u2014at most, an isotropic Gaussian density model has been used. We estimate the full uncertainty of the optical flow and propose a new eight-point algorithm based on the statistical Mahalanobis distance. Combined with the pose-graph optimisation, the proposed method demonstrates enhanced robustness and accuracy for the public autonomous car dataset (KITTI) and aerial monocular dataset.<\/jats:p>","DOI":"10.3390\/s21227603","type":"journal-article","created":{"date-parts":[[2021,11,17]],"date-time":"2021-11-17T09:16:11Z","timestamp":1637140571000},"page":"7603","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Uncertainty Estimation of Dense Optical Flow for Robust Visual Navigation"],"prefix":"10.3390","volume":"21","author":[{"given":"Yonhon","family":"Ng","sequence":"first","affiliation":[{"name":"College of Engineering & Computer Science, The Australian National University, Canberra, ACT 2601, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hongdong","family":"Li","sequence":"additional","affiliation":[{"name":"College of Engineering & Computer Science, The Australian National University, Canberra, ACT 2601, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4505-1103","authenticated-orcid":false,"given":"Jonghyuk","family":"Kim","sequence":"additional","affiliation":[{"name":"School of Mechanical and Mechatronics Engineering, University of Technology Sydney, Sydney, NSW 2007, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,11,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1260\/1369-4332.17.3.289","article-title":"Quality assessment of unmanned aerial vehicle (UAV) based visual inspection of structures","volume":"17","author":"Morgenthal","year":"2014","journal-title":"Adv. Struct. Eng."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Nikolic, J., Burri, M., Rehder, J., Leutenegger, S., Huerzeler, C., and Siegwart, R. (2013, January 2\u20139). A UAV system for inspection of industrial facilities. Proceedings of the Aerospace Conference, Big Sky, MT, USA.","DOI":"10.1109\/AERO.2013.6496959"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Herwitz, S., Johnson, L., Arvesen, J., Higgins, R., Leung, J., and Dunagan, S. (2002, January 20\u201323). Precision agriculture as a commercial application for solar-powered unmanned aerial vehicles. Proceedings of the 1st UAV Conference, Portsmouth, VA, USA.","DOI":"10.2514\/6.2002-3404"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1016\/j.agwat.2015.01.020","article-title":"UAVs challenge to assess water stress for sustainable agriculture","volume":"153","author":"Gago","year":"2015","journal-title":"Agric. Water Manag."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"914","DOI":"10.1002\/rob.20401","article-title":"Autonomous transportation and deployment with aerial robots for search and rescue missions","volume":"28","author":"Bernard","year":"2011","journal-title":"J. Field Robot."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Waharte, S., and Trigoni, N. (2010, January 6\u20137). Supporting search and rescue operations with UAVs. Proceedings of the 2010 International Conference on Emerging Security Technologies (EST), Canterbury, UK.","DOI":"10.1109\/EST.2010.31"},{"key":"ref_7","unstructured":"K\u00fcmmerle, R., Grisetti, G., Strasdat, H., Konolige, K., and Burgard, W. (2011, January 9\u201313). g 2 o: A general framework for graph optimization. Proceedings of the 2011 IEEE International on Robotics and Automation (ICRA), Shanghai, China."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Stachniss, C., and Kretzschmar, H. (2017). Pose graph compression for laser-based slam. 18th International Symposium on Robotics Research, Springer.","DOI":"10.1007\/978-3-319-29363-9_16"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Klein, G., and Murray, D. (2007, January 13\u201316). Parallel tracking and mapping for small AR workspaces. Proceedings of the 2007 6th IEEE and ACM International Symposium on Mixed and Augmented Reality NW, Washington, DC, USA.","DOI":"10.1109\/ISMAR.2007.4538852"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"730","DOI":"10.1109\/TPAMI.2015.2469274","article-title":"High Accuracy Monocular SFM and Scale Correction for Autonomous Driving","volume":"38","author":"Song","year":"2016","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1016\/j.imavis.2017.08.002","article-title":"Predictive monocular odometry (PMO): What is possible without RANSAC and multiframe bundle adjustment?","volume":"68","author":"Fanani","year":"2017","journal-title":"Image Vis. Comput."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Bradler, H., Anne Wiegand, B., and Mester, R. (2015, January 7\u201313). The Statistics of Driving Sequences\u2014And What We Can Learn from Them. Proceedings of the IEEE International Conference on Computer Vision (ICCV) Workshops, Santiago, Chile.","DOI":"10.1109\/ICCVW.2015.24"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Xu, J., Ranftl, R., and Koltun, V. (2017, January 21\u201326). Accurate Optical Flow via Direct Cost Volume Processing. Proceedings of the 2017 IEEE Conference on Computer Vision and Pattern Recognition, Honolulu, HI, USA.","DOI":"10.1109\/CVPR.2017.615"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Hui, T.W., Tang, X., and Loy, C.C. (2018, January 18\u201323). LiteFlowNet: A Lightweight Convolutional Neural Network for Optical Flow Estimation. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, Salt Lake City, UT, USA.","DOI":"10.1109\/CVPR.2018.00936"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Sun, D., Yang, X., Liu, M.Y., and Kautz, J. (2018, January 18\u201323). PWC-Net: CNNs for Optical Flow Using Pyramid, Warping, and Cost Volume. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, Salt Lake City, UT, USA.","DOI":"10.1109\/CVPR.2018.00931"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Hartley, R., and Zisserman, A. (2003). Multiple View Geometry in Computer Vision, Cambridge University Press.","DOI":"10.1017\/CBO9780511811685"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1016\/j.robot.2015.04.010","article-title":"Robust linear pose graph-based SLAM","volume":"72","author":"Cheng","year":"2015","journal-title":"Robot. Auton. Syst."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Mur-Artal, R., and Tard\u00f3s, J.D. (2016). ORB-SLAM2: An Open-Source SLAM System for Monocular, Stereo and RGB-D Cameras. arXiv.","DOI":"10.1109\/TRO.2017.2705103"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Engel, J., St\u00fcckler, J., and Cremers, D. (October, January 28). Large-scale direct SLAM with stereo cameras. Proceedings of the 2015 IEEE\/RSJ International Conference on Intelligent Robots and Systems (IROS), Hamburg, Germany.","DOI":"10.1109\/IROS.2015.7353631"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Cheviron, T., Hamel, T., Mahony, R., and Baldwin, G. (2007, January 10\u201314). Robust nonlinear fusion of inertial and visual data for position, velocity and attitude estimation of UAV. Proceedings of the IEEE International Conference on Robotics and Automation, Roma, Italy.","DOI":"10.1109\/ROBOT.2007.363617"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"299","DOI":"10.1007\/s10846-008-9304-8","article-title":"Visual 3-d slam from uavs","volume":"55","author":"Artieda","year":"2009","journal-title":"J. Intell. Robot. Syst."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Geiger, A., Ziegler, J., and Stiller, C. (2011). StereoScan: Dense 3D Reconstruction in Real-time. Intelligent Vehicles Symposium (IV), IEEE.","DOI":"10.1109\/IVS.2011.5940405"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Chen, Q., and Koltun, V. (2016, January 27\u201330). Full flow: Optical flow estimation by global optimization over regular grids. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, Las Vegas, NV, USA.","DOI":"10.1109\/CVPR.2016.509"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Revaud, J., Weinzaepfel, P., Harchaoui, Z., and Schmid, C. (2015, January 7\u201312). Epicflow: Edge-preserving interpolation of correspondences for optical flow. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, Boston, MA, USA.","DOI":"10.1109\/CVPR.2015.7298720"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"580","DOI":"10.1109\/34.601246","article-title":"In defense of the eight-point algorithm","volume":"19","author":"Hartley","year":"1997","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_26","unstructured":"Torr, P., and Zisserman, A. (1998, January 7). Robust computation and parametrization of multiple view relations. Proceedings of the Sixth International Conference on Computer Vision, Bombay, India."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1023\/A:1007941100561","article-title":"Determining the Epipolar Geometry and its Uncertainty: A Review","volume":"27","author":"Zhang","year":"1998","journal-title":"Int. J. Comput. Vis."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1016\/S0262-8856(02)00154-3","article-title":"Overall view regarding fundamental matrix estimation","volume":"21","author":"Salvi","year":"2003","journal-title":"Image Vis. Comput."},{"key":"ref_29","unstructured":"Shi, J., and Tomasi, C. (1994, January 21\u201323). Good features to track. 1994. Proceedings of the CVPR\u201994, 1994 IEEE Computer Society Conference, New York, NY, USA."},{"key":"ref_30","unstructured":"Mahalanobis, P.C. (1936). On the Generalised Distance in Statistics, National Institute of Sciences of India."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Douc, R., and Cappe, O. (2005, January 15\u201317). Comparison of resampling schemes for particle filtering. Proceedings of the 4th International Symposium on Image and Signal Processing and Analysis, Zagreb, Croatia.","DOI":"10.1109\/ISPA.2005.195385"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"930","DOI":"10.1109\/TPAMI.2003.1217599","article-title":"Complete solution classification for the perspective-three-point problem","volume":"25","author":"Gao","year":"2003","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_33","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":"Wang","year":"2004","journal-title":"IEEE Trans. Image Process."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Geiger, A., Lenz, P., and Urtasun, R. (2012, January 16\u201321). Are we ready for Autonomous Driving? The KITTI Vision Benchmark Suite. Proceedings of the Conference on Computer Vision and Pattern Recognition (CVPR), Providence, RI, USA.","DOI":"10.1109\/CVPR.2012.6248074"},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Menze, M., and Geiger, A. (2015, January 7\u201312). Object Scene Flow for Autonomous Vehicles. Proceedings of the Conference on Computer Vision and Pattern Recognition (CVPR), Boston, MA, USA.","DOI":"10.1109\/CVPR.2015.7298925"},{"key":"ref_36","unstructured":"Ng, Y., Kim, J., and Li, H. (2017, January 11\u201313). Robust Dense Optical Flow with Uncertainty for Monocular Pose-Graph SLAM. Proceedings of the Australasian Conference on Robotics and Automation, Sydney, Australia."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"1192","DOI":"10.1109\/LRA.2016.2532928","article-title":"A filter formulation for computing real time optical flow","volume":"1","author":"Adarve","year":"2016","journal-title":"IEEE Robot. Autom. Lett."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/22\/7603\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T07:30:59Z","timestamp":1760167859000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/22\/7603"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,11,16]]},"references-count":37,"journal-issue":{"issue":"22","published-online":{"date-parts":[[2021,11]]}},"alternative-id":["s21227603"],"URL":"https:\/\/doi.org\/10.3390\/s21227603","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,11,16]]}}}