{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T01:52:34Z","timestamp":1760233954369,"version":"build-2065373602"},"reference-count":30,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2021,3,15]],"date-time":"2021-03-15T00:00:00Z","timestamp":1615766400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Sichuan Province Goverment, China","award":["2019YFG0117"],"award-info":[{"award-number":["2019YFG0117"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>To reconstruct point geometry from multiple images, computation of the fundamental matrix is always necessary. With a new optimization criterion, i.e., the re-projective 3D metric geometric distance rather than projective space under RANSAC (Random Sample And Consensus) framework, our method can reveal the quality of the fundamental matrix visually through 3D reconstruction. The geometric distance is the projection error of 3D points to the corresponding image pixel coordinates in metric space. The reasonable visual figures of the reconstructed scenes are shown but only some numerical result were compared, as is standard practice. This criterion can lead to a better 3D reconstruction result especially in 3D metric space. Our experiments validate our new error criterion and the quality of fundamental matrix under the new criterion.<\/jats:p>","DOI":"10.3390\/a14030089","type":"journal-article","created":{"date-parts":[[2021,3,15]],"date-time":"2021-03-15T11:38:58Z","timestamp":1615808338000},"page":"89","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Fundamental Matrix Computing Based on 3D Metrical Distance"],"prefix":"10.3390","volume":"14","author":[{"given":"Xinsheng","family":"Li","sequence":"first","affiliation":[{"name":"College of Computer Science, Sichuan University, Chengdu 610064, China"}]},{"given":"Xuedong","family":"Yuan","sequence":"additional","affiliation":[{"name":"College of Computer Science, Sichuan University, Chengdu 610064, China"}]}],"member":"1968","published-online":{"date-parts":[[2021,3,15]]},"reference":[{"key":"ref_1","unstructured":"Feng, C.L., and Hung, Y.S. (2003, January 10\u201312). A Robust Method for Estimating the Fundamental Matrix. Proceedings of the International Conference on Digital Image Computing, Sydney, Australia."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1038\/293133a0","article-title":"A Computer Alorithm for Reconstructing a Scene from Two Projections","volume":"293","year":"1981","journal-title":"Nature"},{"key":"ref_3","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_4","doi-asserted-by":"crossref","first-page":"756","DOI":"10.1109\/TPAMI.2004.17","article-title":"An efficient solution to the five-point relative pose problem","volume":"26","author":"Nister","year":"2004","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Nister, D., Hartley, R.I., and Henrik, S. (2007, January 17\u201322). Using Galois Theory to Prove Structure from Motion Algorithms are Optimal. Proceedings of the IEEE Conf. on Computer Vision and Pattern Recognition (CVPR), Minneapolis, MN, USA.","DOI":"10.1109\/CVPR.2007.383089"},{"key":"ref_6","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_7","doi-asserted-by":"crossref","first-page":"312","DOI":"10.1006\/cviu.1997.0559","article-title":"Robust Detection of Degenerate Configurations while Estimating the Fundamental Matrix","volume":"71","author":"Torr","year":"1998","journal-title":"Comput. Vis. Image Underst."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1023\/A:1007927408552","article-title":"The Development and Comparison of Robust Methods for Estimating the Fundamental Matrix","volume":"24","author":"Torr","year":"1997","journal-title":"Int. J. Comput. Vis."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Li, W., and Li, B. (2006, January 8\u201311). Map estimation of epipolar geometry by em algorithm and local diffusion. Proceedings of the International Conference on Image Processing, ICIP, Atlanta, GA, USA.","DOI":"10.1109\/ICIP.2007.4379800"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"3881","DOI":"10.1016\/j.neucom.2009.04.018","article-title":"Estimation of epipolar geometry by linear mixed-effect modelling","volume":"72","author":"Zhou","year":"2009","journal-title":"Neurocomputing"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"3638","DOI":"10.1016\/j.neucom.2011.07.002","article-title":"Estimating the fundamental matrix based on least absolute deviation","volume":"74","author":"Yang","year":"2011","journal-title":"Neurocomputing"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Sengupta, S., Amir, T., Galun, M., Goldstein, T., Jacobs, D.W., Singer, A., and Basri, R. (2017, January 21\u201326). A new rank constraint on multi-view fundamental matrices, and its application to camera location recovery. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, Honolulu, HI, USA.","DOI":"10.1109\/CVPR.2017.259"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Kukelova, Z., Bujnak, M., and Pajdla, T. (2008, January 10\u201313). Polynomial Eigenvalue Solutions to the 5-pt and 6-pt Relative Pose Problems. Proceedings of the British Machine Vision Conference, Leeds, UK.","DOI":"10.5244\/C.22.56"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"284","DOI":"10.1016\/j.isprsjprs.2006.03.005","article-title":"Recent developments on direct relative orientation","volume":"60","author":"Stewenius","year":"2006","journal-title":"ISPRS J. Photogramm. Remote Sens."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Barath, D. (2018, January 18\u201323). Five-point fundamental matrix estimation for uncalibrated cameras. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, Salt Lake City, UT, USA.","DOI":"10.1109\/CVPR.2018.00032"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"140","DOI":"10.1016\/j.ins.2011.08.019","article-title":"Estimation of F-Matrix and image rectification by double quaternion","volume":"183","author":"Banno","year":"2012","journal-title":"Inf. Sci."},{"key":"ref_17","unstructured":"Benartzi, G., Halperin, T., Werman, M., and Peleg, S. (2016). Two Points Fundamental Matrix. arXiv."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1023\/A:1020224303087","article-title":"Bayesian Model Estimation and Selection for Epipolar Geometry and Generic Manifold Fitting","volume":"50","author":"Torr","year":"2002","journal-title":"Int. J. Comput. Vis."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Tolba, M.E.F.A.S.H.M.F. (2011). Fundamental matrix estimation: A study of error criteria. Pattern Recognit. Lett., 383\u2013391.","DOI":"10.1016\/j.patrec.2010.09.019"},{"key":"ref_20","unstructured":"Kanatani, K., Sugaya, Y., and Niitsuma, H. (, January September). Triangulation from Two Views Revisited: Hartley-Sturm vs. Proceedings of the British Machine Vision Conference, Leeds, UK."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"266","DOI":"10.1007\/s11263-009-0269-2","article-title":"Camera network calibration and synchronization from silhouettes in archived video","volume":"87","author":"Sinha","year":"2010","journal-title":"Int. J. Comput. Vis."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Ben-Artzi, G., Kasten, Y., Peleg, S., and Werman, M. (2016, January 27\u201330). Camera calibration from dynamic silhouettes using motion barcodes. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, Las Vegas, NV, USA.","DOI":"10.1109\/CVPR.2016.444"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Kasten, Y., Ben-Artzi, G., Peleg, S., and Werman, M. (2016, January 11\u201314). Fundamental matrices from moving objects using line motion barcodes. Proceedings of the European Conference on Computer Vision, Amsterdam, The Netherlands.","DOI":"10.1007\/978-3-319-46475-6_14"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"300","DOI":"10.1016\/j.neucom.2015.02.033","article-title":"Method for fundamental matrix estimation combined with feature lines","volume":"160","author":"Zhou","year":"2015","journal-title":"Neurocomputing"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Poursaeed, O., Yang, G., Prakash, A., Fang, Q., Jiang, H., Hariharan, B., and Belongie, S. (2018, January 8\u201314). Deep Fundamental Matrix Estimation without Correspondences. Proceedings of the European Conference on Computer Vision (ECCV), Munich, Germany.","DOI":"10.1007\/978-3-030-11015-4_35"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1007\/BF00127818","article-title":"The Fundamental Matrix: Theory, Algorithms, and Stability Analysis","volume":"17","author":"Luong","year":"1996","journal-title":"Int. J. Comput. Vis."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Agrawal, A., and Ramalingam, S. (2013, January 23\u201328). Single image calibration of multi-axial imaging systems. Proceedings of the 2013 IEEE Conference onComputer Vision and Pattern Recognition (CVPR), Portland, OR, USA.","DOI":"10.1109\/CVPR.2013.184"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1023\/A:1008109111715","article-title":"Self-calibration and metric reconstruction inspite of varying and unknown intrinsic camera parameters","volume":"32","author":"Pollefeys","year":"1999","journal-title":"Int. J. Comput. Vis."},{"key":"ref_29","first-page":"131","article-title":"A taxonomy and evaluation of dense two-frame stereo correspondence algorithms","volume":"47","author":"Scharstein","year":"2001","journal-title":"Int. J. Comput. Vis."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1023\/B:VISI.0000029664.99615.94","article-title":"Distinctive image features from scale-invariant keypoints","volume":"60","author":"Lowe","year":"2004","journal-title":"Int. J. Comput. Vis."}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/14\/3\/89\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T05:35:40Z","timestamp":1760160940000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/14\/3\/89"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,3,15]]},"references-count":30,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2021,3]]}},"alternative-id":["a14030089"],"URL":"https:\/\/doi.org\/10.3390\/a14030089","relation":{},"ISSN":["1999-4893"],"issn-type":[{"type":"electronic","value":"1999-4893"}],"subject":[],"published":{"date-parts":[[2021,3,15]]}}}