{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:06:52Z","timestamp":1760234812380,"version":"build-2065373602"},"reference-count":28,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2021,6,25]],"date-time":"2021-06-25T00:00:00Z","timestamp":1624579200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100010822","name":"Chengdu Science and Technology Bureau","doi-asserted-by":"publisher","award":["2019-YF05 -02641-SN"],"award-info":[{"award-number":["2019-YF05 -02641-SN"]}],"id":[{"id":"10.13039\/501100010822","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004829","name":"Department of Science and Technology of Sichuan Province","doi-asserted-by":"publisher","award":["2020YFG0146 2020YFG0144 2019YFS0472"],"award-info":[{"award-number":["2020YFG0146 2020YFG0144 2019YFS0472"]}],"id":[{"id":"10.13039\/501100004829","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["41771535 41601422"],"award-info":[{"award-number":["41771535 41601422"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"School Undergraduate Teaching Project","award":["BKJX2020030"],"award-info":[{"award-number":["BKJX2020030"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IJGI"],"abstract":"<jats:p>Computing the homography matrix using the known matching points is a key step in computer vision for image registration. In practice, the number, accuracy, and distribution of the known matching points can affect the uncertainty of the homography matrix. This study mainly focuses on the effect of matching point distribution on image registration. First, horizontal dilution of precision (HDOP) is derived to measure the influence of the distribution of known points on fixed point position accuracy on the image. The quantization function, which is the average of the center points\u2019 HDOP* of the overlapping region, is then constructed to measure the uncertainty of matching distribution. Finally, the experiments in the field of image registration are performed to verify the proposed function. We test the consistency of the relationship between the proposed function and the average of symmetric transfer errors. Consequently, the proposed function is appropriate for measuring the uncertainty of matching point distribution on image registration.<\/jats:p>","DOI":"10.3390\/ijgi10070438","type":"journal-article","created":{"date-parts":[[2021,6,25]],"date-time":"2021-06-25T11:07:40Z","timestamp":1624619260000},"page":"438","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["A Cost Function for the Uncertainty of Matching Point Distribution on Image Registration"],"prefix":"10.3390","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0890-814X","authenticated-orcid":false,"given":"Yuxia","family":"Bian","sequence":"first","affiliation":[{"name":"College of Resources and Environment, Chengdu University of Information Technology, Chengdu 610000, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4135-5073","authenticated-orcid":false,"given":"Meizhen","family":"Wang","sequence":"additional","affiliation":[{"name":"Ministry of Education Key Laboratory of Virtual Geographic Environment, Nanjing Normal University, Nanjing 210000, China"}]},{"given":"Yongbin","family":"Chu","sequence":"additional","affiliation":[{"name":"College of Resources and Environment, Chengdu University of Information Technology, Chengdu 610000, China"}]},{"given":"Zhihong","family":"Liu","sequence":"additional","affiliation":[{"name":"College of Resources and Environment, Chengdu University of Information Technology, Chengdu 610000, China"}]},{"given":"Jun","family":"Chen","sequence":"additional","affiliation":[{"name":"College of Resources and Environment, Chengdu University of Information Technology, Chengdu 610000, China"}]},{"given":"Zhiye","family":"Xia","sequence":"additional","affiliation":[{"name":"College of Resources and Environment, Chengdu University of Information Technology, Chengdu 610000, China"}]},{"given":"Shuhong","family":"Fang","sequence":"additional","affiliation":[{"name":"College of Resources and Environment, Chengdu University of Information Technology, Chengdu 610000, China"}]}],"member":"1968","published-online":{"date-parts":[[2021,6,25]]},"reference":[{"key":"ref_1","unstructured":"Brand, P., and Mohr, R. (1994, January 6). Accuracy in image measure. Proceedings of the SPIE Conference on Videometrics, Boston, MA, USA."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"70","DOI":"10.1016\/j.imavis.2017.02.005","article-title":"Estimation of measurement uncertainty in stereo vision system","volume":"61","author":"Sankowski","year":"2017","journal-title":"Image Vis. Comput."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"451","DOI":"10.1109\/34.24779","article-title":"Motion and structure from two perspective views: Algorithms, error analysis, and error estimation","volume":"11","author":"Weng","year":"1989","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1002\/ecjc.10042","article-title":"Do we really have to consider covariance matrices for image feature points?","volume":"86","author":"Kanazawa","year":"2002","journal-title":"Electron. Commun. Jpn."},{"key":"ref_5","unstructured":"Brooks, M.J., Chojnacki, W., Gawley, D., and Hengel, A.V.D. (2001, January 7\u201314). What value covariance information in estimating vision parameters?. Proceedings of the IEEE International Conference on Computer Vision 2001, Vancouver, BC, Canada."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Haralick, R.M. (1996). Propagating Covariance in Computer Vision. Int. J. Pattern Recognit. Artif. Intell., 10.","DOI":"10.1142\/S0218001496000347"},{"key":"ref_7","unstructured":"Steele, R.M., and Jaynes, C. (2005, January 20\u201326). Feature Uncertainty Arising from Covariant Image Noise. Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, San Diego, CA, USA."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1664","DOI":"10.1109\/TIM.2011.2113070","article-title":"Covariance Propagation for the Uncertainty Estimation in Stereo Vision","volume":"60","author":"Liguori","year":"2011","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"917","DOI":"10.1109\/42.952729","article-title":"The distribution of target registration error in rigid-body point-based registration","volume":"20","author":"Fitzpatrick","year":"2001","journal-title":"IEEE Trans. Med Imaging"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"383","DOI":"10.1016\/j.patrec.2010.09.019","article-title":"Fundamental matrix estimation: A study of error criteria","volume":"32","author":"Fathy","year":"2011","journal-title":"Pattern Recognit. Lett."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Hartley, R., Zisserman, A., and Faugeras, O. (2003). Multiple View Geometry in Computer Vision, Cambridge University Press. [2nd ed.].","DOI":"10.1017\/CBO9780511811685"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1869","DOI":"10.1016\/j.ijleo.2012.05.037","article-title":"Point-pattern matching method using SURF and Shape Context","volume":"124","author":"Gui","year":"2013","journal-title":"Int. J. Light Electron. Optics"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Tong, G., Wang, C., and Wang, P. (2015, January 10\u201311). Study on Improving Image Feature Points Detection and Matching Accuracy in Binocular Vision System. Proceedings of the International Industrial Informatics and Computer Engineering Conference, Xi\u2019an, China.","DOI":"10.2991\/iiicec-15.2015.150"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"13011","DOI":"10.1117\/1.JEI.23.1.013011","article-title":"Local sharpness distribution\u2013based feature points matching algorithm","volume":"23","author":"Zhao","year":"2014","journal-title":"J. Electron. Imaging"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Hu, M., Liu, Y., and Fan, Y. (2015, January 10\u201312). Robust Image Feature Point Matching Based on Structural Distance. Proceedings of the Chinese Conference on Image and Graphics Technologies, Berlin, Germany.","DOI":"10.1007\/978-3-662-47791-5_17"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1155\/2020\/3285431","article-title":"Impact of Matching Point Selections on Image Registration Accuracy between Optical Scan and Computed Tomography","volume":"2020","author":"Mai","year":"2020","journal-title":"BioMed Res. Int."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Tan, X., Sun, C., Sirault, X., Furbank, R., and Pham, T.D. (2012, January 14). Feature Correspondence with Even Distribution. Proceedings of the International Conference on Digital Image Computing Techniques and Applications, Perth, Australia.","DOI":"10.1109\/DICTA.2012.6411723"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"2530","DOI":"10.1016\/j.patcog.2015.02.026","article-title":"Feature matching in stereo images encouraging uniform spatial distribution","volume":"48","author":"Tan","year":"2015","journal-title":"Pattern Recognit."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"872","DOI":"10.1016\/j.patrec.2011.08.021","article-title":"Good match exploration using triangle constraint","volume":"33","author":"Guo","year":"2012","journal-title":"Pattern Recognit. Lett."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1109\/LGRS.2005.861735","article-title":"Seed Point Selection Method for Triangle Constrained Image Matching Propagation","volume":"3","author":"Zhu","year":"2006","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"119367","DOI":"10.1109\/ACCESS.2019.2936647","article-title":"A Reliable Distribution Quality Measure in Image Registration","volume":"7","author":"Mahmood","year":"2019","journal-title":"IEEE Access"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"733","DOI":"10.1016\/j.patrec.2004.01.014","article-title":"Two quantitative measures of inlier distributions for precise fundamental matrix estimation","volume":"25","author":"Seo","year":"2004","journal-title":"Pattern Recognit. Lett."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Bian, Y., Liu, X., Wang, M., Liu, H., Fang, S., and Yu, L. (2020). Quantification Method for the Uncertainty of Matching Point Distribution on 3D Reconstruction. Int. J. Geo-Inf., 9.","DOI":"10.3390\/ijgi9040187"},{"key":"ref_24","unstructured":"Zhang, X.-D. (2013). Matrix Analysis and Applications, Tsinghua University Press. [2nd ed.]."},{"key":"ref_25","unstructured":"Bu, C.J., and Luo, Y.S. (2003). Matrix Theory, Harbin Engineer University Press."},{"key":"ref_26","first-page":"22","article-title":"The Minimum Value of GDOP in Pseudo-range Positioning","volume":"34","author":"Sheng","year":"2009","journal-title":"Fire Control Command Control"},{"key":"ref_27","first-page":"85","article-title":"Study on the Minimum of GDOP in Satellite Navigation and its Applications","volume":"40","author":"Li","year":"2011","journal-title":"Acta Geod. Cartogr. Sin."},{"key":"ref_28","unstructured":"Qu, Z.G. (2013). Image Structure Description and Matching based on Graph Theory. [Ph.D. Thesis, National University of Defense Technology]."}],"container-title":["ISPRS International Journal of Geo-Information"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2220-9964\/10\/7\/438\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T06:24:21Z","timestamp":1760163861000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2220-9964\/10\/7\/438"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,6,25]]},"references-count":28,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2021,7]]}},"alternative-id":["ijgi10070438"],"URL":"https:\/\/doi.org\/10.3390\/ijgi10070438","relation":{},"ISSN":["2220-9964"],"issn-type":[{"type":"electronic","value":"2220-9964"}],"subject":[],"published":{"date-parts":[[2021,6,25]]}}}