{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,6]],"date-time":"2026-02-06T23:41:26Z","timestamp":1770421286707,"version":"3.49.0"},"reference-count":36,"publisher":"MDPI AG","issue":"17","license":[{"start":{"date-parts":[[2024,9,4]],"date-time":"2024-09-04T00:00:00Z","timestamp":1725408000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Key R&amp;D Program of China","award":["2022YFF0706400"],"award-info":[{"award-number":["2022YFF0706400"]}]},{"name":"China Jiliang University","award":["2022YFF0706400"],"award-info":[{"award-number":["2022YFF0706400"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Industrial computed tomography (CT) is widely used in the measurement field owing to its advantages such as non-contact and high precision. To obtain accurate size parameters, fitting parameters can be obtained rapidly by processing volume data in the form of point clouds. However, due to factors such as artifacts in the CT reconstruction process, many abnormal interference points exist in the point clouds obtained after segmentation. The classic least squares algorithm is easily affected by these points, resulting in significant deviation of the solution of linear equations from the normal value and poor robustness, while the random sample consensus (RANSAC) approach has insufficient fitting accuracy within a limited timeframe and the number of iterations. To address these shortcomings, we propose a spherical point cloud fitting algorithm based on projection filtering and K-Means clustering (PK-RANSAC), which strategically integrates and enhances these two methods to achieve excellent accuracy and robustness. The proposed method first uses RANSAC for rough parameter estimation, then corrects the deviation of the spherical center coordinates through two-dimensional projection, and finally obtains the spherical center point set by sampling and performing K-Means clustering. The largest cluster is weighted to obtain accurate fitting parameters. We conducted a comparative experiment using a three-dimensional ball-plate standard. The sphere center fitting deviation of PK-RANSAC was 1.91 \u03bcm, which is significantly better than RANSAC\u2019s value of 25.41 \u03bcm. The experimental results demonstrate that PK-RANSAC has higher accuracy and stronger robustness for fitting geometric parameters.<\/jats:p>","DOI":"10.3390\/s24175762","type":"journal-article","created":{"date-parts":[[2024,9,5]],"date-time":"2024-09-05T02:34:06Z","timestamp":1725503646000},"page":"5762","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Target Fitting Method for Spherical Point Clouds Based on Projection Filtering and K-Means Clustered Voxelization"],"prefix":"10.3390","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0009-0007-7331-4819","authenticated-orcid":false,"given":"Zhe","family":"Wang","sequence":"first","affiliation":[{"name":"Key Laboratory of In-Situ Metrology, Ministry of Education, China Jiliang University, Hangzhou 310018, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jiacheng","family":"Hu","sequence":"additional","affiliation":[{"name":"Key Laboratory of In-Situ Metrology, Ministry of Education, China Jiliang University, Hangzhou 310018, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yushu","family":"Shi","sequence":"additional","affiliation":[{"name":"National Institute of Metrology, Beijing 102200, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2881-2927","authenticated-orcid":false,"given":"Jinhui","family":"Cai","sequence":"additional","affiliation":[{"name":"Key Laboratory of In-Situ Metrology, Ministry of Education, China Jiliang University, Hangzhou 310018, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lei","family":"Pi","sequence":"additional","affiliation":[{"name":"National Institute of Metrology, Beijing 102200, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,9,4]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"486","DOI":"10.1016\/S0022-5223(19)38282-0","article-title":"Computed tomography","volume":"88","author":"Daly","year":"1984","journal-title":"J. Thorac. Cardiovasc. Surg."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"052109","DOI":"10.1117\/1.JMI.8.5.052109","article-title":"Computed tomography recent history and future perspectives","volume":"8","author":"Hsieh","year":"2021","journal-title":"J. Med. Imaging"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"496","DOI":"10.1088\/0957-0233\/18\/2\/S24","article-title":"AFM investigation on surface damage caused by mechanical probing with small ruby spheres","volume":"18","author":"Meli","year":"2007","journal-title":"Meas. Sci. Technol."},{"key":"ref_4","first-page":"323","article-title":"3D laser scanners\u2019 techniques overview","volume":"4","author":"Ebrahim","year":"2015","journal-title":"Int. J. Sci. Res."},{"key":"ref_5","first-page":"1","article-title":"Comparative study of the representative algorithms for fitting spherical target based on point cloud","volume":"60","author":"Shi","year":"2022","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1179\/sre.2005.38.297.243","article-title":"Determination of the optimal diameter for spherical targets used in 3D laser scanning","volume":"38","author":"Reshetyuk","year":"2005","journal-title":"Surv. Rev."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Lu, T., Zhou, S., Zhang, L., and Guan, Y. (2009, January 15). Sphere target fitting of point cloud data based on TLS. Proceedings of the International Symposium on Spatial Analysis, Spatial-Temporal Data Modeling, and Data Mining, Wuhan, China.","DOI":"10.1117\/12.838400"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Le, H., and Zach, C. (2021, January 1\u20133). Robust fitting with truncated least squares: A bilevel optimization approach. Proceedings of the 2021 International Conference on 3D Vision (3DV), London, UK.","DOI":"10.1109\/3DV53792.2021.00146"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1590\/S1982-21702015000200019","article-title":"Least squares fitting of ellipsoid using orthogonal distances","volume":"21","author":"Bektas","year":"2015","journal-title":"Bol. Ci\u00eanc. Geod."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"617","DOI":"10.1016\/j.measurement.2019.02.025","article-title":"Novel method for sphere target detection and center estimation from mobile terrestrial laser scanner data","volume":"137","author":"Liu","year":"2019","journal-title":"Measurement"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Wu, Q., Liu, J., Gao, C., Wang, B., Shen, G., and Li, Z. (2022). Improved RANSAC point cloud spherical target detection and parameter estimation method based on principal curvature constraint. Sensors, 22.","DOI":"10.3390\/s22155850"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"48062","DOI":"10.1109\/ACCESS.2018.2866935","article-title":"An improved point-to-plane registration method for terrestrial laser scanning data","volume":"6","author":"Tao","year":"2018","journal-title":"IEEE Access"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"015012","DOI":"10.1088\/1361-6501\/abae3c","article-title":"A new high-precision sphere-fitting method with small segment angles","volume":"32","author":"Fei","year":"2020","journal-title":"Meas. Sci. Technol."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1148","DOI":"10.1080\/01431161.2024.2305633","article-title":"Efficient shrub modelling based on terrestrial laser scanning (TLS) point clouds","volume":"45","author":"Li","year":"2024","journal-title":"Int. J. Remote Sens."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"7217","DOI":"10.1109\/JSEN.2023.3243388","article-title":"Toward Efficient and Complete Line Segment Extraction for Large-Scale Point Clouds via Plane Segmentation and Projection","volume":"23","author":"Zong","year":"2023","journal-title":"IEEE Sens. J."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"025021","DOI":"10.1088\/1361-6501\/aca116","article-title":"Three-dimensional defects detection of high-voltage cable joint based on iterative residual fitting","volume":"34","author":"Zheng","year":"2022","journal-title":"Meas. Sci. Technol."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s10700-019-09310-y","article-title":"Parameter estimation in uncertain differential equations","volume":"19","author":"Yao","year":"2020","journal-title":"Fuzzy Optim. Decis. Mak."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"86","DOI":"10.1016\/j.jvcir.2013.04.001","article-title":"Continuous plane detection in point-cloud data based on 3D Hough transform","volume":"25","author":"Hulik","year":"2014","journal-title":"J. Vis. Commun. Image Represent."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"053609","DOI":"10.1117\/1.3562323","article-title":"Automated detection of planes in 3-D point clouds using fast Hough transforms","volume":"50","author":"Coggrave","year":"2011","journal-title":"Opt. Eng."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"214","DOI":"10.1111\/j.1467-8659.2007.01016.x","article-title":"Efficient RANSAC for point-cloud shape detection","volume":"26","author":"Schnabel","year":"2007","journal-title":"Comput. Graph. Forum"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"103608","DOI":"10.1016\/j.csi.2021.103608","article-title":"Efficient plane extraction using normal estimation and RANSAC from 3D point cloud","volume":"82","author":"Yang","year":"2022","journal-title":"Comput. Stand. Interfaces"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Roman-Rivera, L.-R., Pedraza-Ortega, J.C., Aceves-Fernandez, M.A., Ramos-Arregu\u00edn, J.M., Gorrostieta-Hurtado, E., and Tovar-Arriaga, S. (2023). A robust sphere detection in a realsense point cloud by using Z-score and RANSAC. Mathematics, 11.","DOI":"10.3390\/math11041023"},{"key":"ref_23","first-page":"2","article-title":"Shape detection in point clouds","volume":"2","author":"Schnabel","year":"2006","journal-title":"Comput. Graph. Tech. Rep."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Nguatem, W., and Mayer, H. (2017, January 22\u201329). Modeling urban scenes from pointclouds. Proceedings of the 2017 IEEE International Conference on Computer Vision (ICCV), Venice, Italy.","DOI":"10.1109\/ICCV.2017.414"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1842","DOI":"10.1109\/LGRS.2016.2614749","article-title":"An efficient planar feature fitting method using point cloud simplification and threshold-independent BaySAC","volume":"13","author":"Kang","year":"2016","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"182","DOI":"10.1080\/10095020.2016.1235818","article-title":"The applications of robust estimation method BaySAC in indoor point cloud processing","volume":"19","author":"Kang","year":"2016","journal-title":"Geo-Spat. Inf. Sci."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Kang, Z., and Li, Z. (2015). Primitive fitting based on the efficient multiBaySAC algorithm. PLoS ONE, 10.","DOI":"10.1371\/journal.pone.0117341"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Shi, Y., Zhao, G., Wang, M., Xu, Y., and Zhu, D. (2021). An algorithm for fitting sphere target of terrestrial LiDAR. Sensors, 21.","DOI":"10.3390\/s21227546"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"111430","DOI":"10.1016\/j.measurement.2022.111430","article-title":"An adaptive grid search algorithm for fitting spherical target of terrestrial LiDAR","volume":"198","author":"Shi","year":"2022","journal-title":"Measurement"},{"key":"ref_30","first-page":"1","article-title":"A novel robust point cloud fitting algorithm based on nonlinear Gauss\u2013Helmert model","volume":"72","author":"Wang","year":"2023","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"105493","DOI":"10.1016\/j.autcon.2024.105493","article-title":"Point cloud and machine learning-based automated recognition and measurement of corrugated pipes and rebars for large precast concrete beams","volume":"165","author":"Shu","year":"2024","journal-title":"Autom. Constr."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"5743","DOI":"10.1109\/LRA.2024.3397072","article-title":"Automatic Extrinsic Parameter Calibration for Camera-LiDAR Fusion using Spherical Target","volume":"9","author":"Zhang","year":"2024","journal-title":"IEEE Robot. Autom. Lett."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"343","DOI":"10.5194\/isprs-archives-XLVIII-4-W9-2024-343-2024","article-title":"Suitable Landing Site Selection for Unmanned Aerial Vehicles Using Airborne Laser Scanning Point Cloud","volume":"48","author":"Singh","year":"2024","journal-title":"Int. Arch. Photogramm. Remote Sens. Spat. Inf. Sci."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Li, R., Chen, X., Dong, Q., Wang, S., Chu, Z., and Gu, X. (2023, January 6\u20138). Point Cloud-Based Pavement Crack Extraction Using MSAC and KNN Algorithm. Proceedings of the International Conference on Road and Airfield Pavement Technology 2023, Beijing, China.","DOI":"10.1061\/9780784485255.068"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"075008","DOI":"10.1088\/1361-6501\/ad3bde","article-title":"Exact computation of projected sphere centres in cone beam x-ray projections","volume":"35","author":"Burkhard","year":"2024","journal-title":"Meas. Sci. Technol."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Hong, Y., Xu, J., Wu, C., Pang, Y., Zhang, S., Chen, D., and Yang, B. (2023). Combining Multisource Data and Machine Learning Approaches for Multiscale Estimation of Forest Biomass. Forests, 14.","DOI":"10.3390\/f14112248"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/24\/17\/5762\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T15:48:46Z","timestamp":1760111326000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/24\/17\/5762"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,9,4]]},"references-count":36,"journal-issue":{"issue":"17","published-online":{"date-parts":[[2024,9]]}},"alternative-id":["s24175762"],"URL":"https:\/\/doi.org\/10.3390\/s24175762","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,9,4]]}}}