{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,19]],"date-time":"2026-01-19T00:39:14Z","timestamp":1768783154621,"version":"3.49.0"},"reference-count":21,"publisher":"MDPI AG","issue":"16","license":[{"start":{"date-parts":[[2021,8,18]],"date-time":"2021-08-18T00:00:00Z","timestamp":1629244800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Projective transformation of spheres onto images produce ellipses, whose centers do not coincide with the projected center of the sphere. This results in an eccentricity error, which must be treated in high precision metrology. This article provides closed formulations for modeling this error in images to enable 3-dimensional (3D) reconstruction of the center of spherical objects. The article also provides a new direct robust method for detecting spherical pattern in point clouds. It was shown that the eccentricity error in an image has only one component in the direction of the major axis of the ellipse. It was also revealed that the eccentricity is zero if and only if the center of the projected sphere lies on the camera\u2019s perspective center. The effectiveness of the robust sphere detection and the eccentricity error modeling method was evaluated on simulated point clouds of spheres and real-world images, respectively. It was observed that the proposed robust sphere fitting method outperformed the popular M-estimator sample consensus in terms of radius and center estimation accuracy by a factor of 13, and 14 on average, respectively. Using the proposed eccentricity adjustment, the estimated 3D center of the sphere using modeled eccentricity was superior to the unmodeled case. It was also observed that the accuracy of the estimated 3D center using modeled eccentricity continuously improved as the number of images increased, whereas the unmodeled eccentricity did not show improvements after eight image views. The results of the investigation show that: (i) the proposed method effectively modeled the eccentricity error, and (ii) the effects of eliminating the eccentricity error in the 3D reconstruction become even more pronounced in a larger number of image views.<\/jats:p>","DOI":"10.3390\/rs13163269","type":"journal-article","created":{"date-parts":[[2021,8,18]],"date-time":"2021-08-18T22:51:00Z","timestamp":1629327060000},"page":"3269","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Correcting the Eccentricity Error of Projected Spherical Objects in Perspective Cameras"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6825-2691","authenticated-orcid":false,"given":"Reza","family":"Maalek","sequence":"first","affiliation":[{"name":"Department of Digital Engineering and Construction, Institute for Technology and Management in Construction, Karlsruhe Institute of Technology, 76131 Karlsruhe, Germany"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7038-073X","authenticated-orcid":false,"given":"Derek D.","family":"Lichti","sequence":"additional","affiliation":[{"name":"Department of Geomatics Engineering, Schulich School of Engineering, University of Calgary, Calgary, AB T2N 1N4, Canada"}]}],"member":"1968","published-online":{"date-parts":[[2021,8,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"485","DOI":"10.1111\/0031-868X.00138","article-title":"Systematic Geometric Image Measurement Errors of Circular Object Targets: Mathematical Formulation and Correction","volume":"16","author":"Ahn","year":"1999","journal-title":"Photogramm. 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Mag."},{"key":"ref_6","first-page":"83","article-title":"Linking Geometry, Algebra and Mathematics Teachers: GeoGebra Software and the Establishment of the International GeoGebra Institute","volume":"16","author":"Hohenwarter","year":"2009","journal-title":"Int. J. Technol. Math. Educ."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1007\/s10817-015-9326-4","article-title":"Automated Theorem Proving in GeoGebra: Current Achievements","volume":"55","author":"Botana","year":"2015","journal-title":"J. Autom. Reason."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1111\/phor.12315","article-title":"Geometric modelling and calibration of a spherical camera imaging system","volume":"35","author":"Lichti","year":"2020","journal-title":"Photogramm. Rec."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"124","DOI":"10.1111\/phor.12364","article-title":"Automated calibration of smartphone cameras for 3D reconstruction of mechanical pipes","volume":"36","author":"Maalek","year":"2021","journal-title":"Photogramm. Rec."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Maalek, R., and Lichti, D.D. (2021). New confocal hyperbola-based ellipse fitting with applications to estimating parameters of mechanical pipes from point clouds. Pattern Recognit., 116.","DOI":"10.1016\/j.patcog.2021.107948"},{"key":"ref_11","unstructured":"Sch\u00f6nberger, J.L. (2018). Robust Methods for Accurate and Efficient 3D Modeling from Unstructured Imagery, ETH Zurich."},{"key":"ref_12","first-page":"405","article-title":"The interpretation of structure from motion","volume":"203","author":"Ullman","year":"1979","journal-title":"Proc. R. Soc. Lond. Ser. B Biol. Sci."},{"key":"ref_13","first-page":"886","article-title":"Error analysis for circle fitting algorithms","volume":"3","author":"Chernov","year":"2009","journal-title":"Electron. J. Stat."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Chernov, N. (2010). Circular and Linear Regression, CRC Press.","DOI":"10.1201\/EBK1439835906"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Maalek, R. (2021). Field Information Modeling (FIM)\u2122: Best Practices Using Point Clouds. Remote Sens., 13.","DOI":"10.20944\/preprints202102.0304.v1"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"150","DOI":"10.1016\/j.autcon.2019.03.013","article-title":"Extraction of pipes and flanges from point clouds for automated verification of pre-fabricated modules in oil and gas refinery projects","volume":"103","author":"Maalek","year":"2019","journal-title":"Autom. Constr."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Maalek, R., Lichti, D.D., and Maalek, S. (2021). Towards automatic digital documentation and progress reporting of mechanical construction pipes using smartphones. Autom. Constr., 127.","DOI":"10.1016\/j.autcon.2021.103735"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"138","DOI":"10.1006\/cviu.1999.0832","article-title":"MLESAC: A New Robust Estimator with Application to Estimating Image Geometry","volume":"78","author":"Torr","year":"2000","journal-title":"Comput. Vis. Image Underst."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Maalek, R., Lichti, D.D., and Ruwanpura, J.Y. (2018). Robust Segmentation of Planar and Linear Features of Terrestrial Laser Scanner Point Clouds Acquired from Construction Sites. Sensors, 18.","DOI":"10.3390\/s18030819"},{"key":"ref_20","unstructured":"Olson, D.L., and Delen, D. (2008). Advanced Data Mining Techniques, Springer Science and Business Media LLC."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Hartley, R., Zisserman, A., and Faugeras, O. (2004). Multiple View Geometry in Computer Vision, Cambridge University Press. 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