{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,15]],"date-time":"2026-01-15T13:30:59Z","timestamp":1768483859354,"version":"3.49.0"},"reference-count":37,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2021,3,23]],"date-time":"2021-03-23T00:00:00Z","timestamp":1616457600000},"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>Automated fruit inspection using cameras involves the analysis of a collection of views of the same fruit obtained by rotating a fruit while it is transported. Conventionally, each view is analyzed independently. However, in order to get a global score of the fruit quality, it is necessary to match the defects between adjacent views to prevent counting them more than once and assert that the whole surface has been examined. To accomplish this goal, this paper estimates the 3D rotation undergone by the fruit using a single camera. A 3D model of the fruit geometry is needed to estimate the rotation. This paper proposes to model the fruit shape as a 3D spheroid. The spheroid size and pose in each view is estimated from the silhouettes of all views. Once the geometric model has been fitted, a single 3D rotation for each view transition is estimated. Once all rotations have been estimated, it is possible to use them to propagate defects to neighbor views or to even build a topographic map of the whole fruit surface, thus opening the possibility to analyze a single image (the map) instead of a collection of individual views. A large effort was made to make this method as fast as possible. Execution times are under 0.5 ms to estimate each 3D rotation on a standard I7 CPU using a single core.<\/jats:p>","DOI":"10.3390\/s21062232","type":"journal-article","created":{"date-parts":[[2021,3,23]],"date-time":"2021-03-23T23:59:41Z","timestamp":1616543981000},"page":"2232","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Fast 3D Rotation Estimation of Fruits Using Spheroid Models"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0679-912X","authenticated-orcid":false,"given":"Antonio","family":"Albiol","sequence":"first","affiliation":[{"name":"ITEAM Research Institute, Universitat Polit\u00e8cnica de Val\u00e8ncia, 46022 Valencia, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1970-3289","authenticated-orcid":false,"given":"Alberto","family":"Albiol","sequence":"additional","affiliation":[{"name":"ITEAM Research Institute, Universitat Polit\u00e8cnica de Val\u00e8ncia, 46022 Valencia, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3878-4379","authenticated-orcid":false,"given":"Carlos","family":"S\u00e1nchez de Mer\u00e1s","sequence":"additional","affiliation":[{"name":"MultiScan Technologies S.L., 03820 Cocentaina, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,3,23]]},"reference":[{"key":"ref_1","unstructured":"Food and Agriculture Organization of the United Nations (2003). Assuring Food Safety and Quality: Guidelines for Strengthening National Food Control Systems, Food and Agriculture Organization of the United Nations, World Health Organization."},{"key":"ref_2","unstructured":"Li, D., and Zhao, C. (2010). A Review of Non-destructive Detection for Fruit Quality. Computer and Computing Technologies in Agriculture III, Springer."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1007\/s13197-011-0321-4","article-title":"Machine vision system: A tool for quality inspection of food and agricultural products","volume":"49","author":"Patel","year":"2012","journal-title":"J. Food Sci. Technol."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Guo, Z., Zhang, M., Dah-Jye, L., and Simons, T. (2020). Smart Camera for Quality Inspection and Grading of Food Products. Electronics, 9.","DOI":"10.3390\/electronics9030505"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"254","DOI":"10.1590\/S1981-67232013005000031","article-title":"Review: Computer vision applied to the inspection and quality control of fruits and vegetables","volume":"16","author":"Saldana","year":"2013","journal-title":"Braz. J. Food Technol."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Anish, P. (2017). Quality Inspection of Fruits and Vegetables using Colour Sorting in Machine Vision System: A review. Int. J. Emerg. Trends Eng. Dev., 6.","DOI":"10.26808\/rs.ed.i7v6.06"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1179\/1743131X14Y.0000000088","article-title":"Machine vision technology for detecting the external defects of fruits\u2014A review","volume":"63","author":"Li","year":"2015","journal-title":"Imaging Sci. J."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Demant, C., Streicher-Abel, B., Waszkewitz, P., Strick, M., and Schmidt, G. (1999). Industrial Image Processing: Visual Quality Control in Manufacturing, Springer-Electronic-Media.","DOI":"10.1007\/978-3-642-58550-0"},{"key":"ref_9","first-page":"225","article-title":"Block matching algorithms for motion estimation","volume":"8","author":"Barjatya","year":"2004","journal-title":"IEEE Trans. Evol. Comput."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"487","DOI":"10.1007\/s11947-010-0411-8","article-title":"Advances in Machine Vision Applications for Automatic Inspection and Quality Evaluation of Fruits and Vegetables","volume":"4","author":"Cubero","year":"2011","journal-title":"Food Bioprocess Technol."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.compag.2008.11.006","article-title":"Automatic sorting of satsuma (Citrus unshiu) segments using computer vision and morphological features","volume":"66","author":"Blasco","year":"2009","journal-title":"Comput. Electron. Agric."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Shiraishi, Y., and Takeda, F. (2011, January 19\u201321). Proposal of whole surface inspection system by simultaneous six-image capture of prolate spheroid-shaped fruit and vegetables. Proceedings of the 2011 Fourth International Conference on Modeling, Simulation and Applied Optimization, Kuala Lumpur, Malaysia.","DOI":"10.1109\/ICMSAO.2011.5775528"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1016\/j.jfoodeng.2017.02.008","article-title":"Automatic detection of defective apples using NIR coded structured light and fast lightness correction","volume":"203","author":"Zhang","year":"2017","journal-title":"J. Food Eng."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1016\/j.compag.2009.09.014","article-title":"In-line detection of apple defects using three color cameras system","volume":"70","author":"Zou","year":"2010","journal-title":"Comput. Electron. Agric."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1016\/S0168-1699(02)00093-5","article-title":"Computer vision based system for apple surface defect detection","volume":"36","author":"Li","year":"2002","journal-title":"Comput. Electron. Agric."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"449","DOI":"10.13031\/2013.20394","article-title":"Three-dimensional shape measurement of strawberries by volume intersection method","volume":"49","author":"Imou","year":"2006","journal-title":"Trans. ASABE"},{"key":"ref_17","first-page":"140","article-title":"Whole Surface Image Reconstruction for Machine Vision Inspection of Fruit","volume":"Volume 6761","author":"Chen","year":"2007","journal-title":"Optics for Natural Resources, Agriculture, and Foods II"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"4499","DOI":"10.1016\/j.biortech.2008.11.059","article-title":"Using parabolic mirrors for complete imaging of apple surfaces","volume":"100","author":"Reese","year":"2009","journal-title":"Bioresour. Technol."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1007\/s11694-008-9065-x","article-title":"Robotization in fruit grading system","volume":"3","author":"Kondo","year":"2009","journal-title":"Sens. Instrum. Food Qual. Saf."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Pham, Q.T., and Liou, N.S. (2020). Hyperspectral Imaging System with Rotation Platform for Investigation of Jujube Skin Defects. Appl. Sci., 10.","DOI":"10.3390\/app10082851"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1016\/j.biosystemseng.2014.03.009","article-title":"Early detection of mechanical damage in mango using NIR hyperspectral images and machine learning","volume":"122","author":"Rivera","year":"2014","journal-title":"Biosyst. Eng."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1135","DOI":"10.1007\/s11694-018-9728-1","article-title":"Mechatronic components in apple sorting machines with computer vision","volume":"12","author":"Navid","year":"2018","journal-title":"J. Food Meas. Charact."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"62","DOI":"10.1016\/j.jfoodeng.2014.09.002","article-title":"Development of a multispectral imaging system for online detection of bruises on apples","volume":"146","author":"Huang","year":"2015","journal-title":"J. Food Eng."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Wang, Y., and Chen, Y. (2020). Fruit Morphological Measurement Based on Three-Dimensional Reconstruction. Agronomy, 10.","DOI":"10.3390\/agronomy10040455"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1127","DOI":"10.1109\/34.62602","article-title":"On recognizing and positioning curved 3-D objects from image contours","volume":"12","author":"Kriegman","year":"1990","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"301","DOI":"10.1117\/12.976232","article-title":"3D-Motion Estimation from Projections","volume":"Volume 0697","author":"Tescher","year":"1986","journal-title":"Applications of Digital Image Processing IX"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1109\/ICPR.2006.983","article-title":"Reconstruction of Spheres using Occluding Contours from Stereo Images","volume":"Volume 1","author":"Wijewickrema","year":"2006","journal-title":"Proceedings of the 18th International Conference on Pattern Recognition"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/3DRes.02(2012)1","article-title":"3D reconstruction of polyhedral objects from single perspective projections using cubic corner","volume":"3","author":"Fang","year":"2012","journal-title":"3D Res."},{"key":"ref_29","unstructured":"Hilbert, D., and Cohn-Vossen, S. (1999). Geometry and the Imagination, AMS Chelsea Pub."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"124","DOI":"10.1006\/cgip.1994.1012","article-title":"Reconstructing Ellipsoids from Projections","volume":"56","author":"Karl","year":"1994","journal-title":"CVGIP Graph. Model. Image Process."},{"key":"ref_31","unstructured":"Hartley, R.I., and Zisserman, A. (2000). Multiple View Geometry in Computer Vision, Cambridge University Press."},{"key":"ref_32","unstructured":"Stirzaker, D. (1999). Jointly Distributed Random Variables. Probability and Random Variables: A Beginner\u2019s Guide, Cambridge University Press."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"144","DOI":"10.1016\/j.mechmachtheory.2015.03.004","article-title":"Euler-Rodrigues formula variations, quaternion conjugation and intrinsic connections","volume":"92","author":"Dai","year":"2015","journal-title":"Mech. Mach. Theory"},{"key":"ref_34","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."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1016\/0165-1684(95)00020-E","article-title":"Recursive implementation of the Gaussian filter","volume":"44","author":"Young","year":"1995","journal-title":"Signal Process."},{"key":"ref_36","unstructured":"(2021, January 01). Image Data Set. Available online: https:\/\/github.com\/alalbiol\/3d-rotation-estimation-fruits."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"26","DOI":"10.2478\/ausi-2018-0002","article-title":"Fruit recognition from images using deep learning","volume":"10","author":"Oltean","year":"2018","journal-title":"Acta Univ. Sapientiae Inform."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/6\/2232\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T05:39:34Z","timestamp":1760161174000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/6\/2232"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,3,23]]},"references-count":37,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2021,3]]}},"alternative-id":["s21062232"],"URL":"https:\/\/doi.org\/10.3390\/s21062232","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,3,23]]}}}