{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,5]],"date-time":"2026-03-05T03:34:05Z","timestamp":1772681645201,"version":"3.50.1"},"reference-count":41,"publisher":"MDPI AG","issue":"16","license":[{"start":{"date-parts":[[2021,8,4]],"date-time":"2021-08-04T00:00:00Z","timestamp":1628035200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["U19A2061"],"award-info":[{"award-number":["U19A2061"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Japan Science and Technology Agency (JST) CREST program","award":["JPMJCR1512"],"award-info":[{"award-number":["JPMJCR1512"]}]},{"name":"Japan Science and Technology Agency (JST) SICORP Program","award":["JPMJSC16H2"],"award-info":[{"award-number":["JPMJSC16H2"]}]},{"name":"International Science &amp; Technology Innovation Program of Chinese Academy of Agricultural Sciences (CAASTIP)","award":["CAAS-ZDRW202107"],"award-info":[{"award-number":["CAAS-ZDRW202107"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Convenient, efficient, and high-throughput estimation of wheat heading dates is of great significance in plant sciences and agricultural research. However, documenting heading dates is time-consuming, labor-intensive, and subjective on a large-scale field. To overcome these challenges, model- and image-based approaches are used to estimate heading dates. Phenology models usually require complicated parameters calibrations, making it difficult to model other varieties and different locations, while in situ field-image recognition usually requires the deployment of a large amount of observational equipment, which is expensive. Therefore, in this study, we proposed a growth curve-based method for estimating wheat heading dates. The method first generates a height-based continuous growth curve based on five time-series unmanned aerial vehicle (UAV) images captured over the entire wheat growth cycle (&gt;200 d). Then estimate the heading date by generated growth curve. As a result, the proposed method had a mean absolute error of 2.81 d and a root mean square error of 3.49 d for 72 wheat plots composed of different varieties and densities sown on different dates. Thus, the proposed method is straightforward, efficient, and affordable and meets the high-throughput estimation requirements of large-scale fields and underdeveloped areas.<\/jats:p>","DOI":"10.3390\/rs13163067","type":"journal-article","created":{"date-parts":[[2021,8,4]],"date-time":"2021-08-04T21:44:24Z","timestamp":1628113464000},"page":"3067","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["An Efficient Method for Estimating Wheat Heading Dates Using UAV Images"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9712-7822","authenticated-orcid":false,"given":"Licheng","family":"Zhao","sequence":"first","affiliation":[{"name":"Key Laboratory of Agricultural Remote Sensing (AGRIRS), Ministry of Agriculture and Rural Affairs, Institute of Agricultural Resources and Regional Planning, Chinese Academy of Agricultural Sciences, Beijing 100081, China"},{"name":"Institute for Sustainable Agro-Ecosystem Services, Graduate School of Agricultural and Life Science, The University of Tokyo, Tokyo 188-0002, Japan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3017-5464","authenticated-orcid":false,"given":"Wei","family":"Guo","sequence":"additional","affiliation":[{"name":"Institute for Sustainable Agro-Ecosystem Services, Graduate School of Agricultural and Life Science, The University of Tokyo, Tokyo 188-0002, Japan"}]},{"given":"Jian","family":"Wang","sequence":"additional","affiliation":[{"name":"Institute of Cotton Research, Shanxi Agricultural University, Yuncheng 044000, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6135-402X","authenticated-orcid":false,"given":"Haozhou","family":"Wang","sequence":"additional","affiliation":[{"name":"Institute for Sustainable Agro-Ecosystem Services, Graduate School of Agricultural and Life Science, The University of Tokyo, Tokyo 188-0002, Japan"}]},{"given":"Yulin","family":"Duan","sequence":"additional","affiliation":[{"name":"Key Laboratory of Agricultural Remote Sensing (AGRIRS), Ministry of Agriculture and Rural Affairs, Institute of Agricultural Resources and Regional Planning, Chinese Academy of Agricultural Sciences, Beijing 100081, China"}]},{"given":"Cong","family":"Wang","sequence":"additional","affiliation":[{"name":"Key Laboratory of Agricultural Remote Sensing (AGRIRS), Ministry of Agriculture and Rural Affairs, Institute of Agricultural Resources and Regional Planning, Chinese Academy of Agricultural Sciences, Beijing 100081, China"}]},{"given":"Wenbin","family":"Wu","sequence":"additional","affiliation":[{"name":"Key Laboratory of Agricultural Remote Sensing (AGRIRS), Ministry of Agriculture and Rural Affairs, Institute of Agricultural Resources and Regional Planning, Chinese Academy of Agricultural Sciences, Beijing 100081, China"}]},{"given":"Yun","family":"Shi","sequence":"additional","affiliation":[{"name":"Key Laboratory of Agricultural Remote Sensing (AGRIRS), Ministry of Agriculture and Rural Affairs, Institute of Agricultural Resources and Regional Planning, Chinese Academy of Agricultural Sciences, Beijing 100081, China"}]}],"member":"1968","published-online":{"date-parts":[[2021,8,4]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"19703","DOI":"10.1073\/pnas.0701976104","article-title":"Global food security under climate change","volume":"104","author":"Schmidhuber","year":"2007","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"20260","DOI":"10.1073\/pnas.1116437108","article-title":"Global food demand and the sustainable intensification of agriculture","volume":"108","author":"Tilman","year":"2011","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1146\/annurev-publhealth-031816-044356","article-title":"Climate Change and Global Food Systems: Potential Impacts on Food Security and Undernutrition","volume":"38","author":"Myers","year":"2017","journal-title":"Annu. Rev. Public. Health"},{"key":"ref_4","unstructured":"IFPRI (2015). Actions and Accountability to Advance Nutrition & Sustainable Development\u2014Global Nutrition Report 2015, International Food Policy Research Institute."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"795","DOI":"10.3389\/fpls.2016.00795","article-title":"Wheat Phenological Development and Growth Studies As Affected by Drought and Late Season High Temperature Stress under Arid Environment","volume":"7","author":"Ihsan","year":"2016","journal-title":"Front. Plant Sci."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1016\/j.agrformet.2013.02.011","article-title":"Automatic image-based detection technology for two critical growth stages of maize: Emergence and three-leaf stage","volume":"174\u2013175","author":"Yu","year":"2013","journal-title":"Agric. For. Meteorol."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Kawakita, S., Takahashi, H., and Moriya, K. (2020). Prediction and parameter uncertainty for winter wheat phenology models depend on model and parameterization method differences. Agric. For. Meteorol., 290.","DOI":"10.1016\/j.agrformet.2020.107998"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Velumani, K., Madec, S., de Solan, B., Lopez-Lozano, R., Gillet, J., Labrosse, J., Jezequel, S., Comar, A., and Baret, F. (2020). An automatic method based on daily in situ images and deep learning to date wheat heading stage. Field Crop. Res., 252.","DOI":"10.1016\/j.fcr.2020.107793"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1016\/j.biosystemseng.2015.12.015","article-title":"In-field automatic observation of wheat heading stage using computer vision","volume":"143","author":"Zhu","year":"2016","journal-title":"Biosyst. Eng."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"260","DOI":"10.1016\/j.agrformet.2018.05.001","article-title":"Rice heading stage automatic observation by multi-classifier cascade based rice spike detection method","volume":"259","author":"Bai","year":"2018","journal-title":"Agric. For. Meteorol."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"s13007","DOI":"10.1186\/s13007-019-0457-1","article-title":"Automatic estimation of heading date of paddy rice using deep learning","volume":"15","author":"Desai","year":"2019","journal-title":"Plant Methods"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Wang, X., Xuan, H., Evers, B., Shrestha, S., Pless, R., and Poland, J. (2019). High-throughput phenotyping with deep learning gives insight into the genetic architecture of flowering time in wheat. Gigascience, 8.","DOI":"10.1101\/527911"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"374","DOI":"10.1080\/1343943X.2020.1740600","article-title":"Detection and characterization of quantitative trait loci for coleoptile elongation under anaerobic conditions in rice","volume":"23","author":"Nishimura","year":"2020","journal-title":"Plant Prod. Sci."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Holman, F., Riche, A., Michalski, A., Castle, M., Wooster, M., and Hawkesford, M. (2016). High Throughput Field Phenotyping of Wheat Plant Height and Growth Rate in Field Plot Trials Using UAV Based Remote Sensing. Remote Sens., 8.","DOI":"10.3390\/rs8121031"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Guo, W., Zheng, B., Duan, T., Fukatsu, T., Chapman, S., and Ninomiya, S. (2017). EasyPCC: Benchmark Datasets and Tools for High-Throughput Measurement of the Plant Canopy Coverage Ratio under Field Conditions. Sensors, 17.","DOI":"10.3390\/s17040798"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.isprsjprs.2019.05.008","article-title":"Pixel size of aerial imagery constrains the applications of unmanned aerial vehicle in crop breeding","volume":"154","author":"Hu","year":"2019","journal-title":"ISPRS J. Photogramm. Remote Sens."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"699","DOI":"10.1016\/j.foreco.2018.11.032","article-title":"Canopy temperature from an Unmanned Aerial Vehicle as an indicator of tree stress associated with red band needle blight severity","volume":"433","author":"Smigaj","year":"2019","journal-title":"For. Ecol. Manag."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"3243","DOI":"10.1080\/01431161.2019.1673914","article-title":"UAV-based thermal imaging in the assessment of water status of soybean plants","volume":"41","author":"Crusiol","year":"2020","journal-title":"Int. J. Remote Sens."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"3813","DOI":"10.1109\/JSTARS.2019.2938544","article-title":"Optimizing Spectral and Spatial Resolutions of Unmanned Aerial System Imaging Sensors for Monitoring Antarctic Vegetation","volume":"12","author":"Turner","year":"2019","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Jay, S., Baret, F., Dutartre, D., Malatesta, G., H\u00e9no, S., Comar, A., Weiss, M., and Maupas, F. (2019). Exploiting the centimeter resolution of UAV multispectral imagery to improve remote-sensing estimates of canopy structure and biochemistry in sugar beet crops. Remote Sens. Environ., 231.","DOI":"10.1016\/j.rse.2018.09.011"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"10395","DOI":"10.3390\/rs61110395","article-title":"Estimating Biomass of Barley Using Crop Surface Models (CSMs) Derived from UAV-Based RGB Imaging","volume":"6","author":"Bendig","year":"2014","journal-title":"Remote Sens."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Maimaitijiang, M., Sagan, V., Sidike, P., Hartling, S., Esposito, F., and Fritschi, F.B. (2020). Soybean yield prediction from UAV using multimodal data fusion and deep learning. Remote Sens. Environ., 237.","DOI":"10.1016\/j.rse.2019.111599"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1016\/j.isprsjprs.2020.02.013","article-title":"Above-ground biomass estimation and yield prediction in potato by using UAV-based RGB and hyperspectral imaging","volume":"162","author":"Li","year":"2020","journal-title":"ISPRS J. Photogramm. Remote Sens."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Siebring, J., Valente, J., Domingues Franceschini, M.H., Kamp, J., and Kooistra, L. (2019). Object-Based Image Analysis Applied to Low Altitude Aerial Imagery for Potato Plant Trait Retrieval and Pathogen Detection. Sensors, 19.","DOI":"10.3390\/s19245477"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1186\/s13007-019-0528-3","article-title":"DeepSeedling: Deep convolutional network and Kalman filter for plant seedling detection and counting in the field","volume":"15","author":"Jiang","year":"2019","journal-title":"Plant Methods"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Borra-Serrano, I., De Swaef, T., Quataert, P., Aper, J., Saleem, A., Saeys, W., Somers, B., Rold\u00e1n-Ruiz, I., and Lootens, P. (2020). Closing the Phenotyping Gap: High Resolution UAV Time Series for Soybean Growth Analysis Provides Objective Data from Field Trials. Remote Sens., 12.","DOI":"10.3390\/rs12101644"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"232","DOI":"10.1016\/j.compag.2017.07.008","article-title":"Crop height monitoring with digital imagery from Unmanned Aerial System (UAS)","volume":"141","author":"Chang","year":"2017","journal-title":"Comput. Electron. Agric."},{"key":"ref_28","unstructured":"The People\u2019s Government of Salt Lake District (2020, November 17). Y.C. Yuncheng Climate and Environment, Available online: http:\/\/www.yanhu.gov.cn\/zjyh\/yhrw\/qhhj\/index.shtml."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"415","DOI":"10.1111\/j.1365-3180.1974.tb01084.x","article-title":"A decimal code for the growth stages of cereals","volume":"14","author":"Zadoks","year":"1974","journal-title":"Weed Res."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Wang, H., Duan, Y., Shi, Y., Kato, Y., Ninomiya, S., and Guo, W. (2021). EasyIDP: A Python Package for Intermediate Data Processing in UAV-Based Plant Phenotyping. Remote Sens., 13.","DOI":"10.3390\/rs13132622"},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Verhulst, P.F. (1845). Recherches Math\u00e9matiques sur la loi D\u2019accroissement de la Population, par P.F. Verhulst, M. Hayez.","DOI":"10.3406\/marb.1845.3438"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"180","DOI":"10.1515\/opag-2018-0019","article-title":"How big is the potato (Solanum tuberosum L.) yield gap in Sub-Saharan Africa and why? A participatory approach","volume":"3","author":"Harahagazwe","year":"2018","journal-title":"Open Agric."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"150","DOI":"10.1186\/s13007-020-00693-3","article-title":"Nondestructive estimation of potato yield using relative variables derived from multi-period LAI and hyperspectral data based on weighted growth stage","volume":"16","author":"Luo","year":"2020","journal-title":"Plant Methods"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1016\/j.ecolmodel.2015.09.012","article-title":"Capture the time when plants reach their maximum body size by using the beta sigmoid growth equation","volume":"320","author":"Shi","year":"2016","journal-title":"Ecol. Model."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"261","DOI":"10.1038\/s41592-019-0686-2","article-title":"SciPy 1.0: Fundamental algorithms for scientific computing in Python","volume":"17","author":"Virtanen","year":"2020","journal-title":"Nat. Methods"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"2223","DOI":"10.2135\/cropsci2015.06.0357","article-title":"Phenotypic Plasticity of Winter Wheat Heading Date and Grain Yield across the US Great Plains","volume":"56","author":"Grogan","year":"2016","journal-title":"Crop Sci."},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Zhao, L., Shi, Y., Liu, B., Hovis, C., Duan, Y., and Shi, Z. (2019). Finer Classification of Crops by Fusing UAV Images and Sentinel-2A Data. Remote Sens., 11.","DOI":"10.3390\/rs11243012"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"359","DOI":"10.1016\/j.cam.2003.12.030","article-title":"Least-squares fitting Gompertz curve","volume":"169","author":"Kralik","year":"2004","journal-title":"J. Comput. Appl. Math."},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Bj\u00f6rck, A. (1996). Numerical Methods for Least Squares Problems, Society for Industrial and Applied Mathematics.","DOI":"10.1137\/1.9781611971484"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1080\/03610929608831686","article-title":"On the existence of the least squares estimate in nonlinear growth curve models of exponential type","volume":"25","author":"Demidenko","year":"1996","journal-title":"Commun. Stat. Theory Methods"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"437","DOI":"10.1093\/biomet\/87.2.437","article-title":"Is this the least squares estimate?","volume":"87","author":"Demidenko","year":"2000","journal-title":"Biometrika"}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/13\/16\/3067\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T06:40:36Z","timestamp":1760164836000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/13\/16\/3067"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,8,4]]},"references-count":41,"journal-issue":{"issue":"16","published-online":{"date-parts":[[2021,8]]}},"alternative-id":["rs13163067"],"URL":"https:\/\/doi.org\/10.3390\/rs13163067","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,8,4]]}}}