{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,12]],"date-time":"2026-05-12T05:27:03Z","timestamp":1778563623371,"version":"3.51.4"},"reference-count":30,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2022,4,25]],"date-time":"2022-04-25T00:00:00Z","timestamp":1650844800000},"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":["42171250"],"award-info":[{"award-number":["42171250"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["41801300"],"award-info":[{"award-number":["41801300"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["41901316"],"award-info":[{"award-number":["41901316"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>The rapid transformation from UTM (Universal Transverse Mecator) projection to Lambert projection helps to realize timely merging, inversion, and analysis of high-frequency partitioned remote sensing images. In this study, the transformation error and the efficiency of the linear rule approximation method, the improved linear rule approximation method, the hyperbolic transformation method, and the conformal transformation method were compared in transforming the coordinates of sample points on WGS84 (The World Geodetic System 1984)-UTM zonal projections to WGS84-Lambert projection coordinates. The effect of the grid aspect ratio on the coordinate transformation error of the conformal transformation method was examined. In addition, the conformal transformation method-based error spatial pattern of the sample points was analyzed. The results show that the conformal transformation method can better balance error and efficiency than other numerical methods. The error of the conformal transformation method is less affected by grid size. The maximum x-error is less than 0.36 m and the maximum y-error is less than 1.22 m when the grid size reaches 300 km \u00d7 300 km. The x- and y-error values decrease when square grids are used; namely, setting the grid aspect ratio close to 1 helps to weaken the effect of increasing grid area on the error. The dispersion of the error distribution and the maximum error of sample points both decrease relative to their minimum distance to the grid edge and stabilize at a minimum distance equal to 70 km. This study can support the rapid integration of massive remote sensing data over large areas.<\/jats:p>","DOI":"10.3390\/rs14092056","type":"journal-article","created":{"date-parts":[[2022,4,26]],"date-time":"2022-04-26T02:14:39Z","timestamp":1650939279000},"page":"2056","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Optimization of Numerical Methods for Transforming UTM Plane Coordinates to Lambert Plane Coordinates"],"prefix":"10.3390","volume":"14","author":[{"given":"Kuangxu","family":"Wang","sequence":"first","affiliation":[{"name":"State Key Laboratory of Earth Surface Processes and Resource Ecology, Beijing Normal University, Beijing 100875, China"},{"name":"Faculty of Geographical Science, Beijing Normal University, Beijing 100875, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8805-8914","authenticated-orcid":false,"given":"Sijing","family":"Ye","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Earth Surface Processes and Resource Ecology, Beijing Normal University, Beijing 100875, China"},{"name":"Faculty of Geographical Science, Beijing Normal University, Beijing 100875, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1714-779X","authenticated-orcid":false,"given":"Peichao","family":"Gao","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Earth Surface Processes and Resource Ecology, Beijing Normal University, Beijing 100875, China"},{"name":"Faculty of Geographical Science, Beijing Normal University, Beijing 100875, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8068-9415","authenticated-orcid":false,"given":"Xiaochuang","family":"Yao","sequence":"additional","affiliation":[{"name":"College of Land Science and Technology, China Agricultural University, Beijing 100083, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7100-1794","authenticated-orcid":false,"given":"Zuliang","family":"Zhao","sequence":"additional","affiliation":[{"name":"Zhejiang Development & Planning Institute, Hangzhou 310030, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,4,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"222","DOI":"10.1177\/0308518X211062232","article-title":"Visualizing Clustering Characteristics of Multidimensional Arable Land Quality Indexes at the County Level in Mainland China","volume":"54","author":"Ye","year":"2022","journal-title":"Environ. Plan. A Econ. Space"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"107757","DOI":"10.1016\/j.agee.2021.107757","article-title":"Spatial Patterns of County-level Arable Land Productive-capacity and Its Coordination with Land-use Intensity in Mainland China","volume":"326","author":"Ye","year":"2022","journal-title":"Agric. Ecosyst. Environ."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1016\/j.isprsjprs.2013.11.010","article-title":"CPU\/GPU Near Real-time Preprocessing for ZY-3 Satellite Images: Relative Radiometric Correction, MTF Compensation, and Geocorrection","volume":"87","author":"Fang","year":"2014","journal-title":"ISPRS J. Photogramm. Remote Sens."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"8501","DOI":"10.1109\/TGRS.2020.3045093","article-title":"Multisystem Interferometric Data Fusion Framework: A Three-Step Sensing Approach","volume":"59","author":"Yu","year":"2021","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_5","unstructured":"Chen, J., Xing, M., Yu, H., Liang, B., Peng, J., and Sun, G. (2021). Motion Compensation\/Autofocus in Airborne Synthetic Aperture Radar: A Review. IEEE Geosci. Remote Sens. Mag., 2\u201323."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Zhu, Y., Wang, M., Cheng, Y., He, L., and Xue, L. (2019). An Improved Jitter Detection Method Based on Parallax Observation of Multispectral Sensors for Gaofen-1 02\/03\/04 Satellites. Remote Sens., 11.","DOI":"10.3390\/rs11010016"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1559\/152304002782064619","article-title":"An Inverse Solution to the Winkel Tripel Projection Using Partial Derivatives","volume":"29","author":"Ipbuker","year":"2002","journal-title":"Cartogr. Geogr. Inf. Sci."},{"key":"ref_8","first-page":"55","article-title":"How to Transform the Coordinates of One Kind of Map Projection Point to Another Kind of Map Projection Point Coordinate Problem","volume":"1","author":"Wu","year":"1979","journal-title":"Acta Geogr. Sin."},{"key":"ref_9","unstructured":"Yang, Q., Snyder, J., and Tobler, W. (1999). Map Projection Transformation: Principles and Applications, CRC Press."},{"key":"ref_10","first-page":"150","article-title":"A Comprehensive Appraisial of Numerical Transformation Method for Map Projection","volume":"19","author":"Liu","year":"2002","journal-title":"J. Inst. Surv. Mapp."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Liu, D., Zhou, G., Huang, J., Zhang, R., Shu, L., Zhou, X., and Xin, C. (2019). On-board Georeferencing Using FPGA-based Optimized Second-order Polynomial Equation. Remote Sens., 11.","DOI":"10.3390\/rs11020124"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1003","DOI":"10.1016\/S0098-3004(03)00090-6","article-title":"Numerical Inverse Transformation for Map Projections","volume":"29","author":"Bildirici","year":"2003","journal-title":"Comput. Geosci."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"44","DOI":"10.1016\/j.cageo.2016.01.007","article-title":"Developing a Reversible Rapid Coordinate Transformation Model for the Cylindrical Projection","volume":"89","author":"Ye","year":"2016","journal-title":"Comput. Geosci."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1905","DOI":"10.1029\/JB076i008p01905","article-title":"Multiquadric Equations of Topography and Other Irregular Surfaces","volume":"76","author":"Hardy","year":"1971","journal-title":"J. Geophys. Res."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1016\/0898-1221(90)90272-L","article-title":"Theory and Applications of the Multiquadric-biharmonic Method 20 Years of Discovery 1968\u20131988","volume":"19","author":"Hardy","year":"1990","journal-title":"Comput. Math. Appl."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Zhao, Q., Duan, M., Yin, C., and Qin, C. (2002, January 31). Rapid algorithm of raster map projection transformation. Proceedings of the Second International Conference on Image and Graphics, Hefei, China.","DOI":"10.1117\/12.477135"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Mu, C., Chou, T., Hoang, T.V., Kung, P., Fang, Y., Chen, M., and Yeh, M. (2021). Development of Multilayer-Based Map Matching to Enhance Performance in Large Truck Fleet Dispatching. ISPRS Int. J. Geo-Inf., 10.","DOI":"10.3390\/ijgi10020079"},{"key":"ref_18","first-page":"18","article-title":"On the Numerical Method For transforming The Zones of Gauss Projection","volume":"11","author":"Yang","year":"1982","journal-title":"Acta Geod. Cartogr. Sin."},{"key":"ref_19","first-page":"268","article-title":"A Research on Numerical Transformation between Conformal Projections","volume":"11","author":"Yang","year":"1982","journal-title":"Acta Geod. Cartogr. Sin."},{"key":"ref_20","first-page":"214","article-title":"A Research on Transformation of Finiteelembnt between Conformal Projections","volume":"14","author":"Li","year":"1985","journal-title":"Acta Geod. Cartogr. Sin."},{"key":"ref_21","first-page":"61","article-title":"The Numerical Method of Transformation of Conformal Projection","volume":"14","author":"Liu","year":"1985","journal-title":"Acta Geod. Cartogr. Sin."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"482","DOI":"10.1080\/00330124.2012.700499","article-title":"Head\/tail Breaks: A New Classification Scheme for Data with a Heavy-tailed Distribution","volume":"65","author":"Jiang","year":"2013","journal-title":"Prof. Geogr."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1376","DOI":"10.3390\/rs10091376","article-title":"RDCRMG: A Raster Dataset Clean & Reconstitution Multi-grid Architecture for Remote Sensing Monitoring of Vegetation Dryness","volume":"10","author":"Ye","year":"2018","journal-title":"Remote Sens."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Yang, N., Liu, D., Feng, Q., Xiong, Q., Zhang, L., Ren, T., Zhao, Y., Zhu, D., and Huang, J. (2019). Large-Scale Crop Mapping Based on Machine Learning and Parallel Computation with Grids. Remote Sens., 11.","DOI":"10.3390\/rs11121500"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Zhang, L., Liu, Z., Liu, D., Xiong, Q., Yang, N., Ren, T., Zhang, C., Zhang, X., and Li, S. (2019). Crop Mapping Based on Historical Samples and New Training Samples Generation in Heilongjiang Province, China. Sustainability, 11.","DOI":"10.3390\/su11185052"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Yao, X., Li, G., Xia, J., Ben, J., Cao, Q., Zhao, L., Ma, Y., Zhang, L., and Zhu, D. (2020). Enabling the Big Earth Observation Data via Cloud Computing and DGGS: Opportunities and Challenges. Remote Sens., 12.","DOI":"10.3390\/rs12010062"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"104845","DOI":"10.1016\/j.landusepol.2020.104845","article-title":"Spatial Pattern of Arable Land-use Intensity in China","volume":"99","author":"Ye","year":"2020","journal-title":"Land Use Policy"},{"key":"ref_28","first-page":"102485","article-title":"Large-scale Crop Mapping from Multi-source Optical Satellite Imageries Using Machine Learning with Discrete Grids","volume":"103","author":"Yan","year":"2021","journal-title":"Int. J. Appl. Earth Obs. Geoinf."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"4432","DOI":"10.1109\/JSTARS.2014.2320635","article-title":"Development of a Highly Flexible Mobile GIS-Based System for Collecting Arable Land Quality Data","volume":"7","author":"Ye","year":"2014","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"4889","DOI":"10.1002\/ldr.4077","article-title":"A Soil Sampling Design for Arable Land Quality Observation by Using SPCOSA-CLHS Hybrid Approach","volume":"32","author":"Wan","year":"2021","journal-title":"Land Degrad. Dev."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/14\/9\/2056\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T23:00:44Z","timestamp":1760137244000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/14\/9\/2056"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,4,25]]},"references-count":30,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2022,5]]}},"alternative-id":["rs14092056"],"URL":"https:\/\/doi.org\/10.3390\/rs14092056","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,4,25]]}}}