{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,25]],"date-time":"2026-03-25T07:51:46Z","timestamp":1774425106647,"version":"3.50.1"},"reference-count":40,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2022,4,18]],"date-time":"2022-04-18T00:00:00Z","timestamp":1650240000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Science Foundation Committee of China","award":["41930101"],"award-info":[{"award-number":["41930101"]}]},{"name":"National Science Foundation Committee of China","award":["42161066"],"award-info":[{"award-number":["42161066"]}]},{"name":"Education Department of Gansu: &quot;Star of Innovation&quot; Fund for outstanding Graduate students","award":["2021CXZX-548"],"award-info":[{"award-number":["2021CXZX-548"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IJGI"],"abstract":"<jats:p>Quantitative relations between topological similarity degree and map scale change of multi-scale contour clusters are vital to the automation of map generalization. However, no method has been proposed to calculate the relations. This paper aims at filling the gap by proposing a new approach. It firstly constructed a directed contour tree by pre-processing of unclosed contours, and then developed a quantitative expression of topological relations of contour cluster based on directed contour tree. After this, it employed 108 groups of multi-scale contour clusters with different geomorphological types to explore the changing regularity of topological indices with map scale. Last, it used 416 points to calculate the quantitative relations between topological similarity degree and map scale change by curve fitting method. The results show that the quantitative expression of multi-scale topological indexes is closely related to the contour interval change, and power function is the best fit among the candidate functions.<\/jats:p>","DOI":"10.3390\/ijgi11040268","type":"journal-article","created":{"date-parts":[[2022,4,18]],"date-time":"2022-04-18T22:04:02Z","timestamp":1650319442000},"page":"268","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Quantitative Relations between Topological Similarity Degree and Map Scale Change of Contour Clusters in Multi-Scale Map Spaces"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5497-3447","authenticated-orcid":false,"given":"Rong","family":"Wang","sequence":"first","affiliation":[{"name":"College of Resources and Environmental Engineering, Tianshui Normal University, Tianshui 741001, China"},{"name":"Faculty of Geomatics, Lanzhou Jiaotong University, Lanzhou 730070, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2792-3425","authenticated-orcid":false,"given":"Haowen","family":"Yan","sequence":"additional","affiliation":[{"name":"Faculty of Geomatics, Lanzhou Jiaotong University, Lanzhou 730070, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaomin","family":"Lu","sequence":"additional","affiliation":[{"name":"Faculty of Geomatics, Lanzhou Jiaotong University, Lanzhou 730070, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,4,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Yan, H.W., and Li, J. (2014). Spatial Similarity Relations in Multi-Scale Map Spaces, Springer International Publishing.","DOI":"10.1007\/978-3-319-09743-5"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"471","DOI":"10.1080\/10106049.2016.1155659","article-title":"An assessment of spatial similarity degree between polylines on multi-scale, multi-source maps","volume":"32","author":"Chehreghan","year":"2017","journal-title":"Geocarto Int."},{"key":"ref_3","first-page":"1683","article-title":"Shape similarity measurement based on DNA alignment for buildings with multiple orthogonal features","volume":"50","author":"Wei","year":"2021","journal-title":"Acta Geod. Cartogr. Sin."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1415","DOI":"10.1080\/13658816.2011.635595","article-title":"Semantic similarity measurement based on knowledge mining: An artificial neural net approach","volume":"26","author":"Li","year":"2012","journal-title":"Int. J. Geogr. Inf. Sci."},{"key":"ref_5","first-page":"95","article-title":"Semantic similarity measurement for building polygon aggregation in multi-scale map space","volume":"51","author":"Gao","year":"2022","journal-title":"Acta Geod. Cartogr. Sin."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1207\/s15427633scc0601_2","article-title":"TDD: A comprehensive model for qualitative spatial similarity assessment","volume":"6","author":"Li","year":"2006","journal-title":"Spat. Cogn. Comput."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Zhang, L., and Guilbert, E. (2016). Evaluation of river network generalization methods for preserving the drainage pattern. Int. J. Geo-Inf., 5.","DOI":"10.3390\/ijgi5120230"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1016\/j.isprsjprs.2019.02.010","article-title":"A graph convolution neural network for classification of building patterns using spatial vector data","volume":"150","author":"Yan","year":"2019","journal-title":"ISPRS J. Photogramm. Remote Sens."},{"key":"ref_9","first-page":"874","article-title":"A simplification of residential feature by the shape cognition and template matching method","volume":"45","author":"Yan","year":"2016","journal-title":"Acta Geod. Cartogr. Sin."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"700","DOI":"10.1080\/13658816.2013.867495","article-title":"Quality assessment for building footprints data on OpenStreetMap","volume":"28","author":"Fan","year":"2014","journal-title":"Int. J. Geogr. Inf. Sci."},{"key":"ref_11","first-page":"728","article-title":"Geographical entity-oriented semantic similarity measurement method and its application in road matching","volume":"45","author":"Zhao","year":"2020","journal-title":"Geomat. Inf. Sci. Wuhan Univ."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"748","DOI":"10.1080\/13658816.2015.1100732","article-title":"A polygon-based approach for matching openstreetmap road network with regional transit authority data","volume":"30","author":"Fan","year":"2016","journal-title":"Int. J. Geogr. Inf. Sci."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"255","DOI":"10.1080\/15230406.2017.1324823","article-title":"A geometric-based approach for road matching on multi-scale datasets using a genetic algorithm","volume":"45","author":"Chehreghan","year":"2018","journal-title":"Cartogr. Geogr. Inf. Sci."},{"key":"ref_14","unstructured":"Ruas, A. (2010, January 18). Automating the generalization of geographical data. Proceedings of the 20th International Cartographic Conference, Beijing, China."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1016\/j.geog.2015.03.002","article-title":"Formula for calculating spatial similarity degrees between point clouds on multi-scale maps taking map scale change as the only independent variable","volume":"6","author":"Yang","year":"2015","journal-title":"Geod. Geodyn."},{"key":"ref_16","unstructured":"Wang, J.Y., He, Z.Y., and Pu, Y.X. (2016). Cartography, Surveying and Mapping Press."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1179\/caj.2000.37.1.29","article-title":"An integrated technique for automated generalization of contour maps","volume":"37","author":"Li","year":"2000","journal-title":"Cartogr. J."},{"key":"ref_18","unstructured":"Guo, R.Z. (2001). Spatial Analysis, Higher Education Press."},{"key":"ref_19","unstructured":"Yan, H.W., and Wang, J.Y. (2009). Description Approaches and Automates Generalization Algorithms for Groups of Map Objects, The Science Press."},{"key":"ref_20","first-page":"801","article-title":"A voronoi interior adjacency-based approach for generating a contour tree","volume":"30","author":"Qiao","year":"2005","journal-title":"Geomat. Inf. Sci. Wuhan Univ."},{"key":"ref_21","first-page":"461","article-title":"The method of generating contour tree based on contour Delaunay triangulation","volume":"41","author":"Zhang","year":"2012","journal-title":"Acta Geod. Cartogr. Sin."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1080\/13658810151072831","article-title":"A Voronoi-based 9-intersection Model for Spatial Relations","volume":"15","author":"Chen","year":"2001","journal-title":"ISPRS J. Geogr. Inf. Sci."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"60","DOI":"10.1016\/j.isprsjprs.2004.04.001","article-title":"Voronoi-based k-order Neighbor Relations for Spatial Analysis","volume":"59","author":"Chen","year":"2004","journal-title":"ISPRS J. Photogramm. Remote Sens."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"699","DOI":"10.1080\/13658810210149416","article-title":"Quantitative Measures for Spatial Information of Maps","volume":"16","author":"Li","year":"2002","journal-title":"Int. J. Geogr. Inf. Sci."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1007\/BF02838664","article-title":"A method for generating contour tree based on voronoi interior adjacency","volume":"8","author":"Qiao","year":"2005","journal-title":"Geo-Spat. Inf. Sci."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"355","DOI":"10.1016\/j.cageo.2003.06.001","article-title":"A Voronoi Interior Adjacency based Approach for Generating a Contour Tree","volume":"30","author":"Chen","year":"2004","journal-title":"Comput. Geosci."},{"key":"ref_27","first-page":"147","article-title":"A Contour Group Mixed Similarity Measurement Model for Region Incremental Updating","volume":"21","author":"Guo","year":"2019","journal-title":"J. Geo-Inf. Sci."},{"key":"ref_28","first-page":"643","article-title":"A multisource contour matching method considering the similarity of geometric features","volume":"48","author":"Guo","year":"2019","journal-title":"Acta Geod. Cartogr. Sin."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1016\/j.isprsjprs.2007.04.002","article-title":"The drainage network extraction from contour lines for contour line generalization","volume":"62","author":"Ai","year":"2007","journal-title":"ISPRS J. Photogramm. Remote Sens."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"666","DOI":"10.1080\/13658816.2018.1554814","article-title":"A spatio-contextual probabilistic model for extracting linear feature in hilly terrain from high-resolution DEM data","volume":"33","author":"Zhou","year":"2019","journal-title":"Int. J. Geogr. Inf. Sci."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"601","DOI":"10.1080\/1365881031000135500","article-title":"Wavelets applied to simplification of digital terrain models","volume":"17","author":"Bjorke","year":"2003","journal-title":"Int. J. Geogr. Inf. Sci."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"198","DOI":"10.1016\/j.isprsjprs.2009.11.001","article-title":"A DEM generalization by minor valley branch detection and grid filling","volume":"65","author":"Ai","year":"2010","journal-title":"ISPRS J. Photogramm. Remote Sens."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"38","DOI":"10.1016\/j.isprsjprs.2010.08.005","article-title":"Generalization of DEM for terrain analysis using a compound method","volume":"66","author":"Zhou","year":"2011","journal-title":"ISPRS J. Photogramm. Remote Sens."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"154","DOI":"10.1080\/13658816.2012.674136","article-title":"An orthogonal least-square-based method for DEM generalization","volume":"27","author":"Chen","year":"2013","journal-title":"Int. J. Geogr. Inf. Sci."},{"key":"ref_35","unstructured":"Wang, J.Y. (2019). Geomorphology and Its Generalization, Surveying & Mapping Publishing House."},{"key":"ref_36","first-page":"771","article-title":"Quantitative extraction and analysis of basic morphological types of land geomorphology in china","volume":"21","author":"Chen","year":"2011","journal-title":"J. Geogr. Sci."},{"key":"ref_37","unstructured":"Hao, X.Y. (2001). Map Information Recognition and Extraction Technology, Surveying & Mapping Publishing House."},{"key":"ref_38","unstructured":"Wu, H.H. (2012). GIS and Basic Model and Algorithm of Map Information Generalization, Wuhan University Press."},{"key":"ref_39","first-page":"31","article-title":"Spatial relation rules and progressive graphic simplification of contours","volume":"25","author":"Guo","year":"2000","journal-title":"Geomat. Inf. Sci. Wuhan Univ."},{"key":"ref_40","unstructured":"Nigel, W. (1995). Geographical Data Analysis, Wiley & Sons Ltd."}],"container-title":["ISPRS International Journal of Geo-Information"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2220-9964\/11\/4\/268\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T22:56:17Z","timestamp":1760136977000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2220-9964\/11\/4\/268"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,4,18]]},"references-count":40,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2022,4]]}},"alternative-id":["ijgi11040268"],"URL":"https:\/\/doi.org\/10.3390\/ijgi11040268","relation":{},"ISSN":["2220-9964"],"issn-type":[{"value":"2220-9964","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,4,18]]}}}