{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T00:54:13Z","timestamp":1760057653885,"version":"build-2065373602"},"reference-count":28,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2025,2,13]],"date-time":"2025-02-13T00:00:00Z","timestamp":1739404800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["42371461"],"award-info":[{"award-number":["42371461"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IJGI"],"abstract":"<jats:p>Natural language spatial relations are often ambiguous and polysemic. They are also pluralistic and subjective in nature. Their descriptive methods are crucial but difficult in cartography, geographic information science, and map generalization. \u201cBetween\u201d is a context-concerned spatial concept which is widely used to describe the arrangement of spatial objects. It involves the spatial distribution of at least three spatial objects and describes a scenario in which one (or more) object(s) is surrounded by objects on both sides. Existing models based on RCC and the n-intersection model are mainly used to describe binary spatial logic and are inadequate in describing the \u201cbetween\u201d ternary relation effectively. At present, although existing models can describe and reason about such ternary spatial relations, their limitations still exist. The description capability of ternary spatial relations is unspecific and polysemic, and certain results are inconsistent with spatial cognition and perception and application requirements. Therefore, this paper proposes a 4 Sides Intersection Model (4SIM) to express the spatial relation among ternary buildings in detail. Theoretically, 4SIM can effectively describe 45 spatial relations among ternary objects through the topological distances among the four boundaries of the region formed by the intermediate object and the two adjacent objects. The 4SIM has been demonstrated to offer a superior degree of accuracy in the depiction of spatial relations in comparison to the extant RIM method, thus providing new possibilities for map generalization.<\/jats:p>","DOI":"10.3390\/ijgi14020083","type":"journal-article","created":{"date-parts":[[2025,2,13]],"date-time":"2025-02-13T10:36:58Z","timestamp":1739443018000},"page":"83","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["4SIM: A Novel Description Model for the Ternary Spatial Relation \u201cBetween\u201d of Buildings"],"prefix":"10.3390","volume":"14","author":[{"given":"Hanxue","family":"Zhang","sequence":"first","affiliation":[{"name":"Institute of Surveying and Mapping, Information Engineering University, Avenue of Sciences, Zhengzhou 450001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6184-1300","authenticated-orcid":false,"given":"Xianyong","family":"Gong","sequence":"additional","affiliation":[{"name":"Institute of Surveying and Mapping, Information Engineering University, Avenue of Sciences, Zhengzhou 450001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chengyi","family":"Liu","sequence":"additional","affiliation":[{"name":"Institute of Surveying and Mapping, Information Engineering University, Avenue of Sciences, Zhengzhou 450001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fang","family":"Wu","sequence":"additional","affiliation":[{"name":"Institute of Surveying and Mapping, Information Engineering University, Avenue of Sciences, Zhengzhou 450001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4984-4920","authenticated-orcid":false,"given":"Yue","family":"Qiu","sequence":"additional","affiliation":[{"name":"Institute of Surveying and Mapping, Information Engineering University, Avenue of Sciences, Zhengzhou 450001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Andong","family":"Wang","sequence":"additional","affiliation":[{"name":"Institute of Surveying and Mapping, Information Engineering University, Avenue of Sciences, Zhengzhou 450001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0001-7836-1186","authenticated-orcid":false,"given":"Yuyang","family":"Qi","sequence":"additional","affiliation":[{"name":"Institute of Surveying and Mapping, Information Engineering University, Avenue of Sciences, Zhengzhou 450001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,2,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1023\/B:AMAI.0000018575.09226.ff","article-title":"Part and Complement: Fundamental Concepts in Spatial Relations John G","volume":"41","author":"Stell","year":"2004","journal-title":"Stell Ann. Math. Artif. Intell."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"58","DOI":"10.1080\/10095020.2022.2076619","article-title":"Deep Learning Models for Spatial Relation Extraction in Text","volume":"26","author":"Wu","year":"2022","journal-title":"Geo-Spat. Inf. Sci."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"922","DOI":"10.1080\/20445911.2011.586780","article-title":"The Nature of Categorical and Coordinate Spatial Relation Processing: An Interference Study","volume":"23","author":"Borst","year":"2011","journal-title":"J. Cogn. Psychol."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"10756","DOI":"10.1109\/LRA.2024.3477129","article-title":"Hierarchical Spatial Proximity Reasoning for Vision-and-Language Navigation","volume":"9","author":"Xu","year":"2024","journal-title":"IEEE Robot. Autom. Lett."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s10707-011-0146-3","article-title":"Building pattern recognition in topographic data: Examples on collinear and curvilinear alignments","volume":"17","author":"Zhang","year":"2013","journal-title":"Geoinformatica"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"26","DOI":"10.1016\/j.isprsjprs.2017.12.001","article-title":"Recognition of building group patterns in topographic maps based on graph partitioning and random forest","volume":"136","author":"He","year":"2018","journal-title":"ISPRS J. Photogramm. Remote Sens."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1080\/23729333.2019.1574371","article-title":"Using stroke and mesh to recognize building group patterns","volume":"6","author":"Wang","year":"2019","journal-title":"Int. J. Cartogr."},{"key":"ref_8","first-page":"159","article-title":"A Graph Match Approach to Typical Letter-like Pattern Recognition in Urban Building Groups","volume":"43","author":"Gong","year":"2018","journal-title":"Geomat. Inf. Sci. Wuhan Univ."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1016\/j.isprsjprs.2016.10.001","article-title":"Extracting building patterns with multilevel graph partition and building grouping","volume":"122","author":"Du","year":"2016","journal-title":"ISPRS J. Photogramm. Remote Sens."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"400","DOI":"10.1080\/15230406.2020.1757512","article-title":"Recognition of building group patterns using graph convolutional network","volume":"47","author":"Zhao","year":"2020","journal-title":"Cartogr. Geogr. Inf. Sci."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1032","DOI":"10.1080\/13658816.2020.1859513","article-title":"Qualitative-geometric \u2018surrounds\u2019 relations between disjoint regions","volume":"35","author":"Worboys","year":"2021","journal-title":"Int. J. Geogr. Inf. Sci."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"312","DOI":"10.1109\/TSMCB.2005.857095","article-title":"On the Ternary Spatial Relation \u201cBetween\u201d","volume":"36","author":"Bloch","year":"2006","journal-title":"IEEE Trans. Syst. Man Cybern. Part B (Cybern.)"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"893","DOI":"10.1080\/13658816.2020.1778002","article-title":"RIM: A ray intersection model for the analysis of the between relationship of spatial objects in a 2D plane","volume":"35","author":"Majic","year":"2020","journal-title":"Int. J. Geogr. Inf. Sci."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"757","DOI":"10.1016\/j.patcog.2011.06.016","article-title":"Modeling and measuring the spatial relation \u2018\u2018along\u2019\u2019: Regions, contours and fuzzy sets","volume":"45","author":"Takemura","year":"2012","journal-title":"Pattern Recognit."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"333","DOI":"10.3390\/ijgi1030333","article-title":"Spatial Relations Using High Level Concepts","volume":"1","author":"Corcoran","year":"2012","journal-title":"ISPRS Int. J. Geo-Inf."},{"key":"ref_16","first-page":"135","article-title":"Research Progress in Multi-scale Spatial Relations","volume":"17","author":"Du","year":"2015","journal-title":"J. Geo-Inf. Sci."},{"key":"ref_17","first-page":"165","article-title":"A spatial logic based on regions and connection","volume":"92","author":"Randell","year":"1992","journal-title":"Int. Conf. Princ. Knowl. Represent. Reason."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1080\/02693799108927841","article-title":"Point Set Topological Spatial Relations","volume":"5","author":"Egenhofer","year":"1991","journal-title":"Int. J. Geogr. Inf. Syst."},{"key":"ref_19","first-page":"1","article-title":"Categorizing binary topological relations between regions, lines and points in geographic databases","volume":"94","author":"Egenhofer","year":"1990","journal-title":"Santa Barbar. CA Natl. Cent. Geogr. Inf. Anal. Tech. Rep."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1016\/0020-0255(95)00289-8","article-title":"A model for representing topological relationships between complex geometric features in spatial databases","volume":"90","author":"Clementini","year":"1996","journal-title":"Inf. Sci."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BF02826800","article-title":"Improving 9-intersection model by replacing the complement with voronoi region","volume":"3","author":"Chen","year":"2000","journal-title":"Geo-Spat. Inf. Sci."},{"key":"ref_22","first-page":"533","article-title":"Definitions of Natural-Language Spatial Relations in GIS","volume":"30","author":"Du","year":"2005","journal-title":"Geomat. Inf. Sci. Wuhan Univ."},{"key":"ref_23","first-page":"77","article-title":"Natural-language Spatial Relations and Their Applications in GIS","volume":"9","author":"Zhang","year":"2007","journal-title":"J. Geo-Inf. Sci."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Freksa, C. (1992). Using Orientation Information for Qualitative Spatial Reasoning, Springer.","DOI":"10.1007\/3-540-55966-3_10"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1016\/0004-3702(92)90090-K","article-title":"Temporal reasoning based on semi-intervals","volume":"54","author":"Freksa","year":"1992","journal-title":"Artif. Intell."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"799","DOI":"10.1109\/TKDE.2006.102","article-title":"Modeling and Computing Ternary Projective Relations between Regions","volume":"18","author":"Clementini","year":"2006","journal-title":"IEEE Trans. Knowl. Data Eng."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Clementini, E. (2008). Projective Relations on the Sphere, Springer.","DOI":"10.1007\/978-3-540-87991-6_38"},{"key":"ref_28","first-page":"9:1","article-title":"Perceptions of Qualitative Spatial Arrangements of Three Objects","volume":"Volume 240","author":"Xu","year":"2022","journal-title":"Leibniz International Proceedings in Informatics (LIPIcs)"}],"container-title":["ISPRS International Journal of Geo-Information"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2220-9964\/14\/2\/83\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T16:33:50Z","timestamp":1760027630000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2220-9964\/14\/2\/83"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,2,13]]},"references-count":28,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2025,2]]}},"alternative-id":["ijgi14020083"],"URL":"https:\/\/doi.org\/10.3390\/ijgi14020083","relation":{},"ISSN":["2220-9964"],"issn-type":[{"type":"electronic","value":"2220-9964"}],"subject":[],"published":{"date-parts":[[2025,2,13]]}}}