{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:31:47Z","timestamp":1760239907022,"version":"build-2065373602"},"reference-count":37,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2019,1,15]],"date-time":"2019-01-15T00:00:00Z","timestamp":1547510400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IJGI"],"abstract":"<jats:p>Based on probabilistic time-geography, the encounter between two moving objects is random. The quantitative analysis of the probability of encounter needs to consider the actual geographical environment. The existing encounter probability algorithm is based on homogeneous space, ignoring the wide range of obstacles and their impact on encounter events. Based on this, this paper introduces obstacle factors, proposes encounter events that are constrained by obstacles, and constructs a model of the probability of encounters of moving objects based on the influence of obstacles on visual perception with the line-of-sight view analysis principle. In realistic obstacle space, this method provides a quantitative basis for predicting the encountering possibility of two mobile objects and the largest possible encounter location. Finally, the validity of the model is verified by experimental results. The model uses part of the Wuhan digital elevation model (DEM) data to calculate the encounter probability of two moving objects on it, and analyzes the temporal and spatial distribution characteristics of these probabilities.<\/jats:p>","DOI":"10.3390\/ijgi8010032","type":"journal-article","created":{"date-parts":[[2019,1,16]],"date-time":"2019-01-16T03:09:13Z","timestamp":1547608153000},"page":"32","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Probabilistic Model of Random Encounter in Obstacle Space"],"prefix":"10.3390","volume":"8","author":[{"given":"Zhang-Cai","family":"Yin","sequence":"first","affiliation":[{"name":"School of Resources and Environmental Engineering, Wuhan University of Technology, Wuhan 430061, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hui","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Resources and Environmental Engineering, Wuhan University of Technology, Wuhan 430061, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhi-Jun","family":"Zhang","sequence":"additional","affiliation":[{"name":"Tianjin Institute of Surveying and Mapping, Tianjin 300381, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhang-Hao-Nan","family":"Jin","sequence":"additional","affiliation":[{"name":"School of Resources and Environmental Engineering, Wuhan University of Technology, Wuhan 430061, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"San-Juan","family":"Li","sequence":"additional","affiliation":[{"name":"School of Resources and Environmental Engineering, Wuhan University of Technology, Wuhan 430061, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jia-Qiang","family":"Xiao","sequence":"additional","affiliation":[{"name":"School of Resources and Environmental Engineering, Wuhan University of Technology, Wuhan 430061, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,1,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"314","DOI":"10.1111\/gean.12097","article-title":"Latent trajectory models for space-time analysis: An application in deciphering spatial panel data","volume":"48","author":"An","year":"2016","journal-title":"Geogr. Anal."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Zhang, P., and Beernaerts, J. (2018). A Hybrid Approach Combining the Multi-Temporal Scale Spatio-Temporal Network with the Continuous Triangular Model for Exploring Dynamic Interactions in Movement Data: A Case Study of Football. Int. J. Geo-Inf., 7.","DOI":"10.3390\/ijgi7010031"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"38","DOI":"10.1186\/s40462-015-0064-3","article-title":"Mapping areas of spatial-temporal overlap from wildlife tracking data","volume":"3","author":"Long","year":"2015","journal-title":"Mov. Ecol."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1095","DOI":"10.1080\/13658810802097485","article-title":"Modeling uncertainty of moving objects on road networks via space\u2013time prisms","volume":"23","author":"Kuijpers","year":"2009","journal-title":"Int. J. Geogr. Inf. Sci."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1016\/j.proenv.2015.05.004","article-title":"Quantifying spatial-temporal interactions from wildlife tracking data: Issues of space, time, and statistical significance","volume":"26","year":"2015","journal-title":"Procedia Environ. Sci."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"855","DOI":"10.1080\/13658816.2013.818151","article-title":"Toward a kinetic-based probabilistic time geography","volume":"28","author":"Long","year":"2014","journal-title":"Int. J. Geogr. Inf. Sci."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1111\/j.1538-4632.2005.00575.x","article-title":"A measurement theory for time geography","volume":"37","author":"Miller","year":"2015","journal-title":"Geogr. Anal."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1080\/00045600802471049","article-title":"A field-based theory for time geography","volume":"99","author":"Miller","year":"2009","journal-title":"Ann. Assoc. Am. Geogr."},{"key":"ref_9","first-page":"16","article-title":"Time-geographic density estimation for moving point objects","volume":"Volume 6292","author":"Fabrikant","year":"2010","journal-title":"Geographic Information Science. GIScience 2010. Lecture Notes in Computer Science"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"405","DOI":"10.1016\/j.ecolmodel.2005.11.001","article-title":"Kernel-based home range method for data with irregular sampling intervals","volume":"194","author":"Katajisto","year":"2006","journal-title":"Ecol. Model."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1505","DOI":"10.1080\/13658816.2017.1421764","article-title":"Testing time-geographic density estimation for home range analysis using an agent-based model of animal movement","volume":"32","author":"Downs","year":"2018","journal-title":"Int. J. Geogr. Inf. Sci."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Mokbel, M., Scheuermann, P., and Aref, W.G. (2009). Towards a probabilistic time geography. ACM SIGSPATIAL GIS 2009, ACM Press.","DOI":"10.1145\/1773995.1773996"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1349","DOI":"10.1080\/13658811003619150","article-title":"Directed movements in probabilistic time geography","volume":"24","author":"Winter","year":"2010","journal-title":"Int. J. Geogr. Inf. Sci."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"104","DOI":"10.1080\/13658816.2013.830308","article-title":"Simulating visit probability distributions within planar space-time prisms","volume":"28","author":"Song","year":"2014","journal-title":"Int. J. Geogr. Inf. Sci."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"417","DOI":"10.1007\/s10707-010-0108-1","article-title":"The elements of probabilistic time geography","volume":"15","author":"Winter","year":"2011","journal-title":"GeoInformatica"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"875","DOI":"10.1080\/13658816.2013.850170","article-title":"Voxel-based probabilistic space-time prisms for analysing animal movements and habitat use","volume":"28","author":"Downs","year":"2014","journal-title":"Int. J. Geogr. Inf. Sci."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1026","DOI":"10.1080\/13658816.2018.1428748","article-title":"Random encounters in probabilistic time geography","volume":"32","author":"Yin","year":"2018","journal-title":"Int. J. Geogr. Inf. Sci."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1502","DOI":"10.1080\/00045608.2013.834236","article-title":"Reliable Space\u2013Time Prisms Under Travel Time Uncertainty","volume":"103","author":"Chen","year":"2013","journal-title":"Ann. Assoc. Am. Geogr."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1389","DOI":"10.1080\/13658816.2010.518571","article-title":"Modelling potential movement in constrained travel environments using rough space-time prisms","volume":"25","author":"Delafontaine","year":"2011","journal-title":"Int. J. Geogr. Inf. Sci."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"320","DOI":"10.1080\/13658816.2016.1199806","article-title":"Visual analytics of delays and interaction in movement data","volume":"31","author":"Konzack","year":"2017","journal-title":"Int. J. Geogr. Inf. Sci."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1111\/j.1435-5597.1970.tb01464.x","article-title":"What about people in regional science?","volume":"24","year":"1970","journal-title":"Pap. Reg. Sci."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"42","DOI":"10.3141\/2147-06","article-title":"Large Scale Automated Analysis of Vehicle Interactions and Collisions","volume":"2147","author":"Saunier","year":"2010","journal-title":"Transp. Res. Rec. J. Transp. Res. Board"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"74","DOI":"10.1080\/13658816.2015.1083995","article-title":"A wildlife movement approach to optimally locate wildlife crossing structures","volume":"30","author":"Loraamm","year":"2016","journal-title":"Int. J. Geogr. Inf. Sci."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1569","DOI":"10.1080\/13658816.2015.1033421","article-title":"Predicting human mobility with activity changes","volume":"29","author":"Huang","year":"2015","journal-title":"Int. J. Geogr. Inf. Sci."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Long, J.A. (2016). A Field-Based Time Geography for Wildlife Movement Analysis. International Conference on GIScience Short Paper Proceedings, Proceedings of the 9th International Conference on Geographic Information Science, Montreal, QC, Canada, 27\u201330 September 2016, Springer.","DOI":"10.21433\/B3113HT0M7HH"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.apgeog.2014.08.010","article-title":"Quantifying spatio-temporal interactions of animals using probabilistic space\u2013time prisms","volume":"55","author":"Downs","year":"2014","journal-title":"Appl. Geogr."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.apgeog.2015.04.004","article-title":"Personalising the viewshed: Visibility analysis from the human perspective","volume":"62","author":"Nutsford","year":"2015","journal-title":"Appl. Geogr."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"949","DOI":"10.1080\/13658810903473205","article-title":"Adaptive multi-resolution labeling in virtual landscapes","volume":"24","author":"Chen","year":"2010","journal-title":"Int. J. Geogr. Inf. Sci."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"2185","DOI":"10.1007\/s11432-010-4090-x","article-title":"An improved line-of-sight method for visibility analysis in 3D complex landscapes","volume":"53","author":"Liu","year":"2010","journal-title":"Sci. China Inf. Sci."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"84","DOI":"10.4113\/jom.2010.1107","article-title":"Route Ahead Visibility Mapping: A method to model how far ahead a motorist may view a designated route","volume":"6","author":"Bartie","year":"2010","journal-title":"J. Maps"},{"key":"ref_31","first-page":"313","article-title":"Optimal motion planning for mobile observers based on maximum visibility","volume":"11","author":"Wang","year":"2014","journal-title":"Dyn. Contin. Discret. Impuls. Syst. Ser. B Appl. Algorithms"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"e839","DOI":"10.1016\/j.na.2008.12.008","article-title":"Optimal visibility-based path and motion planning of mobile observers for 3-D objects","volume":"71","author":"Wang","year":"2009","journal-title":"Nonlinear Anal. Theory Methods Appl."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1080\/02693799408902004","article-title":"Line-of-sight communication on terrain models","volume":"8","author":"Floriani","year":"1994","journal-title":"Int. J. Geogr. Inf. Sci."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"1216","DOI":"10.1111\/1365-2656.12198","article-title":"A Critical Examination of Indices of Dynamic Interaction for Wildlife Telemetry Studies","volume":"83","author":"Long","year":"2014","journal-title":"J. Anim. Ecol."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1016\/j.anbehav.2014.01.030","article-title":"Movement-based analysis of interactions in African lions","volume":"90","author":"Benhamou","year":"2014","journal-title":"Anim. Behav."},{"key":"ref_36","first-page":"85","article-title":"Modeling movement probabilities within heterogeneous spatial fields","volume":"16","author":"Long","year":"2018","journal-title":"J. Spat. Inform. Sci."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"1223","DOI":"10.1080\/13658810903321339","article-title":"Anchor uncertainty and space-time prisms on road networks","volume":"24","author":"Kuijpers","year":"2014","journal-title":"Int. J. Geogr. Inf. Sci."}],"container-title":["ISPRS International Journal of Geo-Information"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2220-9964\/8\/1\/32\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T12:26:11Z","timestamp":1760185571000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2220-9964\/8\/1\/32"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,1,15]]},"references-count":37,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2019,1]]}},"alternative-id":["ijgi8010032"],"URL":"https:\/\/doi.org\/10.3390\/ijgi8010032","relation":{},"ISSN":["2220-9964"],"issn-type":[{"type":"electronic","value":"2220-9964"}],"subject":[],"published":{"date-parts":[[2019,1,15]]}}}