{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,14]],"date-time":"2025-03-14T04:16:16Z","timestamp":1741925776558,"version":"3.38.0"},"reference-count":34,"publisher":"University of Toronto Press Inc. (UTPress)","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Cartographica"],"published-print":{"date-parts":[[2018,9]]},"abstract":"<jats:p> Visual exploration plays a critical role in point pattern analysis. It permits analysts to grasp a wide variety of spatial patterns in point distributions that are not necessarily detectable by mathematical and statistical methods. Since spatial patterns are scale-dependent, grid and kernel density maps are effective in analysis that can visualize point distributions at various scales from small to large. Visual exploration of these maps, however, takes a considerable amount of time even if the maps are generated automatically in GIS software. In addition, visual exploration inevitably becomes subjective and unstable when treating numerous maps simultaneously. It is not easy to evaluate and memorize spatial patterns in maps in a consistent and objective way. To resolve the problem, this article proposes new quantitative measures summarizing the characteristics of point distributions. The measures can be visualized as maps that help analysts to capture the overall spatial pattern of point distributions efficiently. Numerical experiments and applications to real data analysis are performed to test the validity of the proposed measures. The results reveal the effectiveness of the measures, as well as their shortcomings, to be resolved in future research. <\/jats:p>","DOI":"10.3138\/cart.53.3.2017-0023","type":"journal-article","created":{"date-parts":[[2018,10,1]],"date-time":"2018-10-01T19:03:20Z","timestamp":1538420600000},"page":"185-202","source":"Crossref","is-referenced-by-count":1,"title":["Descriptive Measures of Point Distributions Summarized with Respect to Spatial Scale in Visualization"],"prefix":"10.3138","volume":"53","author":[{"given":"Yukio","family":"Sadahiro","sequence":"first","affiliation":[{"name":"Center for Spatial Information Science\u00a0\/ The University of Tokyo\u00a0\/ Kashiwanoha\u00a0\/ Kashiwa-shi\u00a0\/ Chiba\u00a0\/ Japan"}]}],"member":"1696","reference":[{"key":"r001","first-page":"97","author":"Anselin L","year":"2008","journal-title":"Environmental Criminology and Crime Analysis"},{"issue":"4","key":"r002","doi-asserted-by":"crossref","first-page":"607","DOI":"10.1111\/0033-0124.00250","volume":"52","author":"Atkinson P.M.","year":"2000","journal-title":"Professional Geographer"},{"key":"r003","first-page":"1","author":"Baddeley A.","year":"2007","journal-title":"Stochastic Geometry, Lecture Notes in Mathematics"},{"key":"r004","doi-asserted-by":"crossref","DOI":"10.1002\/9781118658222","volume-title":"Stochastic Geometry and Its Applications","author":"Chiu S.N.","year":"2013"},{"volume-title":"Statistics for Spatial Data","year":"2015","author":"Cressie N.","key":"r005"},{"volume-title":"Spatial Pattern Analysis in Plant Ecology","year":"2000","author":"Dale M.R.","key":"r006"},{"volume-title":"Cartography: Thematic Map Design","year":"1999","author":"Dent B.D.","key":"r007"},{"volume-title":"Statistical Analysis of Spatial Point Patterns","year":"1983","author":"Diggle P.J.","key":"r008"},{"key":"r009","doi-asserted-by":"crossref","DOI":"10.1002\/9780470977811","volume-title":"Cluster Analysis","author":"Everitt B.S.","year":"2011"},{"volume-title":"Spatial Analysis and Geocomputation: Selected Essays","year":"2006","author":"Fischer M.M.","key":"r010"},{"key":"r011","doi-asserted-by":"crossref","DOI":"10.1201\/b19706","volume-title":"Handbook of Cluster Analysis","author":"Hennig C.","year":"2015"},{"volume-title":"Statistical Analysis and Modelling of Spatial Point Patterns","year":"2008","author":"Illian J.","key":"r012"},{"volume-title":"Visual and Spatial Analysis: Advances in Data Mining, Reasoning, and Problem Solving","year":"2005","author":"Kovalerchuk B.","key":"r013"},{"issue":"1","key":"r014","doi-asserted-by":"crossref","first-page":"88","DOI":"10.1111\/j.0033-0124.1992.00088.x","volume":"44","author":"Lam N.S.-N.","year":"1992","journal-title":"Professional Geographer"},{"issue":"4","key":"r015","doi-asserted-by":"crossref","first-page":"301","DOI":"10.1111\/j.1538-4632.1984.tb00818.x","volume":"16","author":"Okabe A.","year":"1984","journal-title":"Geographical Analysis"},{"issue":"4","key":"r016","doi-asserted-by":"crossref","first-page":"286","DOI":"10.1111\/j.1538-4632.1995.tb00912.x","volume":"27","author":"Ord J.K.","year":"1995","journal-title":"Geographical Analysis"},{"key":"r017","doi-asserted-by":"crossref","DOI":"10.1201\/b18808","volume-title":"Spatial Analysis: Statistics, Visualization, and Computational Methods","author":"Oyana T.J.","year":"2015"},{"issue":"1","key":"r018","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1111\/j.1538-4632.1976.tb00530.x","volume":"8","author":"Pfaltz J.L.","year":"1976","journal-title":"Geographical Analysis"},{"volume-title":"Scale in Remote Sensing and GIS","year":"1997","author":"Quattrochi D.A.","key":"r019"},{"issue":"2","key":"r020","doi-asserted-by":"crossref","first-page":"255","DOI":"10.2307\/3212829","volume":"13","author":"Ripley B.D.","year":"1976","journal-title":"Journal of Applied Probability"},{"issue":"2","key":"r021","doi-asserted-by":"crossref","first-page":"172","DOI":"10.1111\/j.2517-6161.1977.tb01615.x","volume":"39","author":"Ripley B.D.","year":"1977","journal-title":"Journal of the Royal Statistical Society Series B (Methodological)"},{"volume-title":"Elements of Cartography","year":"1995","author":"Robinson A.","key":"r022"},{"issue":"6","key":"r023","doi-asserted-by":"crossref","first-page":"523","DOI":"10.1080\/13658810110060433","volume":"15","author":"Sadahiro Y.","year":"2001","journal-title":"International Journal of Geographical Information Science"},{"key":"r024","doi-asserted-by":"crossref","DOI":"10.1002\/9781118575574","volume-title":"Multivariate Density Estimation: Theory, Practice, and Visualization","author":"Scott D.W.","year":"2015"},{"volume-title":"Density Estimation for Statistics and Data Analysis","year":"1986","author":"Silverman B.W.","key":"r025"},{"volume-title":"Thematic Cartography and Geovisualization","year":"2009","author":"Slocum T.A.","key":"r026"},{"volume-title":"Fractals, Random Shapes and Point Fields. 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