{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,13]],"date-time":"2024-09-13T17:38:05Z","timestamp":1726249085291},"reference-count":38,"publisher":"Wiley","issue":"3","license":[{"start":{"date-parts":[[2016,7,4]],"date-time":"2016-07-04T00:00:00Z","timestamp":1467590400000},"content-version":"vor","delay-in-days":33,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Computer Graphics Forum"],"published-print":{"date-parts":[[2016,6]]},"abstract":"Abstract<\/jats:title>For an ensemble of iso\u2010contours in multi\u2010dimensional scalar fields, we present new methods to a) visualize their dominant spatial patterns of variability, and b) to compute the conditional probability of the occurrence of a contour at one location given the occurrence at some other location. We first show how to derive a statistical model describing the contour variability, by representing the contours implicitly via signed distance functions and clustering similar functions in a reduced order space. We show that the spatial patterns of the ensemble can then be derived by analytically transforming the boundaries of a confidence interval computed from each cluster into the spatial domain. Furthermore, we introduce a mathematical basis for computing correlations between the occurrences of iso\u2010contours at different locations. We show that the computation of these correlations can be posed in the reduced order space as an integration problem over a region bounded by four hyper\u2010planes. To visualize the derived statistical properties we employ a variant of variability plots for streamlines, now including the color coding of probabilities of joint contour occurrences. We demonstrate the use of the proposed techniques for ensemble exploration in a number of 2D and 3D examples, using artificial and meteorological data sets.<\/jats:p>","DOI":"10.1111\/cgf.12898","type":"journal-article","created":{"date-parts":[[2016,7,4]],"date-time":"2016-07-04T13:54:40Z","timestamp":1467640480000},"page":"221-230","update-policy":"http:\/\/dx.doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":38,"title":["Visual Analysis of Spatial Variability and Global Correlations in Ensembles of Iso\u2010Contours"],"prefix":"10.1111","volume":"35","author":[{"given":"F.","family":"Ferstl","sequence":"first","affiliation":[{"name":"Computer Graphics and Visualization Group Technische Universit\u00e4t M\u00fcnchen Germany"}]},{"given":"M.","family":"Kanzler","sequence":"additional","affiliation":[{"name":"Computer Graphics and Visualization Group Technische Universit\u00e4t M\u00fcnchen Germany"}]},{"given":"M.","family":"Rautenhaus","sequence":"additional","affiliation":[{"name":"Computer Graphics and Visualization Group Technische Universit\u00e4t M\u00fcnchen Germany"}]},{"given":"R.","family":"Westermann","sequence":"additional","affiliation":[{"name":"Computer Graphics and Visualization Group Technische Universit\u00e4t M\u00fcnchen Germany"}]}],"member":"311","published-online":{"date-parts":[[2016,7,4]]},"reference":[{"key":"e_1_2_10_2_2","volume-title":"Meteorology Today","author":"Ahrens C.D.","year":"2008"},{"key":"e_1_2_10_3_2","doi-asserted-by":"publisher","DOI":"10.1023\/B:MACH.0000033116.57574.95"},{"key":"e_1_2_10_4_2","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1007\/978-1-4471-6497-5_1","volume-title":"Scientific Visualization.","author":"Bonneau G.\u2010P.","year":"2014"},{"key":"e_1_2_10_5_2","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-8659.2009.01689.x"},{"key":"e_1_2_10_6_2","doi-asserted-by":"crossref","unstructured":"BrownR.:Animated visual vibrations as an uncertainty visualisation technique. InGRAPHITE(2004) pp.84\u201389. 2","DOI":"10.1145\/988834.988849"},{"key":"e_1_2_10_7_2","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2006.168"},{"key":"e_1_2_10_8_2","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2015.2467204"},{"key":"e_1_2_10_9_2","doi-asserted-by":"crossref","unstructured":"FofonovA. MolchanovV. LinsenL.:Visual analysis of multi\u2010run spatio\u2010temporal simulations using isocontour similarity for projected views.IEEE Transactions on Visualization and Computer Graphics to appear(2015). 3","DOI":"10.1109\/TVCG.2015.2498554"},{"key":"e_1_2_10_10_2","volume-title":"Probabilistic Curve\u2010Aligned Clustering and Prediction with Mixture Models","author":"GAFFNEY S.","year":"2004"},{"key":"e_1_2_10_11_2","doi-asserted-by":"publisher","DOI":"10.1023\/B:STCO.0000035304.20635.31"},{"key":"e_1_2_10_12_2","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2004.30"},{"key":"e_1_2_10_13_2","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2013.141"},{"key":"e_1_2_10_14_2","first-page":"529","article-title":"Imagesurfer: A tool for visualizing correlations between two volume scalar fields","volume":"2004","author":"Jen D.","journal-title":"IEEE Visualization"},{"key":"e_1_2_10_15_2","doi-asserted-by":"publisher","DOI":"10.1109\/MCG.2003.1231171"},{"key":"e_1_2_10_16_2","first-page":"1842","article-title":"Visualization of anatomic covariance tensor fields","volume":"2004","author":"Kindlmann G.","journal-title":"Proc. IEEE Eng. in Medicine and Biology Society"},{"key":"e_1_2_10_17_2","unstructured":"LeventonM. GrimsonW. FaugerasO.:Statistical shape influence in geodesic active contours. InProc. IEEE Computer Vision and Pattern Recognition(2000) pp.316\u2013323. 3"},{"key":"e_1_2_10_18_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2007.02.014"},{"key":"e_1_2_10_19_2","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2012.150"},{"key":"e_1_2_10_20_2","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2014.2346455"},{"key":"e_1_2_10_21_2","doi-asserted-by":"publisher","DOI":"10.1109\/MCG.2014.52"},{"key":"e_1_2_10_22_2","doi-asserted-by":"crossref","unstructured":"OeltzeS. LehmannD.J. KuhnA. JanigaG. TheiselH. PreimB.:Blood flow clustering and applications in virtual stenting of intracranial aneurysms.IEEE Transactions on Visualization and Computer Graphics 20(5)(2014) 686\u2013701. 2 3","DOI":"10.1109\/TVCG.2013.2297914"},{"key":"e_1_2_10_23_2","first-page":"1","article-title":"Positional uncertainty of isocontours: Condition analysis and probabilistic measures","volume":"99","author":"P\u00f6thkow K.","year":"2010","journal-title":"IEEE Transactions on Visualization and Computer Graphics"},{"key":"e_1_2_10_24_2","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-8659.2011.01944.x"},{"key":"e_1_2_10_25_2","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-8659.2012.03095.x"},{"key":"e_1_2_10_26_2","doi-asserted-by":"crossref","unstructured":"PotterK. WilsonA. BremerP.\u2010T. WilliamsD. DoutriauxC. PascucciV. JohnsonC.R.:Ensemble\u2010Vis: A framework for the statistical visualization of ensemble data. InProc. IEEE Int. Conf. on Data Mining Workshops(2009) pp.233\u2013240. 2","DOI":"10.1109\/ICDMW.2009.55"},{"key":"e_1_2_10_27_2","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-8659.2011.01942.x"},{"key":"e_1_2_10_28_2","doi-asserted-by":"publisher","DOI":"10.1007\/s003710050111"},{"key":"e_1_2_10_29_2","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2015.2467754"},{"key":"e_1_2_10_30_2","doi-asserted-by":"publisher","DOI":"10.1117\/12.641417"},{"key":"e_1_2_10_31_2","doi-asserted-by":"publisher","DOI":"10.5194\/gmd-8-2329-2015"},{"key":"e_1_2_10_32_2","unstructured":"SalvadorS. ChanP.:Determining the number of clusters\/segments in hierarchical clustering\/segmentation algorithms. InProc. of the 16th IEEE International Conference on Tools with Artificial Intelligence(2004) pp.576\u2013584. 7"},{"key":"e_1_2_10_33_2","volume-title":"Level set methods and fast marching methods: evolving interfaces in computational geometry, fluid mechanics, computer vision, and materials science","author":"Sethian J.A.","year":"1999"},{"key":"e_1_2_10_34_2","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2006.165"},{"key":"e_1_2_10_35_2","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2010.181"},{"key":"e_1_2_10_36_2","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2014.2346332"},{"key":"e_1_2_10_37_2","doi-asserted-by":"publisher","DOI":"10.1016\/B978-0-12-385022-5.00008-7"},{"key":"e_1_2_10_38_2","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2013.143"},{"key":"e_1_2_10_39_2","doi-asserted-by":"crossref","unstructured":"ZhangZ. HuangK. TanT.:Comparison of similarity measures for trajectory clustering in outdoor surveillance scenes. InProc. 18th Int. Conf. on Pattern Recognition(2006) pp.1135\u20131138. 2","DOI":"10.1109\/ICPR.2006.392"}],"container-title":["Computer Graphics Forum"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1111%2Fcgf.12898","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1111\/cgf.12898","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,4]],"date-time":"2023-10-04T05:46:49Z","timestamp":1696398409000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1111\/cgf.12898"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,6]]},"references-count":38,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2016,6]]}},"alternative-id":["10.1111\/cgf.12898"],"URL":"https:\/\/doi.org\/10.1111\/cgf.12898","archive":["Portico"],"relation":{},"ISSN":["0167-7055","1467-8659"],"issn-type":[{"value":"0167-7055","type":"print"},{"value":"1467-8659","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,6]]},"assertion":[{"value":"2016-07-04","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}