{"title":"Voronoi Tessellations and the Cosmic Web: Spatial Patterns and Clustering across the Universe","authors":"R. Weygaert","doi":"10.1109/ISVD.2007.48","DOIUrl":"https://doi.org/10.1109/ISVD.2007.48","url":null,"abstract":"The spatial cosmic matter distribution on scales of a few up to more than a hundred Megaparsec displays a salient and pervasive foamlike pattern. Voronoi tessellations are a versatile and flexible mathematical model for such weblike spatial patterns. They would be the natural result of an evolution in which low-density expanding void regions dictate the spatial organization of the Megaparsec Universe, while matter assembles in high-density filamentary and wall-like interstices between the voids. We describe the results of ongoing investigations of a variety of aspects of cosmologically relevant spatial distributions and statistics within the framework of Voronoi tessellations. Particularly enticing is the finding of a profound scaling of both clustering strength and clustering extent for the distribution of tessellation nodes, suggestive for the clustering properties of galaxy clusters. Cellular patterns may be the source of an intrinsic \"geometrically biased\" clustering.","PeriodicalId":280229,"journal":{"name":"International Symposium on Voronoi Diagrams in Science and Engineering","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131509442","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Unbiased Curvilinear Structure Extraction for Cartoon Images","authors":"Ping Yang, Guozhao Wang","doi":"10.1109/ISVD.2011.37","DOIUrl":"https://doi.org/10.1109/ISVD.2011.37","url":null,"abstract":"In this paper, a novel method for unbiased curvilinear structure extraction of cartoon images is proposed. Our method based on Delaunay triangulation can extract two types of curves, decorative curves and boundary curves, with sub-pixel accuracy. In order to make it, we start by estimating edge points from both types of curves, using the information of the curves and their surroundings. According to the properties of Delaunay triangulation on edge points, we not only estimate the precise position of curve points, but also find the connection relationships of decorative curve points. Compared with related curvilinear structure extraction algorithm, our method can compute the unbiased position of decorative curve points and boundary curve points and, more importantly, keep the topological relationship of decorative curves well.","PeriodicalId":280229,"journal":{"name":"International Symposium on Voronoi Diagrams in Science and Engineering","volume":"47 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125670582","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}