Title :
Geometry and Morphology of the Cosmic Web: Analyzing Spatial Patterns in the Universe
Author :
Weygaert, R. ; Jones, Bernard J T ; Platen, Erwin ; Aragón-Calvo, Miguel A.
Author_Institution :
Kapteyn Astron. Inst., Univ. of Groningen, Groningen, Netherlands
Abstract :
We review the analysis of the Cosmic Web by means of an extensive toolset based on the use of Delaunay and Voronoi tessellations. The Cosmic Web is the salientand pervasive foamlike pattern in which matter has organized itself on scales of a few up to more than a hundred Megaparsec. The weblike spatial arrangementof galaxies and mass into elongated filaments,sheetlike walls and dense compact clusters, the existence of large near-empty void regions and the hierarchical nature of this mass distribution are three major characteristics of the comsic matter distribution.First, we describe the Delaunay Tessellation Field Estimator.Using the unique adaptive qualities of Voronoi and Delaunay tessellations, DTFE infers the densityfield from the (contiguous) Voronoi tessellation of a sampled galaxy or simulation particle distribution and uses the Delaunay tessellation as adaptive grid for defining continuous volume-filling fields of density and other measured quantities through linear interpolation. The resulting DTFE formalism is shown to recover the hierarchical nature and the anisotropic morphologyof the cosmic matter distribution. The Multiscale Morphology Filter (MMF) uses the DTFE density field to extract the diverse morphological elements - filaments, sheets and clusters - on the basis of a ScaleSpace analysis which searches for these morphologies over a range of scales. Subsequently, we discuss the Watershed Voidfinder (WVF), which invokes the discrete watershed transform to identify voids in the cosmic matter distribution. The WVF is able todetermine the location, size and shape of the voids. The watershed transform is also a key element in the SpineWeb analysis of the cosmic matter distribution. Finding its mathematical foundation in Morse theory, it allowsthe determination of the filamentary spine and connected walls in the cosmic matter density field through the identification of the singularities and corresponding separatrices. The first results of a directimplem- entation on the Delaunay tessellation itself are presented. Finally, we describe the concept of Alphashapes for assessing the topology of the cosmic matter distribution.
Keywords :
astronomy computing; clusters of galaxies; computational geometry; cosmology; feature extraction; image representation; mathematical morphology; mesh generation; topology; Alphashapes; Cosmic Web; Delaunay tessellation field estimator; Morse theory; ScaleSpace analysis; SpineWeb analysis; Voronoi tessellations; Watershed Voidfinder; adaptive grid; anisotropic morphology; continuous volume-filling density fields; cosmic matter distribution topology; dense compact galaxy clusters; discrete watershed transform; filamentary spine; linear interpolation; multiscale morphology filter; near-empty void regions; simulation particle distribution; universe; weblike spatial arrangement; Anisotropic magnetoresistance; Density measurement; Discrete transforms; Filters; Geometry; Interpolation; Morphology; Particle measurements; Pattern analysis; Volume measurement; Cosmology; Methods; Surveys; large-scale; numerical; structure of Universe; theory;
Conference_Titel :
Voronoi Diagrams, 2009. ISVD '09. Sixth International Symposium on
Conference_Location :
Copenhagen
Print_ISBN :
978-1-4244-4769-5
Electronic_ISBN :
978-0-7695-3781-8
DOI :
10.1109/ISVD.2009.36