宇宙网的几何学和形态学：分析宇宙中的空间模式
Geometry and Morphology of the Cosmic Web: Analyzing Spatial Patterns in the Universe
摘要：
我们回顾了宇宙网络的分析手段的基础上使用的Delaunay和Voronoi镶嵌的广泛的工具集。宇宙网络是一种突出而普遍的泡沫状模式，物质在其中以几兆秒差距到一百多兆秒差距的尺度组织起来。首先，我们描述了Delaunay Tessellation Field Estimation（DTFE）。DTFE形式主义恢复宇宙物质分布的层次性和各向异性形态。多尺度形态滤波器（MMF）使用DTFE密度场来提取不同的形态元素-细丝，薄片和簇-基于ScaleSpace分析，该分析在一系列尺度上搜索这些形态。随后，我们讨论了分水岭空洞探测器（WVF），它调用离散分水岭变换来识别宇宙物质分布中的空洞。退伍军人联合会能够确定空洞的位置、大小和形状。分水岭变换也是SpineWeb分析宇宙物质分布的关键要素。它允许通过识别奇点和相应的分界线来确定宇宙物质密度场中的脊和连接壁。最后，我们描述的概念Alphashapes评估的宇宙物质分布的拓扑结构。
英文摘要：
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 salient and pervasive foamlike pattern in which matter has organized itself on scales of a few up to more than a hundred Megaparsec. First, we describe the Delaunay Tessellation Field Estimator (DTFE). The DTFE formalism is shown to recover the hierarchical nature and the anisotropic morphology of 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 to determine 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. It allows the determination of the filamentary spine and connected walls in the cosmic matter density field through the identification of the singularities and corresponding separatrices. Finally, we describe the concept of Alphashapes for assessing the topology of the cosmic matter distribution.
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