论文标题
球体上的基于Minkowski张量的形状分析方法
Minkowski tensor-based shape analysis methods on the sphere
论文作者
论文摘要
最近，Minkowski Tensors（MT）在形态分析任务中赢得了知名度。与标量Minkowski功能（MF；在2D中给出的2D，周长和Euler特征）相反，MT可以表征身体的对称性和方向。这已用于各种任务，例如通过追溯Hii区域的细丝的起源或搜索CMB中结构的对准，以检测星际气泡。我提出了一种基于游行方的方法，用于计算疗式格式中地图上的MT和MF。 MT是针对当地社区计算的，然后可以使用其添加性属性在较大的区域上求和/平均。这提供了在不同尺度上寻找CMB各向异性和非高斯的局部分析的可能性。
Recently, Minkowski Tensors (MT) have gained popularity for morphological analysis tasks. As opposed to the scalar Minkowski functionals (MF; in 2D given by area, perimeter and Euler characteristic), MT can characterize symmetry and orientation of a body. This has been used for a variety of tasks, e.g. to detect interstellar bubbles by tracing back the origins of filaments in HII-regions, or to search for alignment of structures in the CMB. I present a marching-square-based method for calculating MT and MF on the sphere for maps in the Healpix format. MT are calculated for a local neighborhood and can then be summed up/averaged over a larger region, using their additivity property. This provides the possibility of localized analyses looking for CMB anisotropies and non-Gaussianities at varying scales.
