Morphometry of Spatial Patterns

Abstract

Minkowski functionals constitute a family of order parameters which discriminate spatial patterns according to size, shape and connectivity. Here we point out, that these scalar descriptors can be complemented by vector-valued curvature measures also known as Quermass vectors. Using examples of galaxy clusters, we demonstrate that the Quermass vectors provide additional morphological information on directional features and symmetries displayed by spatial data.

14 pages, Latex, to appear in Physica A

References in corpus (3)

• Minkowski Functionals used in the Morphological Analysis of Cosmic Microwave Background Anisotropy Maps
• Shapefinders: A new shape diagnostic for large scale structure
• Disentangling the Cosmic Web I: Morphology of Isodensity Contours

Cited by in corpus (23)

• Morphological fluctuations of large-scale structure: the PSCz survey
• Topology and Geometry of Gaussian random fields I: on Betti Numbers, Euler characteristic and Minkowski functionals
• Non-Gaussian morphology on large scales: Minkowski functionals of the REFLEX cluster catalogue
• Model-independent analyses of non-Gaussianity in Planck CMB maps using Minkowski Functionals
• Extended morphometric analysis of neuronal cells with Minkowski valuations
• The morphological and dynamical evolution of simulated galaxy clusters
• Neural Network-based Top Tagger with Two-Point Energy Correlations and Geometry of Soft Emissions
• Search for anomalous alignments of structures in Planck data using Minkowski Tensors
• Tensor Minkowski Functionals: first application to the CMB
• Minkowski Tensors in Two Dimensions - Probing the Morphology and Isotropy of the Matter and Galaxy Density Fields
• Minkowski Functionals of SDSS-III BOSS : Hints of Possible Anisotropy in the Density Field?
• Tensor Minkowski Functionals for random fields on the sphere
• Measuring Shapes of Galaxy Images I: Ellipticity and Orientation
• Cosmological Parameter Estimation from the Two-Dimensional Genus Topology -- Measuring the Expansion History using the Genus Amplitude as a Standard Ruler
• Morphology and Evolution of Simulated and Optical Clusters: A Comparative Analysis
• Measuring Shapes of Galaxy Images II: Morphology of 2MASS Galaxies
• Ensemble Average of Three-Dimensional Minkowski Tensors of a Gaussian Random Field in Redshift Space
• Morphology of CMB fields -- effect of weak gravitational lensing
• Minkowski Tensors in Redshift Space -- Beyond the Plane Parallel Approximation
• Vector- and tensor-valued descriptors for spatial patterns
• Cosmic Strings-induced CMB anisotropies in light of Weighted Morphology
• Morphology of dark matter haloes beyond triaxiality
• Effects of Noise on Galaxy Isophotes