# Morphometry of spatial patterns

@article{Beisbart2001MorphometryOS,
title={Morphometry of spatial patterns},
author={Claus Beisbart and Thomas Buchert and H. Wagner},
journal={Physica A-statistical Mechanics and Its Applications},
year={2001},
volume={293},
pages={592-604}
}
• Published 29 July 2000
• Mathematics
• Physica A-statistical Mechanics and Its Applications
28 Citations

## Figures and Tables from this paper

### Vector- und Tensor-Valued Descriptors for Spatial Patterns

• Computer Science
• 2002
Higher-rank Minkowski valuations are efficient means of describing the geometry and connectivity of spatial patterns and are extended to vector- and tensor-valued measures by using simple toy models as well as real data.

### Extended morphometric analysis of neuronal cells with Minkowski valuations

• Biology
• 2006
Abstract.Minkowski valuations provide a systematic framework for quantifying different aspects of morphology. In this paper we apply vector- and tensor-valued Minkowski valuations to neuronal cells

### Non-Gaussian morphology on large scales: Minkowski functionals of the REFLEX cluster catalogue

• Mathematics
• 2001
In order to quantify higher{order correlations of the galaxy cluster distribution we use a complete family of additive measures which give scale{dependent morphological information. Minkowski

### Effects of Noise on Galaxy Isophotes

• Physics
• 2002
The study of shapes of the images of objects is an important issue not only because it reveals its dynamical state but also it helps to understand the object’s evolutionary history. We discuss a new

### Measuring shapes of galaxy images — I. Ellipticity and orientation

• Physics
• 2003
We suggest a set of morphological measures that we believe can help in quantifying the shapes of two-dimensional cosmological images such as galaxies, clusters, and superclusters of galaxies. The

### Minkowski Tensors in Two Dimensions: Probing the Morphology and Isotropy of the Matter and Galaxy Density Fields

• Physics
• 2017
We apply the Minkowski tensor statistics to two-dimensional slices of the three-dimensional matter density field. The Minkowski tensors are a set of functions that are sensitive to directionally

### Tensor Minkowski Functionals for random fields on the sphere

• Mathematics
• 2017
We generalize the translation invariant tensor-valued Minkowski Functionals which are defined on two-dimensional flat space to the unit sphere. We apply them to level sets of random fields. The

### Search for anomalous alignments of structures in Planck data using Minkowski Tensors

• Physics
Journal of Cosmology and Astroparticle Physics
• 2019
Minkowski Tensors are tensorial generalizations of the scalar Minkowski Functionals. Due to their tensorial nature they contain additional morphological information of structures, in particular about

### Topology and geometry of Gaussian random fields I: on Betti numbers, Euler characteristic, and Minkowski functionals

• Mathematics
Monthly Notices of the Royal Astronomical Society
• 2019
This study presents a numerical analysis of the topology of a set of cosmologically interesting three-dimensional Gaussian random fields in terms of their Betti numbers $\beta_0$, $\beta_1$ and

## References

SHOWING 1-10 OF 23 REFERENCES

### Robust Morphological Measures for Large-Scale Structure in the Universe

• Mathematics
• 1993
We propose a novel method for the description of spatial patterns formed by a coverage of point sets representing galaxy samples. This method is based on a complete family of morphological measures

### Shapefinders: A New Shape Diagnostic for Large-Scale Structure

• Physics
• 1998
We construct a set of shapefinders used to determine the shapes of compact surfaces (isodensity surfaces in galaxy surveys or N-body simulations) without fitting them to ellipsoidal configurations,

### Minkowski functionals used in the morphological analysis of cosmic microwave background anisotropy maps

• Mathematics
• 1998
We present a novel approach to quantifying the morphology of cosmic microwave background (CMB) anisotropy maps. As morphological descriptors, we use shape parameters known as Minkowski functionals.

### Beyond Genus Statistics: A Unifying Approach to the Morphology of Cosmic Structure

• Mathematics
• 1997
The genus statistics of isodensity contours has become a well-established tool in cosmology. In this Letter we place the genus in the wider framework of a complete family of morphological

### Morphological characterization of patterns in reaction-diffusion systems.

• Mecke
• Materials Science
Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
• 1996
It is shown that a symmetry breaking of the polynomials when the type of the pattern changes from hexagons to turbulence or stripes means it is possible to describe the pattern transitions quantitatively and it may be possible to classify them in a similar way like thermodynamic phase transitions.

### Minkowski functionals of Abell/ACO clusters

• Mathematics, Physics
• 1997
We determine the Minkowski functionals for a sample of Abell/ACO clusters, 401 with measured and 16 with estimated redshifts. The four Minkowski functionals (including the void probability function

### Morphology of spinodal decomposition

• Materials Science
• 1997
The morphology of homogeneous phases during spinodal decomposition, i.e., the scaling of the content, shape, and connectivity of spatial structures is described by a family of morphological measures,

### Valuations on convex bodies

• Mathematics
• 1983
The investigation of functions on convex bodies which are valuations, or additive in Hadwiger’s sense, has always been of interest in particular parts of geometric convexity, and it has seen some

### Arc statistics with realistic cluster potentials. IV. Clusters in different cosmologies

• Physics
• 1997
We use numerical simulations of galaxy clusters in different cosmologies to study their ability to form large arcs. The cosmological models are: Standard CDM (SCDM; 0 =1 , =0

### Fluctuations in the IRAS 1.2 Jy catalogue

• Physics
• 1997
In an analysis of the IRAS 1.2 Jy redshift catalogue, with emphasis on the separate examination of northern and southern parts (in galactic coordinates), we found that the clustering properties of