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}
}

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TLDR
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References

SHOWING 1-10 OF 23 REFERENCES

Robust Morphological Measures for Large-Scale Structure in the Universe

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

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

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

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
TLDR
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

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

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

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

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

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