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Robust Morphological Measures for Large-Scale Structure in the Universe

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K.R. Mecke, T. Buchert, H. Wagner

Astrophysics · Submitted 14 Dec 1993

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim The method is numerically robust even for small samples, independent of statistical assumptions, and yields global as well as local morphological information.

how it is stated · asserted 1.00 read the record →

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arXiv IDastro-ph/9312028 (version 1)
Pith IDO7K7RN5C, Pith's permanent record of this paper and its review
CitationH. Wagner, K.R. Mecke, T. Buchert. "Robust Morphological Measures for Large-Scale Structure in the Universe." arXiv:astro-ph/9312028 (1993). https://pith.science/paper/O7K7RN5C
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The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,631 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.15 · states limitation 0.10 · human participants 0.01 · controlled comparison 0.07 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.11 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

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 known as Minkowski functionals, which includes the topological Euler characteristic and geometric descriptors to specify the content, shape and connectivity of spatial sets. The method is numerically robust even for small samples, independent of statistical assumptions, and yields global as well as local morphological information. We illustrate the method by applying it to a Poisson process, a `double-Poisson' process, and to the Abell catalogue of galaxy clusters.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We propose a novel method for the description of spatial patterns formed by a coverage of point sets representing galaxy samples. contribution 1.00 0.88 0.15 asserted 0.99
s1 This method is based on a complete family of morphological measures known as Minkowski functionals, which includes the topological Euler characteristic and geometric descriptors to specify the content, shape and connectivity of spatial sets. method 0.95 0.15 0.10 asserted 1.00
s2 The method is numerically robust even for small samples, independent of statistical assumptions, and yields global as well as local morphological information. contribution 0.54 0.72 0.30 asserted 1.00
s3 We illustrate the method by applying it to a Poisson process, a `double-Poisson' process, and to the Abell catalogue of galaxy clusters. method 0.70 0.95 0.07 asserted 1.00

What kind of paper the classifier reports this is: method or tool 1.00 · evidence from simulation or computation 0.56.

What was examined, and what was not

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  • arXiv listing abstract v1
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
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  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

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 known as Minkowski functionals, which includes the topological Euler characteristic and geometric descriptors to specify the content, shape and connectivity of spatial sets. The method is numerically robust even for small samples, independent of statistical assumptions, and yields global as well as local morphological information. We illustrate the method by applying it to a Poisson process, a `double-Poisson' process, and to the Abell catalogue of galaxy clusters.

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References
How the literature uses it

49 arXiv papers cite this in 70 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers whose main result relates to this one's

Found among the papers closest to this one by title and main claim. Pith's classifier compared each pair's main results and a second model family confirmed the relation; checked against two further families, shown conflicts agreed 118 times in 120 and shown same results 218 times in 239. The quoted sentence is the other paper's main claim.

States the same result 1 paper

Papers citing it · 25 sentences without a confident label

Builds on it 1 paper
  • We calculate the generalization of the formulae (59) in [ref] for the Minkowski functionals [ref] of a ball to the Minkowski functionals $W_α, α= 0,1,2,3$, of an oblate spheroid with major semi-axis $a$ and excentricity $e$ ($W_3$ is related to the Euler characteristic which is not needed for the backreaction functional): [equation] where the functionals are evaluated on the boundary $∂$ of the averaging domain, $s = const$.

    Dark Matter from Backreaction? Collapse models on galaxy cluster scales · Regional argument · 0.95

Uses its method or tool 4 papers
  • In order to quantify the higher order content of the surrogate maps we use two comparable real-space image analysis methods sensitive to HOS, namely the scaling index method (SIM) developed in [ref] and a set of three statistics known as the Minkowski functionals (MFs) [ref] , which were introduced into cosmology by [ref] .

    Correlating Fourier phase information with real-space higher order statistics · Introduction · 1.00

  • We compute the 21 cm brightness temperature $δT_b ≈T̅_0(z) x_HI(𝐱) [1 + δ(𝐱)]$ in the saturated spin-temperature limit [ref] and extract power spectra $P_21(k)$, $P_xx(k)$, and two-dimensional Minkowski functionals [ref] $V_0$: area fraction; $V_1$: boundary length; $V_2$: Euler characteristic averaged over 20 slices.

    Reionization Topology as a Probe of Self-Interacting Dark Matter · Introduction · 0.97

  • The morphology of excursion sets are then quantified by three scalar Minkowski Functionals (MFs), defined per unit area by, V_0(ν) ≡1/A∫_Q_ν , V_1(ν) ≡1/4A∫_∂Q_ν , V_2(ν) ≡1/2πA∫_∂Q_ν , where $A$ is the total unmasked area ($4π$ for full sky), $$ is the surface element, $$ is the line element along the excursion boundary $∂Q_ν$, and $κ$ is the geodesic curvature [ref] . $V_0$, $V_1$, and $V_2$ are the area fraction, boundary length, and Euler characteristic (or genus, ignoring a term proportional to the excursion area) of the excursion sets, respectively.

    Understanding the non-Gaussian nature of Galactic foreground emissions towards small scales · Minkowski Functionals and skewness-kurtosis parameters · 0.86

Cites it as background 32 papers

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