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Minkowski Functionals used in the Morphological Analysis of Cosmic Microwave Background Anisotropy Maps

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arxiv astro-ph/9710185 v2 pith:D6B6JOY3 submitted 1997-10-16 astro-ph

Jens Schmalzing , Krzysztof M. Gorski This is my paper · ORCID
classification astro-ph
keywords functionalsminkowskianalysisanisotropybackgroundcosmicdatamaps
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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. Using the mathematical framework provided by the theory of integral geometry on arbitrary curved supports, we point out the differences to their characterization and interpretation in the case of flat space. With restrictions of real data -- such as pixelization and incomplete sky coverage, to mention just a few -- in mind, we derive and test unbiased estimators for all Minkowski functionals. Various examples, among them the analysis of the four-year COBE DMR data, illustrate the application of our method.

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Cited by 4 Pith papers

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