1997/10/31 by Jens Schmalzing, K. M. Górski, Krzysztof M. Gorski · 5 citations
Environmental Science · Mathematics · Medicine · Physics and Astronomy · #Anisotropy #Astrophysics #Characterization (materials science) #Colorectal Cancer Screening and Detection #Cosmic background radiation #Cosmic microwave background #Cosmology and Gravitation Theories #Estimator #Integral geometry #Interpretation (philosophy) #Mathematical analysis #Mathematics #Minkowski space #Optics #Physics #Planck #Quantum mechanics #Remote Sensing in Agriculture #Sky #Statistics #Theoretical physics #astro-ph
paper · pdf · doi:10.1046/j.1365-8711.1998.01467.x
published as Mon. Not. R. Astron. Soc. 297 (1998) 355-365 · 14 pages, 13 figures, most of which look better in color. Uses AMSTeX, epsf.sty, mncite.sty. Very minor changes to match version accepted for publication in MNRAS
arxiv created 1997/12/20 · openalex publication_date 1998/06/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 in their characterization and interpretation in the case of flat space. With the 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.