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S.F. Shandarin (University of Kansas)
Quantifying and objective analysis of the morphology of complex astronomical objects (nebulae, galaxies, galaxy clusters) and maps (COBE, QMASK, etc) is not a simple task. The first problem to occur concerns the quantities needed to be measured.
Differential and integral geometry offers a unique set of simple morphological measures that can be used to characterize both isolated objects and maps. In two-dimensional case they have simple geometrical meanings of the area within the boundary contour, the length of the boundary contour, and the Euler characteristic (or genus), that is the number of isolated parts of the object/map minus the number of holes in them. These quantities were suggested by Minkowski and are called Minkowski functionals.
The Minkowski functionals have been already applied to two-dimensional maps (COBE), three-dimensional galaxy redshift surveys (LCRS, PSCz) as well as to the mocked catalogs from N-body simulations. The new results of morphological studies of two-dimensional astronomical images and maps are reported.
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