minkowski2 - README

A program for calculating Minkowski functionals
of a Boolean grain model with boundary correction

developed by Jens Schmalzing and Martin Kerscher based on a program by Klaus Mecke. May 1996. Updates by Thomas Buchert.
email: buchert@obs.univ-lyon1.fr

Minkowski functionals are discussed in all the references below. The computational method for a Boolean grain model without boundary conditions is discussed in [1,2]. The computational method for boundaries is a generalization of this method [4,5]. The deconvolution of the boundaries is discussed in [4,5,6]. We used this program to calculate the Minkowski functionals of Abell/ACO clusters as shown in [6]. Related applications may be found in [3,7,8,9].


The program is distributed as an uuencoded compressed tar file: walls.uu (Type: uudecode walls.uu; gunzip walls.tar.gz; tar -xvf walls.tar) Now the directory >walls should contain the following files: Readme, boxref.res, cdm.1, cdmref.res, cluster.c, cluster.h, diff1.awk, diff2.awk, geometry.c, geometry.h, main.c, makefile, merge.awk, minkowski.c, minkowski.h, minkowski.sm, objects.c, objects.h, org.c, org.h, points.c, points.h, rand.c, rand.h, recipes.c, recipes.h, romberg.c, romberg.h, trand.c, types.h


Go into the directory >walls and type: make Perhaps you have to choose a different c-compiler and different flags in the makefile. If `make' gives no error you probably generated the program `boxmin' successfully. To check the installation type: make test Then the below mentioned examples are calculated and compared to the reference files boxref.res and cdmref.res. These values are saved for each radius in cdmdiff.res and boxdiff.res. They should be approximately zero. (You may compare these files with a plotting program, too) We tested the program on several hp workstations with HP-UX 9.0x using cc, on ibm workstations with AIX 2.3 using cc, and on a sun workstation under Solaris 2.4 using gcc and acc.


boxmin -h
get a list of options and the actual (default) values of the parameters.
boxmin -n 100 -T -l 10 -o box.res
calculate the Minkowskifunctionals of 10 realization of a Poisson process with 100 points within a cube of sidelength 1, the corresponding theoretical values for a Poisson process, and save both in the file box.res
clustermin -n600 -icdm -l1 -r0.0 -R0.12 -d0.005 -H1 -s99.2857143 -T -ocdm_n.res
calculate the Minkowskifunctionals of a mock cluster catalogue.
-n600 :
to get enough memory for 600 clusters (well somehow a feature)
-icdm :
use file cdm.1
-l1 :
use only one file (no variance)
-r0.0 -R0.12 -d0.005 :
perform the calculation starting with radius 0.0 up to radius 0.12 with stepsize 0.005
-H1 :
calculate for northern hemisphere
-s99.2857143 :
use only 99.3% of the cluster (to get the correct number density of the Abell/ACO)
-T :
calculate the theoretical results for poisson process with same number density -ocdm_n.res :
save the results in cdm_n.res

CPU load:

On a hp 715/80 the box reference calculation and the cluster reference calculation took approx. 10 Minutes pure computing time each using less than 1MByte of memory.


- The definition of the geometry of the sample window is in the file objects.c .
- The input procedure for the cluster data used in reference [6] is in the file cluster.c .
- There is a lot of documentation in the source code.
- The Program calculates the volume densities v of the V-measures.
- If several realizations are drawn, the program computes the mean and the standard error of the v-measures.
- The file minkowski.sm includes SuperMongo plotting routines.


[1] Klaus R. Mecke, Thomas Buchert and Herbert Wagner (1994): `Robust morphological measures for large-scale structure in the Universe', Astron. Astrophys. 288, 697-704.

[2] Thomas Buchert (1996): `Robust morphological measures for large-scale structure', in: 11. Potsdam Cosmology Workshop on Large-scale Structure in the Universe, Geltow 1995, F.R.G., J. Mücket, S. Gottlöber, V. Müller (eds.), World Scientific, 156-161.

[3] M. Platzöder, T. Buchert (1995): `Application of Minkowski functionals to the statistical analysis of dark matter models', in: 1st SFB workshop on Astro-particle physics, report SFB/P1, Ringberg (Tegernsee) 1995, A. Weiss et al. (eds.), 251-263.

[4] Jens Schmalzing, Martin Kerscher and Thomas Buchert (1996): `Minkowski functionals in Cosmology', in: Proc. International School Enrico Fermi, Course CXXXII (Dark Matter in the Universe), Varenna 1995, S. Bonometto, J. Primack, A. Provenzale (eds.), IOS Press Amsterdam, 281-291.

[5] Martin Kerscher, Jens Schmalzing and Thomas Buchert (1996): `Analyzing Galaxy Catalogues with Minkowski Functionals', in: Mapping, Measuring and Modelling the Universe, Valencia 1995, P. Coles, V.J. Martinez, M.J. Pons (eds.), ASP Conference Series, 247-252.

[6] Martin Kerscher, Jens Schmalzing, J&oumrg Retzlaff, Stefano Borgani, Thomas Buchert, Stephan Gottlöber, Volker Müller, Manolis Plionis and Herbert Wagner (1997): `Minkowski Functionals of Abell/ACO clusters', M.N.R.A.S., 284, 73-84.

[7] Martin Kerscher, Jens Schmalzing, Thomas Buchert and Herbert Wagner (1998): `Fluctuations in the IRAS 1.2 Jy catalogue', Astron. Astrophys., 333, 1-12.

[8] Martin Kerscher, Klaus R. Mecke, Jens Schmalzing, Claus Beisbart, Thomas Buchert and Herbert Wagner (2001): `Morphological fluctuations of large-scale structure: The PSCz survey', Astron. Astrophys., 373, 1-11.

[9] C. Hikage, J. Schmalzing, T. Buchert, Y. Suto, I. Kayo, A. Taruya, Michael S. Vogeley, F. Hoyle, J.R. Gott III and J. Brinkmann (2003): `Minkowski Functionals of SDSS Galaxies I : Analysis of Excursion Sets', P.A.S.J., 55, 911-931.

Last Update: July 5, 2009

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