Manual: pgmminkowski

Pgmminkowski User Manual(1)			   General Commands Manual			 Pgmminkowski User Manual(1)

NAME
       pgmminkowski - compute Minkowski integral

SYNOPSIS
       pgmminkowski pgmfile

DESCRIPTION
       This program is part of Netpbm(1).

       pgmminkowski computes the 3 Minkowski integrals of a PGM image.

       The Minkowski integrals mathematically characterize the shapes in the image and hence are the basis of "morphological
       image analysis."

       Hadwiger's  theorem  has it that these integrals are the only motion-invariant, additive and conditionally continuous
       functions of a two-dimensional image, which means that they are preserved under certain kinds of deformations of	 the
       image.	On top of that, they are very easy and quickly calculated.  This makes them of interest for certain kinds of
       pattern recognition.

       Basically, the Minkowski integrals are the area, total perimeter length, and the Euler characteristic of	 the  image,
       where  these  metrics apply to the foreground image, not the rectangular PGM image itself.  The foreground image con‐
       sists of all the pixels in the image that are white.  For a grayscale image, there is some threshold of intensity ap‐
       plied to categorize pixels into black and white, and the Minkowski integrals are calculated as  a  function  of	this
       threshold  value. The total surface area refers to the number of white pixels in the PGM and the perimeter is the sum
       of perimeters of each closed white region in the PGM.

       For a grayscale image, these numbers are a function of the threshold of what you want to call black or  white.	pgm‐
       minkowski  reports  these  numbers as a function of the threshold for all possible threshold values.  Since the total
       surface area can increase only as a function of the threshold, it is a reparameterization of the threshold.  It turns
       out that if you consider the other two functions, the boundary length and the Euler characteristic, as a function  of
       the  first  one,	 the surface, you get two functions that are a fingerprint of the picture.  This fingerprint is e.g.
       sufficient to recognize the difference between pictures of different crystal lattices  under  a	scanning  tunnelling
       electron microscope.

       For more information about Minkowski integrals, see e.g.

       •       J.S.  Kole,  K.	Michielsen,  and H. De Raedt, "Morphological Image Analysis of Quantum Motion in Billiards",
	      Phys. Rev. E 63, 016201-1 - 016201-7 (2001)

       •      K. Michielsen and H. De Raedt, "Integral-Geometry Morphological  Image  Analysis",  Phys.	 Rep.  347,  461-538
	      (2001).

       The output is suitable for direct use as a datafile in gnuplot.

       In addition to the three Minkowski integrals, pgmminkowski also lists the horizontal and vertical edge counts.

OPTIONS
       There  are no command line options defined specifically for pgmminkowski, but it recognizes the options common to all
       programs based on libnetpbm (See	 Common Options .)

SEE ALSO
       pgmmorphconv(1) pbmminkowski(1) pgm(1)

AUTHORS
       Luuk van Dijk, 2001.

       Based on work which is Copyright (C) 1989, 1991 by Jef Poskanzer.

DOCUMENT SOURCE
       This manual page was generated by the Netpbm tool 'makeman' from HTML source.  The master documentation is at

	      http://netpbm.sourceforge.net/doc/pgmminkowski.html

netpbm documentation				       29 October 2002				 Pgmminkowski User Manual(1)