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diff --git a/pgmminkowski.html b/pgmminkowski.html new file mode 100644 index 00000000..29b03a64 --- /dev/null +++ b/pgmminkowski.html @@ -0,0 +1,98 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 3.2//EN"> +<HTML><HEAD><TITLE>Pgmminkowski User Manual</TITLE></HEAD> +<BODY> +<H1>pgmminkowski</H1> +Updated: 29 October 2002 +<BR> +<A HREF="#index">Table Of Contents</A> + +<A NAME="lbAB"> </A> +<H2>NAME</H2> + +pgmminkowski - compute Minkowski integral + +<H2 id="synopsis">SYNOPSIS</H2> + +<B>pgmminkowski</B> <I>pgmfile</I> + +<H2 id="description">DESCRIPTION</H2> + +<p>This program is part of <a href="index.html">Netpbm</a>. + +<b>pgmminkowski</b> computes the 3 Minkowski integrals of a PGM image. + +<p>The Minkowski integrals mathematically characterize the shapes in the +image and hence are the basis of "morphological image analysis." + +<p>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. + +<p>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 consists of all the pixels in the image that are +white. For a grayscale image, there is some threshold of intensity +applied 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. + +<p>For a grayscale image, these numbers are a function of the threshold +of what you want to call black or white. <b>pgmminkowski</b> 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. + +<p>For more information about Minkowski integrals, see e.g. +<ul> +<li><a +href="http://rugth30.phys.rug.nl/compphys0/2001.htm"> K. Michielsen and +H. De Raedt, "Integral-Geometry Morphological Image Analysis", +Phys. Rep. 347, 461-538 (2001).</a> + +<li><a href="http://rugth30.phys.rug.nl/pdf/prechaos.pdf"> +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) +</a> +</ul> + +<p>The output is suitable for direct use as a datafile in <b>gnuplot</b>. + +<p>In addition to the three Minkowski integrals, <b>pgmminkowski</b> also +lists the horizontal and vertical edge counts. + + + +<H2 id="seealso">SEE ALSO</H2> + +<B><A HREF="pgmmorphconv.html">pgmmorphconv</A></B> +<B><A HREF="pgm.html">pgm</A></B> + +<H2 id="authors">AUTHORS</H2> + +Luuk van Dijk, 2001. + +<p>Based on work which is Copyright (C) 1989, 1991 by Jef Poskanzer. + +<HR> +<H2 id="index">Table Of Contents</H2> +<UL> +<LI><A HREF="#synopsis">SYNOPSIS</A> +<LI><A HREF="#description">DESCRIPTION</A> +<LI><A HREF="#seealso">SEE ALSO</A> +<LI><A HREF="#authors">AUTHORS</A> +</UL> +</BODY> +</HTML> |