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1 pagesetup
12 /Times-Bold f
(Pgmminkowski) 2132 1230 w
(User) 2957 1230 w
(Manual) 3226 1230 w
10 /Times-Bold f
(pgmminkowski) 720 1920 w
10 /Times-Roman f
(Updated: 29 October 2002) 720 2076 w
(Table Of Contents) 720 2196 w
10 /Times-Bold f
(NAME) 720 2436 w
10 /Times-Roman f
(pgmminkowski \255 compute Minkowski integral) 720 2592 w
10 /Times-Bold f
(SYNOPSIS) 720 2832 w
(pgmminkowski) 720 2988 w
10 /Times-Italic f
(pgmfile) 1402 2988 w
10 /Times-Bold f
(DESCRIPTION) 720 3228 w
10 /Times-Roman f
(This program is part of Netpbm.) 720 3420 w
10 /Times-Bold f
(pgmminkowski) 2063 3420 w
10 /Times-Roman f
(computes the 3 Minkowski integrals of a PGM image.) 2745 3420 w
(The) 720 3576 w
(Minkowski) 910 3576 w
(integrals) 1401 3576 w
(mathematically) 1780 3576 w
(characterize) 2431 3576 w
(the) 2946 3576 w
(shapes) 3104 3576 w
(in) 3406 3576 w
(the) 3520 3576 w
(image) 3678 3576 w
(and) 3958 3576 w
(hence) 4138 3576 w
(are) 4406 3576 w
(the) 4563 3576 w
(basis) 4721 3576 w
(of) 4957 3576 w
("morphological image analysis.") 720 3696 w
(Hadwiger's theorem has it that these integrals are the only motion\255invariant, additive and conditionally) 720 3852 w
(con\255) 4863 3852 w
(tinuous) 720 3972 w
(functions) 1046 3972 w
(of) 1449 3972 w
(a) 1563 3972 w
(two\255dimensional) 1638 3972 w
(image,) 2341 3972 w
(which) 2641 3972 w
(means) 2916 3972 w
(that) 3202 3972 w
(they) 3382 3972 w
(are) 3584 3972 w
(preserved) 3735 3972 w
(under) 4152 3972 w
(certain) 4409 3972 w
(kinds) 4710 3972 w
(of) 4957 3972 w
(deformations) 720 4092 w
(of) 1276 4092 w
(the) 1388 4092 w
(image.) 1539 4092 w
(On) 1862 4092 w
(top) 2013 4092 w
(of) 2170 4092 w
(that,) 2282 4092 w
(they) 2486 4092 w
(are) 2687 4092 w
(very) 2837 4092 w
(easy) 3043 4092 w
(and) 3249 4092 w
(quickly) 3422 4092 w
(calculated.) 3751 4092 w
(This) 4234 4092 w
(makes) 4442 4092 w
(them) 4727 4092 w
(of) 4957 4092 w
(interest for certain kinds of pattern recognition.) 720 4212 w
(Basically,) 720 4368 w
(the) 1151 4368 w
(Minkowski) 1307 4368 w
(integrals) 1797 4368 w
(are) 2175 4368 w
(the) 2330 4368 w
(area,) 2486 4368 w
(total) 2710 4368 w
(perimeter) 2922 4368 w
(length,) 3338 4368 w
(and) 3647 4368 w
(the) 3826 4368 w
(Euler) 3983 4368 w
(characteristic) 4234 4368 w
(of) 4800 4368 w
(the) 4918 4368 w
(image,) 720 4488 w
(where) 1016 4488 w
(these) 1286 4488 w
(metrics) 1517 4488 w
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(the) 2189 4488 w
(foreground) 2337 4488 w
(image,) 2806 4488 w
(not) 3101 4488 w
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(rectangular) 3403 4488 w
(PGM) 3877 4488 w
(image) 4120 4488 w
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(in) 2340 4608 w
(the) 2452 4608 w
(image) 2608 4608 w
(that) 2886 4608 w
(are) 3070 4608 w
(white.) 3225 4608 w
(For) 3531 4608 w
(a) 3704 4608 w
(grayscale) 3782 4608 w
(image,) 4192 4608 w
(there) 4495 4608 w
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(some) 4829 4608 w
(threshold) 720 4728 w
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(culated) 720 4848 w
(as) 1039 4848 w
(a) 1153 4848 w
(function) 1228 4848 w
(of) 1592 4848 w
(this) 1706 4848 w
(threshold) 1882 4848 w
(value.) 2285 4848 w
(The) 2557 4848 w
(total) 2743 4848 w
(surface) 2952 4848 w
(area) 3270 4848 w
(refers) 3466 4848 w
(to) 3723 4848 w
(the) 3832 4848 w
(number) 3985 4848 w
(of) 4322 4848 w
(white) 4437 4848 w
(pixels) 4691 4848 w
(in) 4962 4848 w
(the PGM and the perimeter is the sum of perimeters of each closed white region in the PGM.) 720 4968 w
(For) 720 5124 w
(a) 897 5124 w
(grayscale) 979 5124 w
(image,) 1393 5124 w
(these) 1700 5124 w
(numbers) 1943 5124 w
(are) 2325 5124 w
(a) 2484 5124 w
(function) 2566 5124 w
(of) 2937 5124 w
(the) 3058 5124 w
(threshold) 3218 5124 w
(of) 3628 5124 w
(what) 3749 5124 w
(you) 3981 5124 w
(want) 4169 5124 w
(to) 4402 5124 w
(call) 4519 5124 w
(black) 4702 5124 w
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(white.) 720 5244 w
10 /Times-Bold f
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10 /Times-Roman f
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(as) 2630 5244 w
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(function) 2819 5244 w
(of) 3182 5244 w
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(threshold) 3447 5244 w
(for) 3849 5244 w
(all) 3995 5244 w
(possible) 4125 5244 w
(threshold) 4483 5244 w
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(ues.) 720 5364 w
(Since) 933 5364 w
(the) 1185 5364 w
(total) 1337 5364 w
(surface) 1545 5364 w
(area) 1862 5364 w
(can) 2057 5364 w
(increase) 2225 5364 w
(only) 2581 5364 w
(as) 2789 5364 w
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(reparameterization) 4293 5364 w
(of) 720 5484 w
(the) 830 5484 w
(threshold.) 979 5484 w
(It) 1428 5484 w
(turns) 1516 5484 w
(out) 1743 5484 w
(that) 1898 5484 w
(if) 2074 5484 w
(you) 2161 5484 w
(consider) 2337 5484 w
(the) 2701 5484 w
(other) 2849 5484 w
(two) 3080 5484 w
(functions,) 3256 5484 w
(the) 3679 5484 w
(boundary) 3827 5484 w
(length) 4230 5484 w
(and) 4506 5484 w
(the) 4676 5484 w
(Euler) 4824 5484 w
(characteristic,) 720 5604 w
(as) 1307 5604 w
(a) 1421 5604 w
(function) 1496 5604 w
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(first) 2127 5604 w
(one,) 2319 5604 w
(the) 2519 5604 w
(surface,) 2672 5604 w
(you) 3015 5604 w
(get) 3196 5604 w
(two) 3349 5604 w
(functions) 3530 5604 w
(that) 3933 5604 w
(are) 4115 5604 w
(a) 4268 5604 w
(fingerprint) 4344 5604 w
(of) 4803 5604 w
(the) 4918 5604 w
(picture.) 720 5724 w
(This) 1081 5724 w
(fingerprint) 1293 5724 w
(is) 1754 5724 w
(e.g.) 1855 5724 w
(sufficient) 2033 5724 w
(to) 2444 5724 w
(recognize) 2556 5724 w
(the) 2977 5724 w
(difference) 3132 5724 w
(between) 3568 5724 w
(pictures) 3933 5724 w
(of) 4282 5724 w
(different) 4398 5724 w
(crystal) 4774 5724 w
(lattices under a scanning tunnelling electron microscope.) 720 5844 w
(For more information about Minkowski integrals, see e.g.) 720 6000 w
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(\031) 720 6156 w
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(K.) 1006 6156 w
(Michielsen) 1139 6156 w
(and) 1619 6156 w
(H.) 1799 6156 w
(De) 1932 6156 w
(Raedt,) 2084 6156 w
("Integral\255Geometry) 2378 6156 w
(Morphological) 3197 6156 w
(Image) 3827 6156 w
(Analysis",) 4112 6156 w
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4528 6156 m 60 build_pw
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(Phys.) 4597 6156 w
(Rep.) 4854 6156 w
(347, 461\255538 \(2001\).) 970 6276 w
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(\031) 720 6432 w
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(J.S.) 970 6432 w
(Kole,) 1148 6432 w
(K.) 1400 6432 w
(Michielsen,) 1530 6432 w
(and) 2032 6432 w
(H.) 2209 6432 w
(De) 2339 6432 w
(Raedt,) 2488 6432 w
("Morphological) 2779 6432 w
(Image) 3447 6432 w
(Analysis) 3729 6432 w
(of) 4112 6432 w
(Quantum) 4228 6432 w
(Motion) 4633 6432 w
(in) 4962 6432 w
(Billiards", Phys. Rev. E 63, 016201\2551 \255 016201\2557 \(2001\)) 970 6552 w
(The output is suitable for direct use as a datafile in) 720 6744 w
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(gnuplot) 2764 6744 w
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(.) 3093 6744 w
(In) 720 6900 w
(addition) 842 6900 w
(to) 1209 6900 w
(the) 1326 6900 w
(three) 1487 6900 w
(Minkowski) 1725 6900 w
(integrals,) 2220 6900 w
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(pgmminkowski) 2628 6900 w
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(also) 3324 6900 w
(lists) 3524 6900 w
(the) 3725 6900 w
(horizontal) 3886 6900 w
(and) 4330 6900 w
(vertical) 4513 6900 w
(edge) 4852 6900 w
(counts.) 720 7020 w
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(\255 2 \255) 2797 480 w
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(SEE ALSO) 720 840 w
(pgmmorphconv pgm) 720 996 w
(AUTHORS) 720 1236 w
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(Luuk van Dijk, 2001.) 720 1392 w
(Based on work which is Copyright \(C\) 1989, 1991 by Jef Poskanzer.) 720 1548 w
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(________________________________________________________________________) 720 1668 w
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(Table Of Contents) 720 1908 w
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(\031) 720 2100 w
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(SYNOPSIS) 970 2100 w
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(\031) 720 2256 w
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(DESCRIPTION) 970 2256 w
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(\031) 720 2412 w
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(SEE ALSO) 970 2412 w
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(\031) 720 2568 w
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(AUTHORS) 970 2568 w
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