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Filename : thresholds.xml
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<?xml version="1.0" encoding="ISO-8859-1"?>
<!DOCTYPE thresholds [
  <!ELEMENT thresholds (threshold)+>
  <!ATTLIST thresholds xmlns CDATA #FIXED ''>
  <!ELEMENT threshold (description,levels)>
  <!ATTLIST threshold xmlns CDATA #FIXED '' alias NMTOKEN #IMPLIED
    map NMTOKEN #REQUIRED>
  <!ELEMENT description (#PCDATA)>
  <!ATTLIST description xmlns CDATA #FIXED ''>
  <!ELEMENT levels (#PCDATA)>
  <!ATTLIST levels xmlns CDATA #FIXED '' divisor CDATA #REQUIRED
    height CDATA #REQUIRED width CDATA #REQUIRED>
]>
<!--
  Threshold Maps for Ordered Posterized Dither

  Each "<threshold>" element defines the map name, description, and an array
  of "levels" used to provide the threshold map for ordered dithering and
  digital halftoning.

  The "alias" attribute provides a backward compatible name for this threshold
  map (pre-dating IM v6.2.9-6), and are deprecated.

  The description is a english description of what the threshold map achieves
  and is only used for 'listing' the maps.

  The map itself is a rectangular array of integers or threshold "levels"
  of the given "width" and "height" declared within the enclosing <levels>
  element.  That is "width*height" integers or "levels" *must* be provided
  within each map.

  Each of the "levels" integer values (each value representing the threshold
  intensity "level/divisor" at which that pixel is turned on.  The "levels"
  integers given can be any postive integers between "0" and the "divisor",
  excluding those limits.

  The "divisor" not only defines the upper limit and threshold divisor for each
  "level" but also the total number of pseudo-levels the threshold mapping
  creates and fills with a dither pattern.  That is a ordered bitmap dither
  of a pure greyscale gradient will use a maximum of "divisor" ordered bitmap
  patterns, including the patterns with all the pixels 'on' and all the pixel
  'off'. It may define less patterns than that, but the color channels will
  be thresholded in units based on "divisor".

  Alternatively for a multi-level posterization, ImageMagick inserts
  "divisor-2" dither patterns (as defined by the threshold map) between each of
  channel color level produced.

  For example the map "o2x2" has a divisor of 5, which will define 3 bitmap
  patterns plus the patterns with all pixels 'on' and 'off'.  A greyscale
  gradient will thus have 5 distinct areas.
-->
<thresholds>

<!-- - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  Minimal Dither and Non-Dither Threshold Maps
-->
  <threshold map="threshold" alias="1x1">
    <description>Threshold 1x1 (non-dither)</description>
    <levels width="1" height="1" divisor="2">
        1
    </levels>
  </threshold>

  <threshold map="checks" alias="2x1">
    <description>Checkerboard 2x1 (dither)</description>
    <levels width="2" height="2" divisor="3">
       1 2
       2 1
    </levels>
  </threshold>

<!-- - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  (dispersed) Ordered Dither Patterns
-->
  <threshold map="o2x2" alias="2x2">
    <description>Ordered 2x2 (dispersed)</description>
    <levels width="2" height="2" divisor="5">
       1  3
       4  2
    </levels>
  </threshold>

  <threshold map="o3x3" alias="3x3">
    <description>Ordered 3x3 (dispersed)</description>
    <levels width="3" height="3" divisor="10">
        3  7  4
        6  1  9
        2  8  5
    </levels>
  </threshold>

  <threshold map="o4x4" alias="4x4">
    <!--
       From "Dithering Algorithms"
       http://www.efg2.com/Lab/Library/ImageProcessing/DHALF.TXT
     -->
    <description>Ordered 4x4 (dispersed)</description>
    <levels width="4" height="4" divisor="17">
       1   9   3  11
      13   5  15   7
       4  12   2  10
      16   8  14   6
    </levels>
  </threshold>

  <threshold map="o8x8" alias="8x8">
    <!-- Extracted from original 'OrderedDither()' Function -->
    <description>Ordered 8x8 (dispersed)</description>
    <levels width="8" height="8" divisor="65">
         1  49  13  61   4  52  16  64
        33  17  45  29  36  20  48  32
         9  57   5  53  12  60   8  56
        41  25  37  21  44  28  40  24
         3  51  15  63   2  50  14  62
        35  19  47  31  34  18  46  30
        11  59   7  55  10  58   6  54
        43  27  39  23  42  26  38  22
    </levels>
  </threshold>

<!-- - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  Halftones - Angled 45 degrees

  Initially added to ImageMagick by Glenn Randers-Pehrson, IM v6.2.8-6,
  modified to be more symmetrical with intensity by Anthony, IM v6.2.9-7

  These patterns initially start as circles, but then form diamonds
  pattern at the 50% threshold level, before forming negated circles,
  as it approached the other threshold extereme.
-->
  <threshold map="h4x4a" alias="4x1">
    <description>Halftone 4x4 (angled)</description>
    <levels width="4" height="4" divisor="9">
       4  2  7  5
       3  1  8  6
       7  5  4  2
       8  6  3  1
    </levels>
  </threshold>

  <threshold map="h6x6a" alias="6x1">
    <description>Halftone 6x6 (angled)</description>
    <levels width="6" height="6" divisor="19">
       14  13  10   8   2   3
       16  18  12   7   1   4
       15  17  11   9   6   5
        8   2   3  14  13  10
        7   1   4  16  18  12
        9   6   5  15  17  11
    </levels>
  </threshold>

  <threshold map="h8x8a" alias="8x1">
    <description>Halftone 8x8 (angled)</description>
    <levels width="8" height="8" divisor="33">
       13   7   8  14  17  21  22  18
        6   1   3   9  28  31  29  23
        5   2   4  10  27  32  30  24
       16  12  11  15  20  26  25  19
       17  21  22  18  13   7   8  14
       28  31  29  23   6   1   3   9
       27  32  30  24   5   2   4  10
       20  26  25  19  16  12  11  15
    </levels>
  </threshold>

<!-- - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  Halftones - Orthogonally Aligned, or Un-angled

  Initially added by Anthony Thyssen, IM v6.2.9-5 using techniques from
  "Dithering & Halftoning" by Gernot Haffmann
  http://www.fho-emden.de/~hoffmann/hilb010101.pdf

  These patterns initially start as circles, but then form square
  pattern at the 50% threshold level, before forming negated circles,
  as it approached the other threshold extereme.
-->
  <threshold map="h4x4o">
    <description>Halftone 4x4 (orthogonal)</description>
    <levels width="4" height="4" divisor="17">
        7  13  11   4
       12  16  14   8
       10  15   6   2
        5   9   3   1
    </levels>
  </threshold>

  <threshold map="h6x6o">
    <description>Halftone 6x6 (orthogonal)</description>
    <levels width="6" height="6" divisor="37">
        7  17  27  14   9   4
       21  29  33  31  18  11
       24  32  36  34  25  22
       19  30  35  28  20  10
        8  15  26  16   6   2
        5  13  23  12   3   1
    </levels>
  </threshold>

  <threshold map="h8x8o">
    <description>Halftone 8x8 (orthogonal)</description>
    <levels width="8" height="8" divisor="65">
        7  21  33  43  36  19   9   4
       16  27  51  55  49  29  14  11
       31  47  57  61  59  45  35  23
       41  53  60  64  62  52  40  38
       37  44  58  63  56  46  30  22
       15  28  48  54  50  26  17  10
        8  18  34  42  32  20   6   2
        5  13  25  39  24  12   3   1
    </levels>
  </threshold>

  <threshold map="h16x16o">
    <!--
       Direct extract from "Dithering & Halftoning" by Gernot Haffmann.
       This may need some fine tuning for symmetry of the halftone dots,
       as it was a mathematically formulated pattern.
    -->
    <description>Halftone 16x16 (orthogonal)</description>
    <levels width="16" height="16" divisor="257">
        4  12  24  44  72 100 136 152 150 134  98  70  42  23  11   3
        7  16  32  52  76 104 144 160 158 142 102  74  50  31  15   6
       19  27  40  60  92 132 168 180 178 166 130  90  58  39  26  18
       36  48  56  80 124 176 188 204 203 187 175 122  79  55  47  35
       64  68  84 116 164 200 212 224 223 211 199 162 114  83  67  63
       88  96 112 156 192 216 232 240 239 231 214 190 154 111  95  87
      108 120 148 184 208 228 244 252 251 243 226 206 182 147 119 107
      128 140 172 196 219 235 247 256 255 246 234 218 194 171 139 127
      126 138 170 195 220 236 248 253 254 245 233 217 193 169 137 125
      106 118 146 183 207 227 242 249 250 241 225 205 181 145 117 105
       86  94 110 155 191 215 229 238 237 230 213 189 153 109  93  85
       62  66  82 115 163 198 210 221 222 209 197 161 113  81  65  61
       34  46  54  78 123 174 186 202 201 185 173 121  77  53  45  33
       20  28  37  59  91 131 167 179 177 165 129  89  57  38  25  17
        8  13  29  51  75 103 143 159 157 141 101  73  49  30  14   5
        1   9  21  43  71  99 135 151 149 133  97  69  41  22  10   2
    </levels>
  </threshold>

<!-- - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  Halftones - Orthogonally Expanding Circle Patterns

  Added by Glenn Randers-Pehrson, 4 Nov 2010, ImageMagick 6.6.5-6

  Rather than producing a diamond 50% threshold pattern, these
  continue to generate larger (overlapping) circles.  They are
  more like a true halftone pattern formed by covering a surface
  with either pure white or pure black circular dots.

  WARNING: true halftone patterns only use true circles even in
  areas of highly varying intensity.  Threshold dither patterns
  can generate distorted circles in such areas.
-->

  <threshold map="c5x5b" alias="c5x5">
    <description>Circles 5x5 (black)</description>
    <levels width="5" height="5" divisor="26">
         1 21 16 15  4
         5 17 20 19 14
         6 21 25 24 12
         7 18 22 23 11
         2  8  9 10  3
    </levels>
  </threshold>


  <threshold map="c5x5w">
    <description>Circles 5x5 (white)</description>
    <levels width="5" height="5" divisor="26">
        25 21 10 11 22
        20  9  6  7 12
        19  5  1  2 13
        18  8  4  3 14
        24 17 16 15 23
    </levels>
  </threshold>

  <threshold map="c6x6b" alias="c6x6">
    <description>Circles 6x6 (black)</description>
    <levels width="6" height="6" divisor="37">
         1  5 14 13 12  4
         6 22 28 27 21 11
        15 29 35 34 26 20
        16 30 36 33 25 19
         7 23 31 32 24 10
         2  8 17 18  9  3
    </levels>
  </threshold>

  <threshold map="c6x6w">
    <description>Circles 6x6 (white)</description>
    <levels width="6" height="6" divisor="37">
        36 32 23 24 25 33
        31 15  9 10 16 26
        22  8  2  3 11 17
        21  7  1  4 12 18
        30 14  6  5 13 27
        35 29 20 19 28 34
    </levels>
  </threshold>

  <threshold map="c7x7b" alias="c7x7">
    <description>Circles 7x7 (black)</description>
    <levels width="7" height="7" divisor="50">
        3  9 18 28 17  8  2
       10 24 33 39 32 23  7
       19 34 44 48 43 31 16
       25 40 45 49 47 38 27
       20 35 41 46 42 29 15
       11 21 36 37 28 22  6
        4 12 13 26 14  5  1
    </levels>
  </threshold>


  <threshold map="c7x7w">
    <description>Circles 7x7 (white)</description>
    <levels width="7" height="7" divisor="50">
       47 41 32 22 33 42 48
       40 26 17 11 18 27 43
       31 16  6  2  7 19 34
       25 10  5  1  3 12 23
       30 15  9  4  8 20 35
       39 29 14 13 21 28 44
       46 38 37 24 36 45 49
    </levels>
  </threshold>


<!-- - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  Special Purpose Dithers
-->

</thresholds>