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            <c val="#008080">INTRODUCTORY MATERIAL</c>
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              <c val="#800080">Tools for Packed Matrices</c>
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            <c val="#800000">Function Definitions and Syntax</c>
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              <c val="#800000">extract(M, n)</c>
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        <phrase>extract function</phrase>
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        <phrase>subcolor function</phrase>
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        <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">These functions allow you to extract or insert a single component matrix from a packed matrix comprising a color image, to pack three color components together, and to selected subsets of packed color matrices. </p>
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            <c val="#800000">Arguments</c>
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              <c val="#008080">• </c>
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              <c val="#008080">•</c>
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          <inlineAttr font-style="normal">,</inlineAttr> the location (1, 2 or 3) from which to extract or insert the component (regardless of the value of the built-in variable ORIGIN),</p>
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              <c val="#008080">• </c>
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          <inlineAttr font-style="normal">:</inlineAttr> the starting and ending rows and columns for subsetting</p>
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          <b>X</b>, <b>Y</b>, <b>Z</b>: three matrices to pack together.</p>
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        <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">These functions are utilities designed to help you create or manipulate packed matrices more easily. They return the appropriate packed or unpacked matrix components.</p>
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        <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">To learn more about packed color image matrices, see the <b><u><link href="./Intro.xmcd" title="Links to section" popup="false">Introduction</link></u></b>.</p>
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            <c val="#800000">Function Details</c>
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              <c val="#800000">extract(M, n)</c>
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        <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">Read in a packed-color RGB color matrix.</p>
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        <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">Now, suppose just the red component of this image is of importance. We can use the <b>extract</b> function to extract it:</p>
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        <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">Now we have the red values, but our matrix is not in RGB color format. So to view it as red, we have two choices. One way is to make it into an RGB image by supplying zeros for the blue and green components:</p>
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      </component>
      <rendering item-idref="13" />
    </region>
    <region region-id="1997" left="0" top="1044" width="6000" height="6" align-x="0" align-y="1044" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <pageBreak />
    </region>
    <region region-id="1998" left="6" top="1056.75" width="330.75" height="42.75" align-x="6" align-y="1068" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <text use-page-width="false" push-down="false" lock-width="true">
        <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">A second possibility is to view it as a grayscale image, but with a false color mapping using the Grayscale Colormap option in the Properties dialog:</p>
      </text>
    </region>
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      <component hide-arguments="false" clsid-buddy="8442da2d-08d7-45ad-a4a6-f28bee6ae06a" item-idref="14" disable-calc="false">
        <inputs>
          <ml:id xml:space="preserve">red</ml:id>
        </inputs>
        <outputs />
      </component>
      <rendering item-idref="15" />
    </region>
    <region region-id="438" left="0" top="1314" width="6000" height="6" align-x="0" align-y="1314" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <pageBreak />
    </region>
    <region region-id="2004" left="6" top="1326.75" width="87.75" height="14.25" align-x="6" align-y="1338" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <text use-page-width="false" push-down="false" lock-width="true">
        <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">
          <b>
            <c val="#800000">Function Details</c>
          </b>
        </p>
      </text>
    </region>
    <region region-id="2006" left="120" top="1326.75" width="87" height="14.25" align-x="120" align-y="1338" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <text use-page-width="false" push-down="false" lock-width="true">
        <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">
          <b>
            <inlineAttr font-style="normal">
              <c val="#800000">replace(M, N, n)</c>
            </inlineAttr>
          </b>
        </p>
      </text>
      <indexes>
        <phrase>replace function</phrase>
      </indexes>
    </region>
    <region region-id="440" left="6" top="1344.75" width="317.25" height="42.75" align-x="6" align-y="1356" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <text use-page-width="false" push-down="false" lock-width="true">
        <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">After removing particular components from a packed color matrix, the individual colors can be manipulated and reassembled. As an example, the intensity of the red component in this image will be halved. </p>
      </text>
    </region>
    <region region-id="441" left="36" top="1396.5" width="70.5" height="33.75" align-x="78" align-y="1416" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <math optimize="false" disable-calc="false">
        <ml:define>
          <ml:id xml:space="preserve">newred</ml:id>
          <ml:apply>
            <ml:div />
            <ml:id xml:space="preserve">red</ml:id>
            <ml:real>2</ml:real>
          </ml:apply>
        </ml:define>
      </math>
      <rendering item-idref="16" />
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      <math optimize="false" disable-calc="false">
        <ml:define>
          <ml:id xml:space="preserve">new</ml:id>
          <ml:apply>
            <ml:id xml:space="preserve">replace</ml:id>
            <ml:sequence>
              <ml:id xml:space="preserve">M</ml:id>
              <ml:id xml:space="preserve">newred</ml:id>
              <ml:real>1</ml:real>
            </ml:sequence>
          </ml:apply>
        </ml:define>
      </math>
      <rendering item-idref="17" />
    </region>
    <region region-id="2064" left="36" top="1458" width="193.5" height="180" align-x="132" align-y="1458" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <component hide-arguments="false" clsid-buddy="8442da2d-08d7-45ad-a4a6-f28bee6ae06a" item-idref="18" disable-calc="false">
        <inputs>
          <ml:id xml:space="preserve">new</ml:id>
        </inputs>
        <outputs />
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      <math optimize="false" disable-calc="false">
        <ml:eval>
          <ml:apply>
            <ml:id xml:space="preserve">cols</ml:id>
            <ml:id xml:space="preserve">M</ml:id>
          </ml:apply>
          <result xmlns="http://schemas.mathsoft.com/math20">
            <ml:real>768</ml:real>
          </result>
        </ml:eval>
      </math>
      <rendering item-idref="20" />
    </region>
    <region region-id="445" left="138" top="1650.75" width="87.75" height="15.75" align-x="192" align-y="1662" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <math optimize="false" disable-calc="false">
        <ml:eval>
          <ml:apply>
            <ml:id xml:space="preserve">cols</ml:id>
            <ml:id xml:space="preserve">new</ml:id>
          </ml:apply>
          <result xmlns="http://schemas.mathsoft.com/math20">
            <ml:real>768</ml:real>
          </result>
        </ml:eval>
      </math>
      <rendering item-idref="21" />
    </region>
    <region region-id="2007" left="6" top="1674.75" width="297" height="85.5" align-x="6" align-y="1686" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <text use-page-width="false" push-down="false" lock-width="true">
        <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">The<f family="Times New Roman" charset="0"><inlineAttr font-weight="normal" line-through="false"> red</inlineAttr></f> component of image matrix M has been completely replaced by <f family="Times New Roman" charset="0"><inlineAttr font-weight="normal" line-through="false">newred</inlineAttr></f>. You could replace any matrix - either the red (1), green (2), or blue (3) - in this way. You could also replace any component matrix in an HLS, HSV, or other representation. For a review of these other color systems, see <b><u><link href="./ColorTrn.xmcd" title="Links to section" popup="false">Manipulating Color in Images</link></u></b>.</p>
      </text>
    </region>
    <region region-id="1954" left="0" top="1776" width="4800" height="6" align-x="0" align-y="1776" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <pageBreak />
    </region>
    <region region-id="2016" left="6" top="1788.75" width="87.75" height="14.25" align-x="6" align-y="1800" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <text use-page-width="false" push-down="false" lock-width="true">
        <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">
          <b>
            <c val="#800000">Function Details</c>
          </b>
        </p>
      </text>
    </region>
    <region region-id="2013" left="120" top="1788.75" width="92.25" height="14.25" align-x="120" align-y="1800" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <text use-page-width="false" push-down="false" lock-width="true">
        <p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">
          <b>
            <inlineAttr font-style="normal">
              <c val="#800000">augment(X, Y, Z)</c>
            </inlineAttr>
          </b>
        </p>
      </text>
      <indexes>
        <phrase>augment function</phrase>
      </indexes>
    </region>
    <region region-id="2014" left="228" top="1788.75" width="117" height="14.25" align-x="228" align-y="1800" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <text use-page-width="false" push-down="false" lock-width="true">
        <p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">
          <b>
            <inlineAttr font-style="normal">
              <c val="#800000">subcolor(M, ir, jr, ic, jc)</c>
            </inlineAttr>
          </b>
        </p>
      </text>
      <indexes>
        <phrase>subcolor function</phrase>
      </indexes>
    </region>
    <region region-id="2017" left="6" top="1806.75" width="327" height="71.25" align-x="6" align-y="1818" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <text use-page-width="false" push-down="false" lock-width="true">
        <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">The <f family="Times New Roman" charset="0"><inlineAttr font-weight="normal" font-style="normal" line-through="false">augment </inlineAttr></f>function is used to combine three matrices, for example representing red, green, and blue, into one color matrix. This was demonstrated above to pad a red component of an RGB matrix. It can be used for RGB, HLS, HSV, YIQ, and YCbCr images, and it simply pastes the three matrices together side by side.</p>
      </text>
    </region>
    <region region-id="2018" left="6" top="1884.75" width="336" height="42.75" align-x="6" align-y="1896" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <text use-page-width="false" push-down="false" lock-width="true">
        <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">The<f family="Times New Roman" charset="0"><inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> subcolor </inlineAttr></f>function is used to subset a color matrix (RGB, HLS, etc.) by taking the proper submatrix from each of the three color sections of the combined matrix. </p>
      </text>
    </region>
    <region region-id="2019" left="6" top="1932.75" width="317.25" height="28.5" align-x="6" align-y="1944" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <text use-page-width="false" push-down="false" lock-width="true">
        <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">First, we will create an HSV image by combining separate H, S, and V parts using <f family="Times New Roman" charset="0"><b><inlineAttr font-style="normal" line-through="false">augment</inlineAttr></b></f><inlineAttr font-style="normal">:</inlineAttr></p>
      </text>
    </region>
    <region region-id="2030" left="36" top="1968.75" width="53.25" height="15.75" align-x="60.75" align-y="1980" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
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        <ml:define>
          <ml:id xml:space="preserve">size</ml:id>
          <ml:real>200</ml:real>
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            <ml:real>0</ml:real>
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    <region region-id="2032" left="174" top="1968.75" width="54.75" height="15.75" align-x="186" align-y="1980" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
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          <ml:id xml:space="preserve">j</ml:id>
          <ml:range>
            <ml:real>0</ml:real>
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      </math>
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    <region region-id="2033" left="240" top="1960.5" width="72.75" height="33.75" align-x="254.25" align-y="1980" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
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        <ml:define>
          <ml:apply>
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            <ml:id xml:space="preserve">i</ml:id>
          </ml:apply>
          <ml:parens>
            <ml:apply>
              <ml:minus />
              <ml:id xml:space="preserve">i</ml:id>
              <ml:apply>
                <ml:div />
                <ml:id xml:space="preserve">size</ml:id>
                <ml:real>2</ml:real>
              </ml:apply>
            </ml:apply>
          </ml:parens>
        </ml:define>
      </math>
      <rendering item-idref="25" />
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    <region region-id="2034" left="36" top="1991.25" width="120" height="24.75" align-x="78.75" align-y="2010" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <math optimize="false" disable-calc="false">
        <ml:define>
          <ml:apply>
            <ml:indexer />
            <ml:id xml:space="preserve">Smat</ml:id>
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              <ml:id xml:space="preserve">i</ml:id>
              <ml:id xml:space="preserve">j</ml:id>
            </ml:sequence>
          </ml:apply>
          <ml:apply>
            <ml:sqrt />
            <ml:apply>
              <ml:plus />
              <ml:apply>
                <ml:pow />
                <ml:parens>
                  <ml:apply>
                    <ml:indexer />
                    <ml:id xml:space="preserve">r</ml:id>
                    <ml:id xml:space="preserve">i</ml:id>
                  </ml:apply>
                </ml:parens>
                <ml:real>2</ml:real>
              </ml:apply>
              <ml:apply>
                <ml:pow />
                <ml:parens>
                  <ml:apply>
                    <ml:indexer />
                    <ml:id xml:space="preserve">r</ml:id>
                    <ml:id xml:space="preserve">j</ml:id>
                  </ml:apply>
                </ml:parens>
                <ml:real>2</ml:real>
              </ml:apply>
            </ml:apply>
          </ml:apply>
        </ml:define>
      </math>
      <rendering item-idref="26" />
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      <math optimize="false" disable-calc="false">
        <ml:define warning="WarnRedefinedUDScalar">
          <ml:id xml:space="preserve">Smat</ml:id>
          <ml:apply>
            <ml:id xml:space="preserve">scale</ml:id>
            <ml:sequence>
              <ml:apply>
                <ml:id xml:space="preserve">threshold</ml:id>
                <ml:sequence>
                  <ml:id xml:space="preserve">Smat</ml:id>
                  <ml:real>-100</ml:real>
                </ml:sequence>
              </ml:apply>
              <ml:real>0</ml:real>
              <ml:real>255</ml:real>
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              <ml:id xml:space="preserve">angle</ml:id>
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                <ml:apply>
                  <ml:plus />
                  <ml:apply>
                    <ml:minus />
                    <ml:id xml:space="preserve">i</ml:id>
                    <ml:apply>
                      <ml:div />
                      <ml:id xml:space="preserve">size</ml:id>
                      <ml:real>2</ml:real>
                    </ml:apply>
                  </ml:apply>
                  <ml:real>.00001</ml:real>
                </ml:apply>
                <ml:apply>
                  <ml:minus />
                  <ml:id xml:space="preserve">j</ml:id>
                  <ml:apply>
                    <ml:div />
                    <ml:id xml:space="preserve">size</ml:id>
                    <ml:real>2</ml:real>
                  </ml:apply>
                </ml:apply>
              </ml:sequence>
            </ml:apply>
            <ml:id xml:space="preserve">deg</ml:id>
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      <math optimize="false" disable-calc="false">
        <ml:define warning="WarnRedefinedUDScalar">
          <ml:id xml:space="preserve">Hmat</ml:id>
          <ml:apply>
            <ml:id xml:space="preserve">rotate90</ml:id>
            <ml:id xml:space="preserve">Hmat</ml:id>
          </ml:apply>
        </ml:define>
      </math>
      <rendering item-idref="29" />
    </region>
    <region region-id="2040" left="192" top="2124.75" width="72.75" height="17.25" align-x="236.25" align-y="2136" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <math optimize="false" disable-calc="false">
        <ml:define>
          <ml:apply>
            <ml:indexer />
            <ml:id xml:space="preserve">Vmat</ml:id>
            <ml:sequence>
              <ml:id xml:space="preserve">i</ml:id>
              <ml:id xml:space="preserve">j</ml:id>
            </ml:sequence>
          </ml:apply>
          <ml:real>255</ml:real>
        </ml:define>
      </math>
      <rendering item-idref="30" />
    </region>
    <region region-id="2039" left="36" top="2148.75" width="177" height="15.75" align-x="70.5" align-y="2160" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <math optimize="false" disable-calc="false">
        <ml:define>
          <ml:id xml:space="preserve">wheel</ml:id>
          <ml:apply>
            <ml:id xml:space="preserve">augment</ml:id>
            <ml:sequence>
              <ml:id xml:space="preserve">Hmat</ml:id>
              <ml:id xml:space="preserve">Smat</ml:id>
              <ml:id xml:space="preserve">Vmat</ml:id>
            </ml:sequence>
          </ml:apply>
        </ml:define>
      </math>
      <rendering item-idref="31" />
    </region>
    <region region-id="2044" left="6" top="2178.75" width="336" height="28.5" align-x="6" align-y="2190" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <text use-page-width="false" push-down="false" lock-width="true">
        <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Select a subset of this image in two ways: <f family="Times New Roman" charset="0"><b><inlineAttr font-style="normal" line-through="false">subcolor</inlineAttr></b></f><f family="Times New Roman" charset="0"><inlineAttr font-weight="normal" font-style="normal" line-through="false">, </inlineAttr></f>or<f family="Times New Roman" charset="0"><inlineAttr font-weight="normal" font-style="normal" line-through="false"><sp /></inlineAttr></f><f family="Times New Roman" charset="0"><b><inlineAttr font-style="normal" line-through="false">augment3</inlineAttr></b></f><f family="Times New Roman" charset="0"><inlineAttr font-weight="normal" font-style="normal" line-through="false"><sp /></inlineAttr></f>of three <f family="Times New Roman" charset="0"><inlineAttr font-weight="normal" font-style="normal" line-through="false">submatrix </inlineAttr></f>calls. These produce the same result.</p>
      </text>
      <indexes>
        <phrase>augment3 function</phrase>
      </indexes>
    </region>
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      <math optimize="false" disable-calc="false">
        <ml:define>
          <ml:id xml:space="preserve">start</ml:id>
          <ml:real>30</ml:real>
        </ml:define>
      </math>
      <rendering item-idref="32" />
    </region>
    <region region-id="1797" left="132" top="2214.75" width="53.25" height="15.75" align-x="156.75" align-y="2226" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <math optimize="false" disable-calc="false">
        <ml:define>
          <ml:id xml:space="preserve">end</ml:id>
          <ml:real>130</ml:real>
        </ml:define>
      </math>
      <rendering item-idref="33" />
    </region>
    <region region-id="2048" left="42" top="2238.75" width="237.75" height="15.75" align-x="98.25" align-y="2250" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
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        <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">View the whole image and its two identical subsets:</p>
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        <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">It is also possible to subset an image graphically by selecting and dragging a selection region on it. See the<f family="Times New Roman" charset="0"><inlineAttr font-weight="normal" underline="false" line-through="false"><sp /><link href="./Viewer.xmcd" title="Links to Viewing Images" popup="false">section on </link></inlineAttr></f><b><u><link href="./Viewer.xmcd" title="Links to section" popup="false">Viewing Images</link></u></b> for more information.</p>
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