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            <b>
              <c val="#800080">2D Image Correlation</c>
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        <phrase>2-D image correlation</phrase>
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            <c val="#800000">Function Definitions and Syntax</c>
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              <c val="#800000">correl2d(M, K)</c>
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        <p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">This function performs the correlation of an arbitrary-sized kernel, K, with the image matrix <f family="Times New Roman" charset="0"><inlineAttr font-weight="normal" line-through="false">M</inlineAttr></f><b><sp /></b>. Correlation is an important filtering technique for template (or prototype) matching. </p>
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            <c val="#800000">Arguments</c>
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              <inlineAttr line-through="false">M</inlineAttr>
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          </f>, the image matrix, and</p>
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              <c val="#008080">•</c>
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        <p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">The function returns a matrix of the same size as M containing the image correlated with the kernel. </p>
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        <p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">The correlation is performed in the spatial domain, and image boundaries are treated by zero padding the input image; however, the size of the output image is the same as the input image. The origin of the kernel is assumed to be at the center of the kernel which ensures a zero-phase-shift correlation output (that is, the corresponding features in the input and output images are not shifted with respect to each other.)</p>
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              <c val="#800000">correl2d(M, K)</c>
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        <p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">Correlation is very similar to convolution (see the <b><u>convol2d</u></b> function). Like convolution, it is the process of sliding a filter matrix (called the kernel) across an image matrix, multiplying each element in the overlapping areas, summing these results, and inserting this sum into an element of the resulting matrix. This is illustrated in the drawing to the right with a 3 <f family="Symbol" charset="2">´ </f>3 kernel, where the colored squares in the correlated matrix correspond to the multiplication and summation in correspondingly colored overlap regions.</p>
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        <phrase>correlated matrix</phrase>
        <phrase>kernel</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">The<f family="Times New Roman" charset="0"><inlineAttr font-style="normal" line-through="false"> difference </inlineAttr></f>between correlation and convolution is that correlation checks the kernel against the image for similarity, while convolution involves flipping the kernel in order to correspond to multiplication in the transform domain. </p>
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        <p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">Suppose we are trying to locate the position of a template, K, on the input matrix, M. The center position where M is most similar to K is given by the point in the correlated output matrix that has the largest value. </p>
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        <p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">The largest value in the correlation output is 23, which occurs at location (2,2). As can be seen from the input matrix M, the template does occur at that location in the image.</p>
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        <p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">When part of the overlapped kernel lies outside the image <f family="Times New Roman" charset="0"><inlineAttr font-weight="normal" line-through="false">M</inlineAttr></f>, the correlation sum contains fewer than nine terms. This is equivalent to padding the input image with zeros. For example, the upper left output element is:</p>
      </text>
    </region>
    <region region-id="452" left="36" top="1062.75" width="132.75" height="15.75" align-x="147" align-y="1074" 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:plus />
            <ml:apply>
              <ml:plus />
              <ml:apply>
                <ml:plus />
                <ml:apply>
                  <ml:mult style="default" />
                  <ml:real>2</ml:real>
                  <ml:real>3</ml:real>
                </ml:apply>
                <ml:apply>
                  <ml:mult style="default" />
                  <ml:real>1</ml:real>
                  <ml:real>1</ml:real>
                </ml:apply>
              </ml:apply>
              <ml:apply>
                <ml:mult style="default" />
                <ml:real>0</ml:real>
                <ml:real>1</ml:real>
              </ml:apply>
            </ml:apply>
            <ml:apply>
              <ml:mult style="default" />
              <ml:real>1</ml:real>
              <ml:real>2</ml:real>
            </ml:apply>
          </ml:apply>
          <result xmlns="http://schemas.mathsoft.com/math20">
            <ml:real>9</ml:real>
          </result>
        </ml:eval>
      </math>
      <rendering item-idref="10" />
    </region>
    <region region-id="451" left="6" top="1092.75" width="251.25" height="14.25" align-x="6" align-y="1104" 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">In <f family="Times New Roman" charset="0"><inlineAttr font-weight="normal" line-through="false">Mathcad</inlineAttr></f>, you could define the correlation function as</p>
      </text>
    </region>
    <region region-id="449" left="36" top="1119.75" width="376.5" height="51" align-x="153" align-y="1146" 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:function>
            <ml:id xml:space="preserve">mcad_corr2d</ml:id>
            <ml:boundVars>
              <ml:id xml:space="preserve">i</ml:id>
              <ml:id xml:space="preserve">j</ml:id>
              <ml:id xml:space="preserve">m</ml:id>
              <ml:id xml:space="preserve">n</ml:id>
            </ml:boundVars>
          </ml:function>
          <ml:apply>
            <ml:summation />
            <ml:lambda>
              <ml:boundVars>
                <ml:id xml:space="preserve">k</ml:id>
              </ml:boundVars>
              <ml:apply>
                <ml:summation />
                <ml:lambda>
                  <ml:boundVars>
                    <ml:id xml:space="preserve">d</ml:id>
                  </ml:boundVars>
                  <ml:parens>
                    <ml:apply>
                      <ml:mult style="default" />
                      <ml:apply>
                        <ml:indexer />
                        <ml:id xml:space="preserve">K</ml:id>
                        <ml:sequence>
                          <ml:id xml:space="preserve">k</ml:id>
                          <ml:id xml:space="preserve">d</ml:id>
                        </ml:sequence>
                      </ml:apply>
                      <ml:apply>
                        <ml:indexer />
                        <ml:id xml:space="preserve">M</ml:id>
                        <ml:sequence>
                          <ml:apply>
                            <ml:minus />
                            <ml:apply>
                              <ml:plus />
                              <ml:id xml:space="preserve">k</ml:id>
                              <ml:id xml:space="preserve">i</ml:id>
                            </ml:apply>
                            <ml:apply>
                              <ml:id xml:space="preserve">floor</ml:id>
                              <ml:apply>
                                <ml:div />
                                <ml:id xml:space="preserve">m</ml:id>
                                <ml:real>2</ml:real>
                              </ml:apply>
                            </ml:apply>
                          </ml:apply>
                          <ml:apply>
                            <ml:minus />
                            <ml:apply>
                              <ml:plus />
                              <ml:id xml:space="preserve">d</ml:id>
                              <ml:id xml:space="preserve">j</ml:id>
                            </ml:apply>
                            <ml:apply>
                              <ml:id xml:space="preserve">floor</ml:id>
                              <ml:apply>
                                <ml:div />
                                <ml:id xml:space="preserve">n</ml:id>
                                <ml:real>2</ml:real>
                              </ml:apply>
                            </ml:apply>
                          </ml:apply>
                        </ml:sequence>
                      </ml:apply>
                    </ml:apply>
                  </ml:parens>
                </ml:lambda>
                <ml:bounds>
                  <ml:real>0</ml:real>
                  <ml:apply>
                    <ml:minus />
                    <ml:id xml:space="preserve">n</ml:id>
                    <ml:real>1</ml:real>
                  </ml:apply>
                </ml:bounds>
              </ml:apply>
            </ml:lambda>
            <ml:bounds>
              <ml:real>0</ml:real>
              <ml:apply>
                <ml:minus />
                <ml:id xml:space="preserve">m</ml:id>
                <ml:real>1</ml:real>
              </ml:apply>
            </ml:bounds>
          </ml:apply>
        </ml:define>
      </math>
      <rendering item-idref="11" />
    </region>
    <region region-id="462" left="6" top="1182.75" width="315" height="28.5" align-x="6" align-y="1194" 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">where<b><sp /></b><f family="Times New Roman" charset="0"><inlineAttr font-weight="normal" line-through="false">i and j</inlineAttr></f> are the row and column indices of the output matrix, and<b><sp /></b><f family="Times New Roman" charset="0"><inlineAttr font-weight="normal" line-through="false">the kernel size is m by n. </inlineAttr></f></p>
      </text>
    </region>
    <region region-id="571" left="30" top="1230.75" width="148.5" height="15.75" align-x="150.75" align-y="1242" 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">mcad_corr2d</ml:id>
            <ml:sequence>
              <ml:real>2</ml:real>
              <ml:real>3</ml:real>
              <ml:real>3</ml:real>
              <ml:real>3</ml:real>
            </ml:sequence>
          </ml:apply>
          <result xmlns="http://schemas.mathsoft.com/math20">
            <ml:real>12</ml:real>
          </result>
        </ml:eval>
      </math>
      <rendering item-idref="12" />
    </region>
    <region region-id="575" left="198" top="1230.75" width="125.25" height="17.25" align-x="295.5" align-y="1242" 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:indexer />
            <ml:apply>
              <ml:id xml:space="preserve">correl2d</ml:id>
              <ml:sequence>
                <ml:id xml:space="preserve">M</ml:id>
                <ml:id xml:space="preserve">K</ml:id>
              </ml:sequence>
            </ml:apply>
            <ml:sequence>
              <ml:real>2</ml:real>
              <ml:real>3</ml:real>
            </ml:sequence>
          </ml:apply>
          <result xmlns="http://schemas.mathsoft.com/math20">
            <ml:real>12</ml:real>
          </result>
        </ml:eval>
      </math>
      <rendering item-idref="13" />
    </region>
    <region region-id="463" left="6" top="1260.75" width="340.5" height="42.75" align-x="6" align-y="1272" 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">Notice that if you give this Mathcad function a<f family="Times New Roman" charset="0"><inlineAttr font-weight="normal" line-through="false">n i or j</inlineAttr></f> corresponding to an edge point, an error results, since we have only made an allowance for the case where the whole kernel overlaps.</p>
      </text>
    </region>
    <region region-id="577" 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="485" left="6" top="1326.75" width="294.75" height="28.5" 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="inherit" text-align="left" list-style-type="inherit" tabs="inherit">One interesting kernel is the <f family="Times New Roman" charset="0"><b><inlineAttr line-through="false">Gaussian kernel</inlineAttr></b></f>, which produces a smoothing effect. Here, a 5 <f family="Symbol" charset="2"><inlineAttr line-through="false">´ </inlineAttr></f>5 kernel is generated.</p>
      </text>
      <indexes>
        <phrase>Gaussian kernel</phrase>
      </indexes>
    </region>
    <region region-id="486" left="36" top="1368.75" width="156" height="15.75" align-x="54.75" align-y="1380" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <math optimize="false" disable-calc="false">
        <ml:define warning="WarnRedefinedUDScalar">
          <ml:id xml:space="preserve">M</ml:id>
          <ml:apply>
            <ml:id xml:space="preserve">READ_IMAGE</ml:id>
            <ml:str xml:space="preserve">bear.gif</ml:str>
          </ml:apply>
        </ml:define>
      </math>
      <rendering item-idref="14" />
    </region>
    <region region-id="493" left="36" top="1392.75" width="42.75" height="15.75" align-x="46.5" align-y="1404" 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">i</ml:id>
          <ml:range>
            <ml:real>0</ml:real>
            <ml:real>4</ml:real>
          </ml:range>
        </ml:define>
      </math>
      <rendering item-idref="15" />
    </region>
    <region region-id="494" left="108" top="1392.75" width="44.25" height="15.75" align-x="120" align-y="1404" 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">j</ml:id>
          <ml:range>
            <ml:real>0</ml:real>
            <ml:real>4</ml:real>
          </ml:range>
        </ml:define>
      </math>
      <rendering item-idref="16" />
    </region>
    <region region-id="495" left="36" top="1415.25" width="189.75" height="39" align-x="64.5" align-y="1440" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <math optimize="false" disable-calc="false">
        <ml:define warning="WarnRedefinedUDScalar">
          <ml:apply>
            <ml:indexer />
            <ml:id xml:space="preserve">K</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:apply>
            <ml:mult style="default" />
            <ml:apply>
              <ml:id xml:space="preserve">exp</ml:id>
              <ml:apply>
                <ml:neg />
                <ml:apply>
                  <ml:div />
                  <ml:apply>
                    <ml:pow />
                    <ml:parens>
                      <ml:apply>
                        <ml:minus />
                        <ml:id xml:space="preserve">i</ml:id>
                        <ml:real>2</ml:real>
                      </ml:apply>
                    </ml:parens>
                    <ml:real>2</ml:real>
                  </ml:apply>
                  <ml:real>1.5</ml:real>
                </ml:apply>
              </ml:apply>
            </ml:apply>
            <ml:apply>
              <ml:id xml:space="preserve">exp</ml:id>
              <ml:apply>
                <ml:neg />
                <ml:apply>
                  <ml:div />
                  <ml:apply>
                    <ml:pow />
                    <ml:parens>
                      <ml:apply>
                        <ml:minus />
                        <ml:id xml:space="preserve">j</ml:id>
                        <ml:real>2</ml:real>
                      </ml:apply>
                    </ml:parens>
                    <ml:real>2</ml:real>
                  </ml:apply>
                  <ml:real>1.5</ml:real>
                </ml:apply>
              </ml:apply>
            </ml:apply>
          </ml:apply>
        </ml:define>
      </math>
      <rendering item-idref="17" />
    </region>
    <region region-id="496" left="36" top="1465.5" width="291.75" height="110.25" align-x="52.5" align-y="1524" 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:id xml:space="preserve">K</ml:id>
          <result xmlns="http://schemas.mathsoft.com/math20">
            <ml:matrix rows="5" cols="5">
              <ml:real>0.0048279499938314414</ml:real>
              <ml:real>0.0356739933472524</ml:real>
              <ml:real>0.069483451222801543</ml:real>
              <ml:real>0.0356739933472524</ml:real>
              <ml:real>0.0048279499938314414</ml:real>
              <ml:real>0.0356739933472524</ml:real>
              <ml:real>0.26359713811572677</ml:real>
              <ml:real>0.513417119032592</ml:real>
              <ml:real>0.26359713811572677</ml:real>
              <ml:real>0.0356739933472524</ml:real>
              <ml:real>0.069483451222801543</ml:real>
              <ml:real>0.513417119032592</ml:real>
              <ml:real>1</ml:real>
              <ml:real>0.513417119032592</ml:real>
              <ml:real>0.069483451222801543</ml:real>
              <ml:real>0.0356739933472524</ml:real>
              <ml:real>0.26359713811572677</ml:real>
              <ml:real>0.513417119032592</ml:real>
              <ml:real>0.26359713811572677</ml:real>
              <ml:real>0.0356739933472524</ml:real>
              <ml:real>0.0048279499938314414</ml:real>
              <ml:real>0.0356739933472524</ml:real>
              <ml:real>0.069483451222801543</ml:real>
              <ml:real>0.0356739933472524</ml:real>
              <ml:real>0.0048279499938314414</ml:real>
            </ml:matrix>
          </result>
        </ml:eval>
      </math>
      <rendering item-idref="18" />
    </region>
    <region region-id="505" left="6" top="1590.75" width="287.25" height="14.25" align-x="6" align-y="1602" 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">Take just a small portion of the picture, to speed the calculation:</p>
      </text>
    </region>
    <region region-id="500" left="36" top="1608.75" width="189" height="15.75" align-x="54.75" align-y="1620" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <math optimize="false" disable-calc="false">
        <ml:define warning="WarnRedefinedUDScalar">
          <ml:id xml:space="preserve">M</ml:id>
          <ml:apply>
            <ml:id xml:space="preserve">submatrix</ml:id>
            <ml:sequence>
              <ml:id xml:space="preserve">M</ml:id>
              <ml:real>100</ml:real>
              <ml:real>230</ml:real>
              <ml:real>100</ml:real>
              <ml:real>230</ml:real>
            </ml:sequence>
          </ml:apply>
        </ml:define>
      </math>
      <rendering item-idref="19" />
    </region>
    <region region-id="501" left="36" top="1632.75" width="124.5" height="15.75" align-x="76.5" align-y="1644" 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">CORR</ml:id>
          <ml:apply>
            <ml:id xml:space="preserve">correl2d</ml:id>
            <ml:sequence>
              <ml:id xml:space="preserve">M</ml:id>
              <ml:id xml:space="preserve">K</ml:id>
            </ml:sequence>
          </ml:apply>
        </ml:define>
      </math>
      <rendering item-idref="20" />
    </region>
    <region region-id="635" left="6" top="1656.75" width="331.5" height="42.75" align-x="6" align-y="1668" 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">Compare the result of correlation with the results of the convolution function. Since the kernel is symmetric, the two functions, convolution and correlation give the same result:</p>
      </text>
    </region>
    <region region-id="642" left="36" top="1704.75" width="130.5" height="15.75" align-x="78.75" align-y="1716" 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">CONV</ml:id>
          <ml:apply>
            <ml:id xml:space="preserve">convol2d</ml:id>
            <ml:sequence>
              <ml:id xml:space="preserve">M</ml:id>
              <ml:id xml:space="preserve">K</ml:id>
            </ml:sequence>
          </ml:apply>
        </ml:define>
      </math>
      <rendering item-idref="21" />
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    <region region-id="614" left="0" top="1728" width="6000" height="6" align-x="0" align-y="1728" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <pageBreak />
    </region>
    <region region-id="665" left="24" top="1746" width="99.75" height="128.25" align-x="72.75" align-y="1746" 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="22" disable-calc="false">
        <inputs>
          <ml:id xml:space="preserve">M</ml:id>
        </inputs>
        <outputs />
      </component>
      <rendering item-idref="23" />
    </region>
    <region region-id="664" left="162" top="1746" width="101.25" height="128.25" align-x="210.75" align-y="1746" 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="24" disable-calc="false">
        <inputs>
          <ml:apply>
            <ml:id xml:space="preserve">scale</ml:id>
            <ml:sequence>
              <ml:id xml:space="preserve">CORR</ml:id>
              <ml:real>0</ml:real>
              <ml:real>255</ml:real>
            </ml:sequence>
          </ml:apply>
        </inputs>
        <outputs />
      </component>
      <rendering item-idref="25" />
    </region>
    <region region-id="663" left="312" top="1746" width="103.5" height="128.25" align-x="360.75" align-y="1746" 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="26" disable-calc="false">
        <inputs>
          <ml:apply>
            <ml:id xml:space="preserve">scale</ml:id>
            <ml:sequence>
              <ml:id xml:space="preserve">CONV</ml:id>
              <ml:real>0</ml:real>
              <ml:real>255</ml:real>
            </ml:sequence>
          </ml:apply>
        </inputs>
        <outputs />
      </component>
      <rendering item-idref="27" />
    </region>
    <region region-id="637" left="6" top="1884.75" width="333.75" height="28.5" 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="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">Let's verify that the maximum difference between the two images is indeed </p>
        <p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">very small (almost zero):</p>
      </text>
    </region>
    <region region-id="616" left="60" top="1924.5" width="149.25" height="24" align-x="187.5" align-y="1944" 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">max</ml:id>
            <ml:apply>
              <ml:vectorize />
              <ml:apply>
                <ml:absval />
                <ml:apply>
                  <ml:minus />
                  <ml:id xml:space="preserve">CONV</ml:id>
                  <ml:id xml:space="preserve">CORR</ml:id>
                </ml:apply>
              </ml:apply>
            </ml:apply>
          </ml:apply>
          <result xmlns="http://schemas.mathsoft.com/math20">
            <ml:real>0</ml:real>
          </result>
        </ml:eval>
      </math>
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