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              <c val="#800080">Smoothing</c>
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              <c val="#800000">orthosmooth5(M)</c>
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        <phrase>orthosmooth5 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 perform the convolution of a specified smoothing kernel with an image matrix <f family="Times New Roman" charset="0"><inlineAttr font-weight="normal" line-through="false">M</inlineAttr></f>. The names indicate whether smoothing is uniform, orthogonal to the center, or weighted at the center, and the number 5 indicates a 5 <f family="Symbol" charset="2">´ </f>5 kernel is used instead of a 3 <f family="Symbol" charset="2">´ </f>3 kernel. Smoothing is an important technique for noise reduction and differentiating artifacts in an image. Smoothing eliminates minor random noise, but is most effective on uniform, smoothly varying types of noise, like Gaussian noise.</p>
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            <c val="#800000">Arguments</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">The functions return a matrix containing the smoothed image. At the edges of the image, the kernel does not completely overlap the image; therefore, these edge pixels are only convolved with a subset of the kernel and divided by the appropriate normalizing factor.</p>
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          <b>
            <c val="#800000">Function Details</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">Each of these functions uses averaging to replace the value at a pixel by a weighted average involving its value and that of its neighbors. In each case the weights are stored in a square matrix which is convolved with the image to produce the smoothed image. For more information on this process, see <b><u>Convolution</u></b>.</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">The output of this function is the convolution of <f family="Times New Roman" charset="0"><inlineAttr font-weight="normal" line-through="false">M</inlineAttr></f><b><sp /></b>with the following kernel matrix: </p>
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              <ml:real>1</ml:real>
              <ml:real>1</ml:real>
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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">This matrix gives equal weight to the central pixel and each of its 8 neighbors when it averages to get a new value.</p>
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            <ml:real>5</ml:real>
            <ml:real>6</ml:real>
            <ml:real>7</ml:real>
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            <ml:real>9</ml:real>
            <ml:real>10</ml:real>
            <ml:real>11</ml:real>
            <ml:real>12</ml:real>
            <ml:real>12</ml:real>
            <ml:real>12</ml:real>
            <ml:real>12</ml:real>
            <ml:real>12</ml:real>
            <ml:real>12</ml:real>
            <ml:real>12</ml:real>
            <ml:real>12</ml:real>
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              <ml:real>4.5</ml:real>
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              <ml:real>9.3333333333333321</ml:real>
              <ml:real>9.6666666666666661</ml:real>
              <ml:real>10.833333333333332</ml:real>
              <ml:real>11</ml:real>
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              <ml:real>11.5</ml:real>
              <ml:real>11.5</ml:real>
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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 smoothed value at (2,2):</p>
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                <ml:plus />
                <ml:apply>
                  <ml:plus />
                  <ml:apply>
                    <ml:plus />
                    <ml:apply>
                      <ml:plus />
                      <ml:apply>
                        <ml:plus />
                        <ml:apply>
                          <ml:plus />
                          <ml:apply>
                            <ml:plus />
                            <ml:real>5</ml:real>
                            <ml:real>9</ml:real>
                          </ml:apply>
                          <ml:real>12</ml:real>
                        </ml:apply>
                        <ml:real>6</ml:real>
                      </ml:apply>
                      <ml:real>10</ml:real>
                    </ml:apply>
                    <ml:real>12</ml:real>
                  </ml:apply>
                  <ml:real>7</ml:real>
                </ml:apply>
                <ml:real>11</ml:real>
              </ml:apply>
              <ml:real>12</ml:real>
            </ml:apply>
            <ml:real>9</ml:real>
          </ml:apply>
          <result xmlns="http://schemas.mathsoft.com/math20">
            <ml:real>9.3333333333333339</ml:real>
          </result>
        </ml:eval>
      </math>
      <rendering item-idref="9" />
    </region>
    <region region-id="430" left="6" top="894.75" width="129.75" height="14.25" align-x="6" align-y="906" 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">The smoothed value at (3,5):</p>
      </text>
    </region>
    <region region-id="426" left="36" top="916.5" width="129.75" height="33.75" align-x="123" align-y="936" 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:div />
            <ml:apply>
              <ml:plus />
              <ml:apply>
                <ml:plus />
                <ml:apply>
                  <ml:plus />
                  <ml:real>12</ml:real>
                  <ml:real>9</ml:real>
                </ml:apply>
                <ml:real>12</ml:real>
              </ml:apply>
              <ml:real>8</ml:real>
            </ml:apply>
            <ml:real>4</ml:real>
          </ml:apply>
          <result xmlns="http://schemas.mathsoft.com/math20">
            <ml:real>10.25</ml:real>
          </result>
        </ml:eval>
      </math>
      <rendering item-idref="10" />
    </region>
    <region region-id="494" left="6" top="960.75" width="333.75" height="42.75" align-x="6" align-y="972" 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">Since the pixel (3,5) lies at the bottom-right corner of the matrix, where only 4 pixels of the kernel overlap, the above sum is divided by 4 to get the smoothed value.</p>
      </text>
    </region>
    <region region-id="471" left="0" top="1020" width="6000" height="6" align-x="0" align-y="1020" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <pageBreak />
    </region>
    <region region-id="442" left="6" top="1032.75" width="345.75" height="57" align-x="6" align-y="1044" 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">Repeated applications of any of the smoothing functions results in increased blurring, or smoothing. Here are three applications of the uniform weighting function on the following image with noise added. Change the input variables on the image viewer to compare them.</p>
      </text>
    </region>
    <region region-id="433" left="36" top="1104.75" width="174" height="15.75" align-x="51.75" align-y="1116" 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="WarnRedefinedBIUnit">
          <ml:id xml:space="preserve">R</ml:id>
          <ml:apply>
            <ml:id xml:space="preserve">READ_IMAGE</ml:id>
            <ml:str xml:space="preserve">pattern.bmp</ml:str>
          </ml:apply>
        </ml:define>
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      <rendering item-idref="11" />
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    <region region-id="434" left="36" top="1128.75" width="129" height="15.75" align-x="51.75" align-y="1140" 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">R</ml:id>
          <ml:apply>
            <ml:id xml:space="preserve">addnoise</ml:id>
            <ml:sequence>
              <ml:id xml:space="preserve">R</ml:id>
              <ml:real>.01</ml:real>
              <ml:real>150</ml:real>
            </ml:sequence>
          </ml:apply>
        </ml:define>
      </math>
      <rendering item-idref="12" />
    </region>
    <region region-id="436" left="36" top="1152.75" width="96" height="15.75" align-x="58.5" align-y="1164" 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">RS</ml:id>
          <ml:apply>
            <ml:id xml:space="preserve">unismooth</ml:id>
            <ml:id xml:space="preserve">R</ml:id>
          </ml:apply>
        </ml:define>
      </math>
      <rendering item-idref="13" />
    </region>
    <region region-id="438" left="36" top="1176.75" width="109.5" height="15.75" align-x="65.25" align-y="1188" 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">RSS</ml:id>
          <ml:apply>
            <ml:id xml:space="preserve">unismooth</ml:id>
            <ml:id xml:space="preserve">RS</ml:id>
          </ml:apply>
        </ml:define>
      </math>
      <rendering item-idref="14" />
    </region>
    <region region-id="440" left="36" top="1200.75" width="116.25" height="15.75" align-x="72" align-y="1212" 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">RSSS</ml:id>
          <ml:apply>
            <ml:id xml:space="preserve">unismooth</ml:id>
            <ml:id xml:space="preserve">RS</ml:id>
          </ml:apply>
        </ml:define>
      </math>
      <rendering item-idref="15" />
    </region>
    <region region-id="519" left="36" top="1218" width="114" height="105" align-x="92.25" align-y="1218" 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="16" disable-calc="false">
        <inputs>
          <ml:id xml:space="preserve">R</ml:id>
        </inputs>
        <outputs />
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      <rendering item-idref="17" />
    </region>
    <region region-id="520" left="174" top="1218" width="114" height="105" align-x="230.25" align-y="1218" 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">RSSS</ml:id>
        </inputs>
        <outputs />
      </component>
      <rendering item-idref="19" />
    </region>
    <region region-id="472" left="0" top="1338" width="4800" height="6" align-x="0" align-y="1338" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <pageBreak />
    </region>
    <region region-id="498" left="6" top="1356.75" width="315" height="28.5" align-x="6" align-y="1368" 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">The rest of the smoothing functions work the same way, with different kernels.</p>
      </text>
    </region>
    <region region-id="444" left="6" top="1392.75" width="79.5" height="14.25" align-x="6" align-y="1404" 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">centsmooth(M)</c>
            </inlineAttr>
          </b>
        </p>
      </text>
      <indexes>
        <phrase>centsmooth function</phrase>
      </indexes>
    </region>
    <region region-id="448" left="6" top="1410.75" width="187.5" height="14.25" align-x="6" align-y="1422" 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">This function convolves <f family="Times New Roman" charset="0"><inlineAttr font-weight="normal" line-through="false">M</inlineAttr></f> with the kernel</p>
      </text>
    </region>
    <region region-id="446" left="36" top="1437.75" width="97.5" height="57.75" align-x="53.25" align-y="1470" 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">K</ml:id>
          <ml:apply>
            <ml:mult style="default" />
            <ml:apply>
              <ml:div />
              <ml:real>1</ml:real>
              <ml:real>10</ml:real>
            </ml:apply>
            <ml:matrix rows="3" cols="3">
              <ml:real>1</ml:real>
              <ml:real>1</ml:real>
              <ml:real>1</ml:real>
              <ml:real>1</ml:real>
              <ml:real>2</ml:real>
              <ml:real>1</ml:real>
              <ml:real>1</ml:real>
              <ml:real>1</ml:real>
              <ml:real>1</ml:real>
            </ml:matrix>
          </ml:apply>
        </ml:define>
      </math>
      <rendering item-idref="20" />
    </region>
    <region region-id="449" left="6" top="1506.75" width="196.5" height="14.25" align-x="6" align-y="1518" 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">which gives more weight to the center pixel.</p>
      </text>
    </region>
    <region region-id="454" left="6" top="1542.75" width="90.75" height="14.25" align-x="6" align-y="1554" 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">orthosmooth(M)</c>
            </inlineAttr>
          </b>
        </p>
      </text>
      <indexes>
        <phrase>orthosmooth function</phrase>
      </indexes>
    </region>
    <region region-id="455" left="6" top="1560.75" width="187.5" height="14.25" align-x="6" align-y="1572" 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">This function convolves<b><sp /></b><f family="Times New Roman" charset="0"><inlineAttr font-weight="normal" line-through="false">M</inlineAttr></f><b><sp /></b>with the kernel</p>
      </text>
    </region>
    <region region-id="452" left="36" top="1587.75" width="97.5" height="57.75" align-x="53.25" 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">K</ml:id>
          <ml:apply>
            <ml:mult style="default" />
            <ml:apply>
              <ml:div />
              <ml:real>1</ml:real>
              <ml:real>16</ml:real>
            </ml:apply>
            <ml:matrix rows="3" cols="3">
              <ml:real>1</ml:real>
              <ml:real>2</ml:real>
              <ml:real>1</ml:real>
              <ml:real>2</ml:real>
              <ml:real>4</ml:real>
              <ml:real>2</ml:real>
              <ml:real>1</ml:real>
              <ml:real>2</ml:real>
              <ml:real>1</ml:real>
            </ml:matrix>
          </ml:apply>
        </ml:define>
      </math>
      <rendering item-idref="21" />
    </region>
    <region region-id="456" left="6" top="1656.75" width="328.5" height="28.5" 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="0" text-align="left" list-style-type="none" tabs="inherit">The kernel gives added weight both to the center and to the orthogonal neighbors, which retains image quality more satisfactorily in some images.</p>
      </text>
    </region>
    <region region-id="457" left="0" top="1704" width="6000" height="6" align-x="0" align-y="1704" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <pageBreak />
    </region>
    <region region-id="458" left="6" top="1722.75" width="76.5" height="14.25" align-x="6" align-y="1734" 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">unismooth5(M)</c>
            </inlineAttr>
          </b>
        </p>
      </text>
      <indexes>
        <phrase>unismooth5 function</phrase>
      </indexes>
    </region>
    <region region-id="459" left="6" top="1740.75" width="187.5" height="14.25" align-x="6" align-y="1752" 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">This function convolves <f family="Times New Roman" charset="0"><inlineAttr font-weight="normal" line-through="false">M</inlineAttr></f><b><sp /></b>with the kernel</p>
      </text>
    </region>
    <region region-id="461" left="36" top="1764.75" width="126" height="99.75" align-x="53.25" align-y="1818" 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">K</ml:id>
          <ml:apply>
            <ml:mult style="default" />
            <ml:apply>
              <ml:div />
              <ml:real>1</ml:real>
              <ml:real>25</ml:real>
            </ml:apply>
            <ml:matrix rows="5" cols="5">
              <ml:real>1</ml:real>
              <ml:real>1</ml:real>
              <ml:real>1</ml:real>
              <ml:real>1</ml:real>
              <ml:real>1</ml:real>
              <ml:real>1</ml:real>
              <ml:real>1</ml:real>
              <ml:real>1</ml:real>
              <ml:real>1</ml:real>
              <ml:real>1</ml:real>
              <ml:real>1</ml:real>
              <ml:real>1</ml:real>
              <ml:real>1</ml:real>
              <ml:real>1</ml:real>
              <ml:real>1</ml:real>
              <ml:real>1</ml:real>
              <ml:real>1</ml:real>
              <ml:real>1</ml:real>
              <ml:real>1</ml:real>
              <ml:real>1</ml:real>
              <ml:real>1</ml:real>
              <ml:real>1</ml:real>
              <ml:real>1</ml:real>
              <ml:real>1</ml:real>
              <ml:real>1</ml:real>
            </ml:matrix>
          </ml:apply>
        </ml:define>
      </math>
      <rendering item-idref="22" />
    </region>
    <region region-id="462" left="6" top="1878.75" width="330" height="71.25" align-x="6" align-y="1890" 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">The 5<f family="Symbol" charset="2">´</f>5 kernel may result in more uniform smoothing of images with small sharp features (such as noise) in uniform backgrounds. It is a better lowpass filter than the 3<f family="Symbol" charset="2">´</f>3 kernel. To understand why this is true, consider the comments on convolution and its equivalent in the frequency domain, as discussed in <b><u>Convolution</u></b>.</p>
      </text>
      <link href="./Convol.xmcd" title="Links to section" popup="false" />
    </region>
    <region region-id="463" left="6" top="1968.75" width="89.25" height="14.25" align-x="6" align-y="1980" 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">orthosmooth5(M)</c>
            </inlineAttr>
          </b>
        </p>
      </text>
      <indexes>
        <phrase>orthosmooth5 function</phrase>
      </indexes>
    </region>
    <region region-id="464" left="6" top="1986.75" width="187.5" height="14.25" align-x="6" align-y="1998" 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">This function convolves<b><sp /></b><f family="Times New Roman" charset="0"><inlineAttr font-weight="normal" line-through="false">M</inlineAttr></f><b><sp /></b>with the kernel</p>
      </text>
    </region>
    <region region-id="465" left="36" top="2010.75" width="126" height="99.75" align-x="53.25" align-y="2064" 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">K</ml:id>
          <ml:apply>
            <ml:mult style="default" />
            <ml:apply>
              <ml:div />
              <ml:real>1</ml:real>
              <ml:real>32</ml:real>
            </ml:apply>
            <ml:matrix rows="5" cols="5">
              <ml:real>1</ml:real>
              <ml:real>1</ml:real>
              <ml:real>1</ml:real>
              <ml:real>1</ml:real>
              <ml:real>1</ml:real>
              <ml:real>1</ml:real>
              <ml:real>1</ml:real>
              <ml:real>2</ml:real>
              <ml:real>1</ml:real>
              <ml:real>1</ml:real>
              <ml:real>1</ml:real>
              <ml:real>2</ml:real>
              <ml:real>4</ml:real>
              <ml:real>2</ml:real>
              <ml:real>1</ml:real>
              <ml:real>1</ml:real>
              <ml:real>1</ml:real>
              <ml:real>2</ml:real>
              <ml:real>1</ml:real>
              <ml:real>1</ml:real>
              <ml:real>1</ml:real>
              <ml:real>1</ml:real>
              <ml:real>1</ml:real>
              <ml:real>1</ml:real>
              <ml:real>1</ml:real>
            </ml:matrix>
          </ml:apply>
        </ml:define>
      </math>
      <rendering item-idref="23" />
    </region>
    <region region-id="166" left="6" top="2124.75" width="326.25" height="42.75" align-x="6" align-y="2136" 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">As with <b>centsmooth</b> and <b>orthosmooth</b>, this kernel may retain image features more appropriately because of the additional weight given to the center pixels.</p>
      </text>
    </region>
    <region region-id="165" left="6" top="2172.75" width="345" height="28.5" align-x="6" align-y="2184" 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">See if you can readily distinguish the effects of the various smoothing kernels. Examine their effects particularly at edges of an image and in noisy regions.</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">Remember that you can design and try out your own smoothing filters using the convolution functions described in <b><u><link href="./Convol.xmcd" title="Links to section" popup="false">Convolution</link></u></b>.</p>
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