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              <c val="#800080">Tracking Moving Objects in Aerial Images</c>
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            <inlineAttr line-through="false">Tracking and monitoring traffic flows from aerial image sequences is of interest for surveillance, traffic control, and military applications. The current manual approach is labor-intensive, costly in terms of time and data storage, and can be inaccurate. This example demonstrates a feasible way of tracking moving vehicles from two consecutive aerial image frames by applying the image-processing techniques available in the Image Processing Extension Pack.</inlineAttr>
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                <ml:real>255</ml:real>
                <ml:id xml:space="preserve">mask2</ml:id>
              </ml:apply>
            </ml:apply>
            <ml:apply>
              <ml:id xml:space="preserve">mask</ml:id>
              <ml:sequence>
                <ml:id xml:space="preserve">M1</ml:id>
                <ml:id xml:space="preserve">mask2</ml:id>
              </ml:sequence>
            </ml:apply>
          </ml:apply>
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      <component hide-arguments="false" clsid-buddy="8442da2d-08d7-45ad-a4a6-f28bee6ae06a" item-idref="25" disable-calc="false">
        <inputs>
          <ml:id xml:space="preserve">car1</ml:id>
        </inputs>
        <outputs />
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        <inputs>
          <ml:id xml:space="preserve">car2</ml:id>
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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">Next, we need to find the corresponding objects among the regions in the second frame. First, we extract all these region labels:</p>
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        <ml:define>
          <ml:id xml:space="preserve">i</ml:id>
          <ml:range>
            <ml:real>0</ml:real>
            <ml:apply>
              <ml:minus />
              <ml:apply>
                <ml:id xml:space="preserve">max</ml:id>
                <ml:id xml:space="preserve">RM2</ml:id>
              </ml:apply>
              <ml:real>1</ml:real>
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          </ml:range>
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      <math optimize="false" disable-calc="false">
        <ml:define>
          <ml:apply>
            <ml:indexer />
            <ml:id xml:space="preserve">reg</ml:id>
            <ml:id xml:space="preserve">i</ml:id>
          </ml:apply>
          <ml:apply>
            <ml:vectorize />
            <ml:parens>
              <ml:apply>
                <ml:equal />
                <ml:id xml:space="preserve">RM2</ml:id>
                <ml:id xml:space="preserve">i</ml:id>
              </ml:apply>
            </ml:parens>
          </ml:apply>
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    </region>
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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">Then, extract the shape features from all the regions in both frames - see the section on <b><u><link href="./shapefea.xmcd" title="Links to section" popup="false">shape features</link></u></b> for more information:</p>
      </text>
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      <math optimize="false" disable-calc="false">
        <ml:define>
          <ml:id xml:space="preserve">shape1</ml:id>
          <ml:apply>
            <ml:id xml:space="preserve">shape_features</ml:id>
            <ml:id xml:space="preserve">RM1</ml:id>
          </ml:apply>
        </ml:define>
      </math>
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    <region region-id="1418" left="204" top="1470.75" width="152.25" height="15.75" align-x="244.5" align-y="1482" 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">shape2</ml:id>
          <ml:apply>
            <ml:id xml:space="preserve">shape_features</ml:id>
            <ml:id xml:space="preserve">RM2</ml:id>
          </ml:apply>
        </ml:define>
      </math>
      <rendering item-idref="32" />
    </region>
    <region region-id="1416" left="0" top="1500" width="6000" height="6" align-x="0" align-y="1500" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <pageBreak />
    </region>
    <region region-id="1409" left="6" top="1512.75" width="358.5" height="114" align-x="6" align-y="1524" 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">Since different shape features vary widely in scale, we use the normalized "distance" between the feature vectors for the two frames as criteria for finding the best match between regions. We don't want to consider the shape features that locate the region (for example, centroid and bounding box). These are excluded from the shape vector; only columns 2 through 9 are considered, containing only relevant features such as area and spatial variance. The normalized distance between each of the features in frame 2 and frame 1 is given by</p>
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      <math optimize="false" disable-calc="false">
        <ml:define>
          <ml:apply>
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          </ml:apply>
          <ml:apply>
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            </ml:lambda>
            <ml:bounds>
              <ml:real>2</ml:real>
              <ml:real>9</ml:real>
            </ml:bounds>
          </ml:apply>
        </ml:define>
      </math>
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      <math optimize="false" disable-calc="false">
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                </ml:apply>
              </ml:apply>
            </ml:lambda>
            <ml:bounds>
              <ml:real>2</ml:real>
              <ml:real>9</ml:real>
            </ml:bounds>
          </ml:apply>
        </ml:define>
      </math>
      <rendering item-idref="34" />
    </region>
    <region region-id="1419" left="6" top="1752.75" width="314.25" height="14.25" align-x="6" align-y="1764" 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">The best match to each car is the region with the lowest total distance:</p>
      </text>
    </region>
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      <math optimize="false" disable-calc="false">
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            <ml:id xml:space="preserve">min</ml:id>
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          </ml:apply>
        </ml:define>
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      <math optimize="false" disable-calc="false">
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      <math optimize="false" disable-calc="false">
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      <math optimize="false" disable-calc="false">
        <ml:eval>
          <ml:id xml:space="preserve">idx1</ml:id>
          <result xmlns="http://schemas.mathsoft.com/math20">
            <ml:matrix rows="10" cols="1">
              <ml:real>0</ml:real>
              <ml:real>0</ml:real>
              <ml:real>0</ml:real>
              <ml:real>0</ml:real>
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              <ml:real>0</ml:real>
              <ml:real>0</ml:real>
              <ml:real>0</ml:real>
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        </ml:eval>
        <resultFormat>
          <general precision="3" show-trailing-zeros="false" radix="dec" complex-threshold="10" exponential-threshold="3" />
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        <ml:eval>
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            <ml:matrix rows="10" cols="1">
              <ml:real>0</ml:real>
              <ml:real>0</ml:real>
              <ml:real>0</ml:real>
              <ml:real>0</ml:real>
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              <ml:real>0</ml:real>
              <ml:real>1</ml:real>
              <ml:real>0</ml:real>
              <ml:real>0</ml:real>
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        <resultFormat>
          <general precision="3" show-trailing-zeros="false" radix="dec" complex-threshold="10" exponential-threshold="3" />
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    </region>
    <region region-id="1358" left="0" top="2034" width="4800" height="6" align-x="0" align-y="2034" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <pageBreak />
    </region>
    <region region-id="1425" left="6" top="2046.75" width="350.25" height="42.75" align-x="6" align-y="2058" 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">The above results show that the best match for car 1 is region #6 in frame 2, and the one for car 2 is region #7. The following visual inspection, using the same masking technique as before, verifies the results.</p>
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    <region region-id="1277" left="42" top="2094.75" width="220.5" height="17.25" align-x="90.75" align-y="2106" 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">reg_car1</ml:id>
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            <ml:minus />
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              <ml:plus />
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              <ml:apply>
                <ml:mult style="default" />
                <ml:real>255</ml:real>
                <ml:apply>
                  <ml:indexer />
                  <ml:id xml:space="preserve">reg</ml:id>
                  <ml:real>6</ml:real>
                </ml:apply>
              </ml:apply>
            </ml:apply>
            <ml:apply>
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          </ml:apply>
        </ml:define>
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      <math optimize="false" disable-calc="false">
        <ml:define>
          <ml:id xml:space="preserve">reg_car2</ml:id>
          <ml:apply>
            <ml:minus />
            <ml:apply>
              <ml:plus />
              <ml:id xml:space="preserve">M2</ml:id>
              <ml:apply>
                <ml:mult style="default" />
                <ml:real>255</ml:real>
                <ml:apply>
                  <ml:indexer />
                  <ml:id xml:space="preserve">reg</ml:id>
                  <ml:real>7</ml:real>
                </ml:apply>
              </ml:apply>
            </ml:apply>
            <ml:apply>
              <ml:id xml:space="preserve">mask</ml:id>
              <ml:sequence>
                <ml:id xml:space="preserve">M2</ml:id>
                <ml:apply>
                  <ml:indexer />
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                  <ml:real>7</ml:real>
                </ml:apply>
              </ml:sequence>
            </ml:apply>
          </ml:apply>
        </ml:define>
      </math>
      <rendering item-idref="44" />
    </region>
    <region region-id="1513" left="36" top="2136" width="151.5" height="180" align-x="111" align-y="2136" 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="45" disable-calc="false">
        <inputs>
          <ml:id xml:space="preserve">car1</ml:id>
        </inputs>
        <outputs />
      </component>
      <rendering item-idref="46" />
    </region>
    <region region-id="1514" left="210" top="2136" width="151.5" height="180" align-x="285" align-y="2136" 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="47" disable-calc="false">
        <inputs>
          <ml:id xml:space="preserve">reg_car1</ml:id>
        </inputs>
        <outputs />
      </component>
      <rendering item-idref="48" />
    </region>
    <region region-id="1519" left="36" top="2316" width="151.5" height="180" align-x="111" align-y="2316" 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="49" disable-calc="false">
        <inputs>
          <ml:id xml:space="preserve">car2</ml:id>
        </inputs>
        <outputs />
      </component>
      <rendering item-idref="50" />
    </region>
    <region region-id="1520" left="210" top="2316" width="151.5" height="180" align-x="285" align-y="2316" 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="51" disable-calc="false">
        <inputs>
          <ml:id xml:space="preserve">reg_car2</ml:id>
        </inputs>
        <outputs />
      </component>
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    </region>
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      <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">Once the corresponding objects have been identified from frame to frame, an analysis can be performed that finds the distance traveled by each object between frames. Using the time from frame to frame, it is then possible to tell the velocity of the objects.</p>
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    <region region-id="1426" left="6" top="2568" width="436.5" height="5.25" align-x="6" align-y="2568" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <png item-idref="53" display-width="435" display-height="3.75" />
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