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              <c val="#008080">IMAGE ENHANCEMENT</c>
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              <c val="#000">This section demonstrates crossfading two images</c>
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              <c val="#000"> using Mathcad's animation feature. Given two image arrays of the same size, a weighted average of the two with time-variable weighting produces the desired effect. Below is an illustration with a vertical bar that fades into a horizontal bar.</c>
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            <c val="#000">The weighting starts at zero,</c>
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              <c val="#000">and the cross-faded image I produces only Im1.</c>
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          <f family="Times New Roman" charset="0" size="12">Adjust the value of w above between 0 and 1 to see other stages in the cross fade.</f>
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              <c val="#000">The ability to fade becomes interesting when combined with animation. We can use the range of FRAME values to generate weighted image averages with weights running from 0 to 1. Below are a number of examples for you to animate.</c>
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        <phrase>FRAME values</phrase>
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                <c val="#008080">Creating an Animation</c>
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            <c val="#000">First we define a function for computing the weighted average of two images.</c>
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            <c val="#000">Next we read in our standard example images.</c>
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            <c val="#000">The model</c>
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            <c val="#000">and the dog</c>
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        <ml:define warning="WarnRedefinedBIUnit">
          <ml:id xml:space="preserve">W</ml:id>
          <ml:apply>
            <ml:id xml:space="preserve">READ_IMAGE</ml:id>
            <ml:str xml:space="preserve">weederma.tga</ml:str>
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          <f family="Times New Roman" charset="0" size="12">
            <inlineAttr font-weight="normal">
              <c val="#000">In animating the examples below, first set the value for Nframes, the number of frames. A large number of frames makes the fading appear smoother when played but is more memory intensive. Once Nframes is set, animate the desired picture letting FRAME run from 0 to the value of Nframes.</c>
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      <pageBreak />
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          <f family="Times New Roman" charset="0" size="12">
            <c val="#000">In the first example you can watch the model's face fade in from an all-black background. Use a range for FRAME from 0 to 30 in the Animate dialog box.</c>
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      <png item-idref="24" display-width="30" display-height="30" />
      <link href=".\Popups\animate.xmcd" title="Pops up more details" popup="true" />
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            <ml:div />
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            <b>
              <inlineAttr line-through="false">
                <c val="#008080">Creating an Animation</c>
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        <ml:define>
          <ml:id xml:space="preserve">Nframes</ml:id>
          <ml:real>30</ml:real>
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        <ml:define warning="WarnRedefinedBIFunction">
          <ml:id xml:space="preserve">Im</ml:id>
          <ml:apply>
            <ml:id xml:space="preserve">Fade</ml:id>
            <ml:sequence>
              <ml:id xml:space="preserve">Black</ml:id>
              <ml:id xml:space="preserve">L</ml:id>
              <ml:apply>
                <ml:div />
                <ml:id xml:space="preserve">FRAME</ml:id>
                <ml:id xml:space="preserve">Nframes</ml:id>
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        </inputs>
        <outputs />
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      <rendering item-idref="30" />
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      <pageBreak />
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          <f family="Times New Roman" charset="0" size="12">
            <inlineAttr font-weight="normal">
              <c val="#000">By simply reversing the image arguments to Fade, you can have the image fade to black.</c>
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          <ml:id xml:space="preserve">Nframes</ml:id>
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        <ml:define warning="WarnRedefinedUDScalar">
          <ml:id xml:space="preserve">Im</ml:id>
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            <ml:sequence>
              <ml:id xml:space="preserve">L</ml:id>
              <ml:id xml:space="preserve">Black</ml:id>
              <ml:apply>
                <ml:div />
                <ml:id xml:space="preserve">FRAME</ml:id>
                <ml:id xml:space="preserve">Nframes</ml:id>
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      <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">
          <f family="Times New Roman" charset="0" size="12">
            <c val="#000">You can also fade into or out from a white background, demonstrating another tip in animating.</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">
          <f family="Times New Roman" charset="0" size="12">
            <inlineAttr font-weight="normal">
              <c val="#000">If you start with a white background</c>
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              <ml:real>0</ml:real>
            </ml:apply>
            <ml:real>255</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">
          <f family="Times New Roman" charset="0" size="12">
            <c val="#000">here is what you see</c>
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      <component hide-arguments="false" clsid-buddy="8442da2d-08d7-45ad-a4a6-f28bee6ae06a" item-idref="36" disable-calc="false">
        <inputs>
          <ml:id xml:space="preserve">White</ml:id>
        </inputs>
        <outputs />
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      <rendering item-idref="37" />
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      <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">
          <f family="Times New Roman" charset="0" size="12">
            <c val="#000">It is very hard to select all of this region when animating since it is essentially invisible. You could change the background color of your document or you could add a border to the white background. </c>
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      <pageBreak />
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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">
          <f family="Times New Roman" charset="0" size="12">
            <c val="#000">The expressions below set up the fade for animating and begin with a white background whose border is identical to the final image border.</c>
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                  <ml:id xml:space="preserve">cols</ml:id>
                  <ml:id xml:space="preserve">BWhite</ml:id>
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                <ml:real>1</ml:real>
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        <ml:define warning="WarnRedefinedUDScalar">
          <ml:id xml:space="preserve">Nframes</ml:id>
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      <png item-idref="45" display-width="30" display-height="30" />
      <link href=".\Popups\animate.xmcd" title="Pops up more details" popup="true" />
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