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          <b>
            <c val="#008080">INTRODUCTORY MATERIAL</c>
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              <c val="#800080">Grayscale and Color in Images</c>
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        <phrase>grayscale and color in images</phrase>
        <phrase>images, grayscale and color in</phrase>
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            <c val="#800000">Function Definitions and Syntax</c>
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              <c val="#800000">rgb_to_gray(RGB)</c>
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        <phrase>rgb_to_gray function</phrase>
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    <region region-id="1932" left="144" top="108.75" width="152.25" height="14.25" align-x="144" align-y="120" 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">
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              <c val="#800000">gray_to_rgb(gray, colormap)</c>
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        <phrase>gray_to_rgb function</phrase>
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    <region region-id="1933" left="6" top="126.75" width="330" height="57" align-x="6" align-y="138" 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">These functions convert between grayscale and color in images. One function takes an RGB color image and converts it to a grayscale image, and the other does the reverse. These functions are useful for converting one type of image to another, and also for false color imaging.</p>
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      <text use-page-width="false" push-down="false" lock-width="true">
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          <b>
            <c val="#800000">Arguments</c>
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      <text use-page-width="false" push-down="false" lock-width="true">
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              <inlineAttr line-through="false">RGB</inlineAttr>
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          </f>, or <f family="Times New Roman" charset="0"><b><inlineAttr line-through="false">gray</inlineAttr></b></f>, an image matrix</p>
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              <f size="14">• </f>
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            <inlineAttr font-style="normal" line-through="false">colormap</inlineAttr>
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          <inlineAttr font-style="normal">,</inlineAttr> a 256 by 4 matrix lookup table mapping grayscale values to RGB colors</p>
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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">The functions return an image matrix in the specified color domain.</p>
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      <text use-page-width="false" push-down="false" lock-width="true">
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      <text use-page-width="false" push-down="false" lock-width="true">
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          <b>
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              <c val="#800000">rgb_to_gray(RGB)</c>
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          </b>
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    <region region-id="1951" left="6" top="318.75" width="342" height="85.5" align-x="6" align-y="330" 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 most commonly used representation for color images is called RGB, where each pixel is represented by three values: the amount of red, green, and blue in the pixel. A grayscale image has only one value for each pixel, giving the intensity or grayscale level. An RGB color image, represented by a <b><u><link href="./Rgbtool.xmcd" title="Links to section" popup="false">packed matrix</link></u></b> with 3 image representations, can be converted to grayscale by using the <f family="Times New Roman" charset="0"><b><inlineAttr font-style="normal" line-through="false">rgbmat_to_gray</inlineAttr></b></f> function.</p>
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        <ml:define>
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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 RGB values are converted to grayscale using the NTSC formula of 0.299 * Red + 0.587 * Green + 0.114 * Blue, which closely represents the average person's relative perception of the brightness of red, green, and blue light.</p>
        <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit" />
        <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">The two images here can be compared by viewing them in the Image Viewer:</p>
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    <region region-id="1962" left="6" top="774.75" width="81.75" height="14.25" align-x="6" align-y="786" 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">
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            <b>
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                <c val="#800000">Function Details</c>
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      <text use-page-width="false" push-down="false" lock-width="true">
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          <b>
            <inlineAttr font-style="normal">
              <c val="#800000">gray_to_rgb(gray, colormap)</c>
            </inlineAttr>
          </b>
        </p>
      </text>
      <indexes>
        <phrase>gray_to_rgb function</phrase>
      </indexes>
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    <region region-id="1964" left="6" top="792.75" width="368.25" height="99.75" align-x="6" align-y="804" 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">Converting a grayscale matrix to RGB is usually done by assigning false colors to the intensity levels in the image. There are two ways to do that in Mathcad. First, the Image Viewer itself can be used to make a simple false color representation that interpolates linearly between two reference colors, for example, red to blue. This process is explained more fully in the <link href="./Viewer.xmcd" title="Links to section " popup="false"><f family="Times New Roman" charset="0"><inlineAttr font-weight="normal" underline="false" line-through="false">section on </inlineAttr></f><b><u>viewing images</u></b></link>. Here is an example using 10 distinct colors between red and green for false color on a grayscale image:</p>
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    <region region-id="1971" left="6" top="1176.75" width="340.5" height="142.5" align-x="6" align-y="1188" 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">More flexible false color imaging can be done using the <f family="Times New Roman" charset="0"><b><inlineAttr font-style="normal" line-through="false">gray_to_rgb</inlineAttr></b></f> function. The first argument is the grayscale matrix, and the second is a colormap matrix, which has four columns. The first column gives grayscale intensity values, ranging from 0 to 255, and the remaining three columns give the red, green, and blue RGB values that will be placed in the output matrix for pixels having that intensity value.</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">As an example, we can read in a file that has a rainbow spectrum colormap in it (see the section on <b><u><link href="./Hlsv.xmcd" title="Links to section" popup="false">HLS and HSV</link></u></b> for one way to create your own colormaps), and use it to view the same image:</p>
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