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                <c val="#008080">IMAGE ENHANCEMENT</c>
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            <b>
              <c val="#800080">Correcting a CCD Image</c>
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            <i>Contributed by:</i>
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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">Dr. Martin Zombeck</p>
        <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">Smithsonian Astrophysical Observatory</p>
        <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">Cambridge, Massachusetts</p>
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            <c val="#800000">Introduction</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">Computer processing of astronomical images was, until recently, the sole province of professional astronomers working at universities and institutions with mainframe computers or powerful workstations. The advent of fast and relatively inexpensive PCs and interactive image-processing software has brought the powerful tool of digital image processing into the hands of amateur astronomers. The coincidental development of the CCD or solid-state TV camera has also placed into the hands of the amateur the means for directly making digitized images of celestial objects. Since the sensitivity of CCDs is about 100 times that of photographic film, the amateur's telescope of moderate aperture outfitted with a CCD camera (for under $1000) becomes a source of useful astronomical data.</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">We demonstrate what can be done to enhance an astronomical image using a picture of Jupiter taken when the fragments of the comet Shoemaker-Levy were plunging toward the planet. (Sorry, this image was not taken by an amateur. It was taken by NASA's Hubble Space Telescope [HST] on May 18, 1994! It's such a beautiful image that we couldn't avoid using it. We have taken the liberty of adding imperfections to the image provided by NASA to produce a pseudo-"raw" image similar to that which one might obtain with a run-of-the-mill CCD.)</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">CCDs are not perfect imaging detectors and substantial imperfections are present in the initial "raw" images. These imperfections must be removed before one can obtain a faithful record of the imaged object. These imperfections consist, among others, of geometric defects in the "chip," electronic offsets or "bias," thermally induced signals, noise, and pixel-to-pixel variations in sensitivity across the field of view. The latter imperfection is the result of the combined effect of CCD chip sensitivity variations and the optical system of the telescope.</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">To remove these effects, one usually makes a "dark frame" (an exposure with the telescope cap on for the same duration as the observational exposure) and a "flat-field frame" (an exposure taken with the telescope pointed at a uniformly illuminated object, for example, a screen painted white). Subtracting the dark frame from the raw image removes the electronic and thermal offsets. Dividing the raw image by the flat-field frame removes the effects of variations in sensitivity. The raw image is now calibrated and is ready for further processing steps to remove the effects of random noise and extract specific information or emphasize specific features in the image. In professional applications, several more "reduction" steps beyond those described above are taken. The bibliography at the end of this document contains several references that discuss these steps in technical detail.</p>
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        <phrase>dark frame</phrase>
        <phrase>flat-field frame</phrase>
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            <c val="#800000">Display the Raw Image</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">Read in the raw image:</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">Determine the number of rows and columns in the image and the minimum and maximum pixel values:</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 black dot in the first quadrant of the image is the shadow of one of Jupiter's moons, the inner moon Io. Io is barely visible in the image, slightly up and to the right of its shadow, approximately 1/6 the diameter of Jupiter away from the shadow.</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">We have purposely degraded the image received from NASA by introducing imperfections to mimic what a home astronomer might be able to achieve. One can clearly see "smudges" and a diagonal line running across the right hemisphere. Also, the image as received from NASA had some "pepper" noise introduced in the reproduction process at several locations in the image. </p>
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            <c val="#800000">Calibration of the Image</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 next image is a flat-field frame of the simulated response of the camera. <b>Warning:</b> This is not the response of the CCD camera on board the HST. It is an example of what one might obtain with a commercial CCD camera. </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">Read in the flat-field frame:</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 flat-field image shows some ugly features. The diagonal stripe of bad pixels is probably due to a cleavage plane in the silicon used to manufacture the chip. The dark lines and columns are due to defects in the CCD that prevent the transfer of electrical charge in the device. The large-scale nonuniformities are due to nonuniformities in the optical system. The "doughnuts" are due to dust particles on an optical element near the focal plane.</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">...rescale the image</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">and view it:</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">All the "imperfections" have now been removed. It is easier to see the image of Io. We still have to remove the noise.</p>
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            <c val="#800000">Noise Removal, or Spatial Filtering</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">Spatial filters incorporate neighborhood operations on pixels. A new value for a pixel is calculated from the value of the pixel and that of its nearest neighbors. The two most widely used filters are the mean and median filter. The mean filter performs a neighborhood average. This filter blurs edges and other details. The median filter replaces a pixel value with the median of the pixel value and that of the neighboring pixel values. This filter is especially useful when the noise is "spiky" ("salt-and-pepper" or "shot" noise) and the sharpness of edges needs to be preserved. Here we use the median filter because of the nature of the noise in the image, and view the median-filtered image: </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 median filter has, unfortunately, managed to remove Io and made the comet fragments very faint. For further image processing it will be better to use the unfiltered image. This is always a judgment call. The interactive nature of this software package makes it relatively easy to try different solutions, and we suggest you experiment with both the filtered and unfiltered image here. </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 preceding sections dealt with the restoration of the image or the recovery from defects. During the restoration, a feature was removed from the image. Image enhancement deals with increasing the visibility of a feature or features in the image, usually at the expense of others. </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">Image enhancement usually starts with a quantitative examination of the image. A very useful tool for this is the generation of an image histogram. </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 histogram is fairly uniform, so it is not useful to use the technique of histogram equalization (a special scaling of the gray levels that generates a flat image histogram).</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">A useful image statistic is the minimum and maximum pixel values: </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">Knowledge of the minimum and maximum values can be useful when you want to use the full range of pixel values available (0 to 255). This scaling operation is known as stretching.</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">We will now exercise some useful enhancement techniques to better distinguish the features of this image.</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">
          <b>
            <c val="#800000">Image Inversion</c>
          </b>
        </p>
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      <indexes>
        <phrase>image inversion</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 conversion of a "positive" image into a "negative" image often brings out faint details.</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 comet fragments' tails are now very easy to see and the faint fragments nearest Jupiter's surface are now clearly visible. Fourteen fragments are visible! The shadow of Io is very apparent and the image of Io is now a dark spot.</p>
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          <b>
            <c val="#800000">Image Scaling</c>
          </b>
        </p>
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      <indexes>
        <phrase>image scaling</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">As shown in the section <b><u><link href="./Maps.xmcd" title="Links to section" popup="false">Function and Level Mapping</link></u></b>, adjusting the shape of the intensity curve can improve feature visibility in an image, either because of the response of a particular electronic viewing system or because of the response of your eye. Here we use a logarithmic transformation on our image:</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">Now additional comet fragments can be seen in the image.</p>
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          <b>
            <c val="#800000">Convolution Edge Finder</c>
          </b>
        </p>
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      <indexes>
        <phrase>convolution edge finder</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">We can isolate certain features (discontinuities) in the image using edge detection. This is called <f family="Times New Roman" charset="0"><i><inlineAttr font-weight="normal" line-through="false">image segmentation</inlineAttr></i></f>. Applying the Sobel gradient operator to the image gives</p>
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      <indexes>
        <phrase>image segmentation</phrase>
        <phrase>Sobel gradient operator</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 shadow of Io and the comet segments are now very clearly delineated. Note that as usual, we view edge images in reverse video.</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">
          <b>
            <c val="#800000">Bibliography</c>
          </b>
        </p>
      </text>
    </region>
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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">Berry, Richard, "Image Processing in Astronomy," <i>Sky and Telescope</i>, April 1994.</p>
      </text>
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    <region region-id="490" left="6" top="5268.75" width="218.25" height="14.25" align-x="6" align-y="5280" 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="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">Buil, C., <i>CCD Astronomy</i>, Willman-Bell, 1991.</p>
      </text>
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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">In <i>Astronomical CCD Observing and Reduction Techniques</i>, ASP Conference Series, Vol. 23, 1992, Steve B. Howell, ed.</p>
      </text>
    </region>
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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">Hanisch, R. J., "Image Processing, Data Analysis Software, and Computer Systems for CCD Data Reduction and Analysis."</p>
      </text>
    </region>
    <region region-id="496" left="6" top="5364.75" width="312.75" height="14.25" align-x="6" align-y="5376" 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="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">Gilliland, R. L., "Details of Noise Sources and Reduction Processes."</p>
      </text>
    </region>
    <region region-id="497" left="6" top="5388.75" width="325.5" height="28.5" align-x="6" align-y="5400" 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="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">Massey, P., and G. H. Jacoby, "CCD Data: The <i>Good</i>, the <i>Bad</i>, and the <i>Ugly</i><i>.</i>"</p>
      </text>
    </region>
    <region region-id="546" left="0" top="5424" width="6000" height="6" align-x="0" align-y="5424" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <pageBreak />
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    <region region-id="499" left="6" top="5436.75" width="143.25" height="14.25" align-x="6" align-y="5448" 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="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">
          <b>
            <c val="#800000">Image Credits</c>
          </b>
        </p>
      </text>
    </region>
    <region region-id="500" left="6" top="5460.75" width="347.25" height="28.5" align-x="6" align-y="5472" 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="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">H. A. Weaver, T. E. Smith (Space Telescope Science Institute)</p>
        <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">J. T. Trauger, R.W. Evans (Jet Propulsion Laboratory) NASA</p>
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