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  6.     <title>5.┬áEdge-detect filters</title>
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  19.           <th colspan="3" align="center" id="chaptername">Chapter┬á6.┬áFilters</th>
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  33.             <h2 class="title" style="clear: both"><a id="filters-edge"></a>5.┬áEdge-detect filters</h2>
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  42.               <h3 class="title"><a id="filters-edges-introduction"></a>5.1.┬áEdge-detect introduction</h3>
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  46.         <p>
  47.       Edge detect filters search for borders between different colors
  48.       and so can detect contours of objects.
  49.     </p>
  50.         <p>
  51.       They are used to make selections and for many artistic purposes.
  52.     </p>
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  54.           <img src="../images/filters/filters-edgedetect-fig.png" />
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  56.         <p>
  57.       Most of them are based on gradient calculation methods and give
  58.       thick border lines.  Look at fig.1 which represents color
  59.       intensity variations. On the left is a slow color gradient which
  60.       is not a border. On the right is a quick variation which is an
  61.       edge. Now, let us calculate the gradient, the variation speed, of
  62.       this edge, i.e the first derivative (fig.2). We have to decide
  63.       that a border is detected when gradient is more than a threshold
  64.       value (the exact border is at top of the curve, but this top
  65.       varies according to borders). In most cases, threshold is under
  66.       top and border is thick.
  67.     </p>
  68.         <p>
  69.       The Laplacian edge detection uses the second derivative (fig.3).
  70.       The top of the curve is now at zero and clearly identified. That's
  71.       why Laplace filter renders a thin border, only a pixel wide. But
  72.       this derivative gives several zeros corresponding to small
  73.       ripples, resulting in false edges. 
  74.     </p>
  75.         <p>
  76.       Some blurring before applying edge filters is often necessary: it
  77.       flattens small ripples in signal and so prevents false edges.
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  96.           <td width="40%" align="right" valign="top">┬á5.2.┬áEdge</td>
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