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<h2>DESCRIPTION</h2>
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-<em>i.rectify</em> uses the control
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-points identified in the
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+<em>i.rectify</em> uses the control points included in the source data
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+or identified with the
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<a href="wxGUI.gcp.html">Ground Control Points Manager</a>
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-
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-to calculate a transformation matrix based on a first,
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-second, or third order polynomial and then converts x,y
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+to calculate a transformation matrix and then converts x,y
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cell coordinates to standard map coordinates for each pixel
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in the image. The result is a planimetric image with a
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transformed coordinate system (i.e., a different coordinate
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-system than before it was rectified).
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+system than before it was rectified). Supported transformation methods
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+are first, second, and third order polynomial and thin plate spline.
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+Thin plate spline is recommended for ungeoreferenced satellite imagery
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+where ground control points (GCPs) are included. Examples are
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+<a href="http://www.gdal.org/frmt_l1b.html">NOAA/AVHRR</a>
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+and <a href="http://www.gdal.org/frmt_various.html#Envisat">ENVISAT</a>
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+imagery which include throusands of GCPs.
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<p>
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-The <a href="wxGUI.gcp.html">Ground Control Points Manager</a>
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-must be run before <em>i.rectify</em>, and both programs
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-are required to rectify an image. An image must be
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-rectified before it can reside in a standard coordinate
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+If no ground control points are available, the
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+<a href="wxGUI.gcp.html">Ground Control Points Manager</a>
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+must be run before <em>i.rectify</em>. An image must be
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+georeferences before it can reside in a standard coordinate
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LOCATION, and therefore be analyzed with the other map
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layers in the standard coordinate LOCATION. Upon
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completion of <em>i.rectify</em>, the rectified image is
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@@ -96,6 +100,30 @@ the user selects a different transformation order from the
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menu bar. The polynomial equations are performed using a
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modified Gaussian elimination method.
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+<h4>Thin plate spline (TPS) transformation</h4>
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+TPS transformation is selected with the <b>-t</b> flag. This method of
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+coordinate transformation is recommended for satellite imagery where
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+hundreds or thousands of GCPs are included, and for historical printed
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+or scanned maps with unknown georeferencing and/or known localized
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+distortions.
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+<p>
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+TPS combines a linear affine transformation with individual
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+transformation coefficients for each GCP, using the radial basis kernel
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+function with the distance <em>dist</em> between any two points:
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+
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+<dl>
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+<dd>dist<sup>2</sup> * log(dist)
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+</dl>
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+
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+As a consequence, localized distortions can be removed with TPS
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+transformation. For example, scan line sensors will have due to the
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+changing viewing angle larger distortions towards the end points of the
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+scan line than at the center of the scan line. Even higher order
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+polynomial transformations are not able to remove these locally
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+different distortions, but TPS transformation can. For best results,
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+TPS requires an even and, for localized distortions, dense spacing of
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+GCPs.
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+
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<h3>Resampling method</h3>
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<p>The rectified data is resampled with one of seven different methods:
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<em>nearest</em>, <em>bilinear</em>, <em>cubic</em>, <em>lanczos</em>,
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Markus Metz