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@@ -3,21 +3,21 @@
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Tykhonov regularization. The input is a raster surface map, e.g. elevation,
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temperature, precipitation etc. Output is a raster map. Optionally, only
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input NULL cells are interpolated, useful to fill NULL cells, an alternative
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-to <a href="r.fillnulls.html">r.fillnulls</a>. Using the -n flag to only
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+to <em><a href="r.fillnulls.html">r.fillnulls</a></em>. Using the <b>-n</b> flag to only
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interpolate NULL cells will considerably speed up the module.
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<p>The input raster map is read at its native resolution, the output raster
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map will be produced for the current computational region set with
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-<a href="g.region.html">g.region</a>. Any MASK will be respected, masked
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+<em><a href="g.region.html">g.region</a></em>. Any MASK will be respected, masked
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values will be treated as NULL cells in both the input and the output map.
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-<p>Spline step values <b><i>se</i></b> for the east-west direction and
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-<b><i>sn</i></b> for the north-south direction should not be smaller than
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+<p>Spline step values <b>se</b> for the east-west direction and
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+<b>sn</b> for the north-south direction should not be smaller than
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the east-west and north-south resolutions of the input map. For a raster
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map without NULL cells, 1 * resolution can be used, but check for
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undershoots and overshoots. For very large areas with missing values
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(NULL cells), larger spline step values may be required, but most of the
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time the defaults (1.5 x resolution) should be fine.
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-<p>The Tykhonov regularization parameter ("<b><i>lambda</i></b>") acts to
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-smooth the interpolation. With a small <b><i>lambda</i></b>, the
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+<p>The Tykhonov regularization parameter (<b>lambda</b>) acts to
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+smooth the interpolation. With a small <b>lambda</b>, the
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interpolated surface closely follows observation points; a larger value
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will produce a smoother interpolation. Reasonable values are 0.0001,
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0.001, 0.005, 0.01, 0.02, 0.05, 0.1 (needs more testing). For seamless
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@@ -28,8 +28,8 @@ these are derived from the observation points using a least squares regression;
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second is the computation of the interpolated surface (or interpolated vector
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points). As used here, the splines are 2D piece-wise non-zero polynomial
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functions calculated within a limited 2D area. The length of each spline step
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-is defined by <b><i>se</i></b> for the east-west direction and
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-<b><i>sn</i></b> for the north-south direction. For optimal performance, the
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+is defined by <b>se</b> for the east-west direction and
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+<b>sn</b> for the north-south direction. For optimal performance, the
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spline step values should be no less than the east-west and north-south
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resolutions of the input map. Each non-NULL cell observation is modeled as a
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linear function of the non-zero splines in the area around the observation.
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@@ -38,14 +38,14 @@ Regularization avoids the need to have one one observation and one coefficient
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for each spline (in order to avoid instability).
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<p>A cross validation "leave-one-out" analysis is available to help to determine
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-the optimal <b><i>lambda</i></b> value that produces an interpolation that
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+the optimal <b>lambda</b> value that produces an interpolation that
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best fits the original observation data. The more points used for
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cross-validation, the longer the time needed for computation. Empirical testing
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indicates a threshold of a maximum of 100 points is recommended. Note that cross
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validation can run very slowly if more than 100 observations are used. The
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cross-validation output reports <i>mean</i> and <i>rms</i> of the residuals from
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the true point value and the estimated from the interpolation for a fixed series
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-of <b><i>lambda</i></b> values. No vector nor raster output will be created
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+of <b>lambda</b> values. No vector nor raster output will be created
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when cross-validation is selected.
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<h2>EXAMPLES</h2>
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@@ -72,46 +72,48 @@ g.region rast=input -p
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r.patch input=input_raster,interpolated_nulls output=input_raster_gapfilled
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</pre></div>
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-<h3>Estimation of <b><i>lambda</i></b> parameter with a cross validation proccess</h3>
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+<h3>Estimation of <b>lambda</b> parameter with a cross validation proccess</h3>
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A random sample of points should be generated first with
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-<a href="r.random.html">r.random</a>, and the current region should not
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+<em><a href="r.random.html">r.random</a></em>, and the current region should not
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include more than 100 non-NULL random cells.
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<div class="code"><pre>
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r.resamp.bspline -c input=input_raster
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</pre></div>
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+<h2>REFERENCES</h2>
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+
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+<ul>
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+<li>Brovelli M. A., Cannata M., and Longoni U.M., 2004, LIDAR Data
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+Filtering and DTM Interpolation Within GRASS, Transactions in GIS,
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+April 2004, vol. 8, iss. 2, pp. 155-174(20), Blackwell Publishing Ltd</li>
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+<li>Brovelli M. A. and Cannata M., 2004, Digital Terrain model
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+reconstruction in urban areas from airborne laser scanning data: the
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+method and an example for Pavia (Northern Italy). Computers and
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+Geosciences 30, pp.325-331</li>
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+<li>Brovelli M. A e Longoni U.M., 2003, Software per il filtraggio di
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+dati LIDAR, Rivista dell'Agenzia del Territorio, n. 3-2003, pp. 11-22
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+(ISSN 1593-2192)</li>
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+<li>Antolin R. and Brovelli M.A., 2007, LiDAR data Filtering with GRASS GIS for the Determination of Digital Terrain Models. Proceedings of Jornadas de SIG Libre,
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+Girona, España. CD ISBN: 978-84-690-3886-9</li>
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+</ul>
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+
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<h2>SEE ALSO</h2>
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<em>
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-<a href="r.fillnulls.html">r.fillnulls</a><br>
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-<a href="r.resamp.rst.html">r.resamp.rst</a><br>
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-<a href="r.resamp.interp.html">r.resamp.interp</a><br>
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+<a href="r.fillnulls.html">r.fillnulls</a>,
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+<a href="r.resamp.rst.html">r.resamp.rst</a>,
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+<a href="r.resamp.interp.html">r.resamp.interp</a>,
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<a href="v.surf.bspline.html">v.surf.bspline</a>
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</em>
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<h2>AUTHORS</h2>
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Markus Metz<br>
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<br>
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-based on <a href="v.surf.bspline.html">v.surf.bspline</a> by
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+based on <em><a href="v.surf.bspline.html">v.surf.bspline</a></em> by
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<br>
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Maria Antonia Brovelli, Massimiliano Cannata, Ulisse Longoni, Mirko Reguzzoni, Roberto Antolin
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-<h2>REFERENCES</h2>
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-
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-Brovelli M. A., Cannata M., and Longoni U.M., 2004, LIDAR Data
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-Filtering and DTM Interpolation Within GRASS, Transactions in GIS,
|
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-April 2004, vol. 8, iss. 2, pp. 155-174(20), Blackwell Publishing Ltd
|
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-<p>Brovelli M. A. and Cannata M., 2004, Digital Terrain model
|
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-reconstruction in urban areas from airborne laser scanning data: the
|
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-method and an example for Pavia (Northern Italy). Computers and
|
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-Geosciences 30, pp.325-331
|
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-<p>Brovelli M. A e Longoni U.M., 2003, Software per il filtraggio di
|
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-dati LIDAR, Rivista dell'Agenzia del Territorio, n. 3-2003, pp. 11-22
|
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-(ISSN 1593-2192)
|
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-<p>Antolin R. and Brovelli M.A., 2007, LiDAR data Filtering with GRASS GIS for the
|
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-Determination of Digital Terrain Models. Proceedings of Jornadas de SIG Libre,
|
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-Girona, España. CD ISBN: 978-84-690-3886-9 <br>
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-
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-<p><i>Last changed: $Date$</i>
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+<p>
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+<i>Last changed: $Date$</i>
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