[GRASSSVN] r36477 
grass/branches/releasebranch_6_4/vector/lidar/v.surf.bspline
svn_grass at osgeo.org
svn_grass at osgeo.org
Wed Mar 25 03:16:16 EDT 2009
Author: neteler
Date: 20090325 03:16:16 0400 (Wed, 25 Mar 2009)
New Revision: 36477
Modified:
grass/branches/releasebranch_6_4/vector/lidar/v.surf.bspline/description.html
Log:
sync to 6.5
Modified: grass/branches/releasebranch_6_4/vector/lidar/v.surf.bspline/description.html
===================================================================
 grass/branches/releasebranch_6_4/vector/lidar/v.surf.bspline/description.html 20090325 07:14:37 UTC (rev 36476)
+++ grass/branches/releasebranch_6_4/vector/lidar/v.surf.bspline/description.html 20090325 07:16:16 UTC (rev 36477)
@@ 1,79 +1,91 @@
<h2>DESCRIPTION</h2>
<em>v.surf.bspline</em> makes a bilinear/bicubic spline interpolation
with Tykhonov regularization. The required input is an only 3d points
vector map that will be used to interpolate a reference surface.
<br>
<br>
Interpolation is carried out by adjusting a LeastSquares (LS) system
in which the parameters to estime are spline functions. The number of
splines doesn't depend on the resolution region, but it depends on the
spline steps values in the northsouth and westeast directions. These
spline steps are set by "<b><i>sin=</i></b>" and "<b><i>sie=</i></b>",
respectively. If the number of splines is bigger than the number of
points, the LS system is bad conditioned because there are more unkowns
than observations. In that case the LS normal matrix can't be inverted.
To allow the inversion of the normal matrix a Tykhonov regularization
is done. The minimizing function is the gradient in the case of a bilinear
interpolation, and the curvature in the bicubic interpolation. The
lambda_i parameter associated with the regularization smooths the
interpolation. The higher the lambda_i parameter, the smoother the
+<em>v.surf.bspline</em> performs a bilinear/bicubic spline interpolation with
+Tykhonov regularization. The input is a 2D or 3D vector points map. Values to
+interpolate can be the z values of 3D points or the values in a userspecified
+attribue column in a 2D or 3D map. Output can be a raster or vector map.
+Optionally, a "sparse point" vector map can be input specify vector points
+output.
+<br> <br>
+From a theoretical perspective, the interpolating procedure takes place in two
+parts: the first is an estimate of the linear coefficients of a spline function
+is derived from the observation points using a least squares regression; the
+second is the computation of the interpolated surface (or interpolated vector
+points). As used here, the splines are 2D piecewise nonzero polynomial
+functions calculated within a limited, 2D area. The length of each spline step
+is defined by <b><i>sie</i></b> for the eastwest direction and
+<b><i>sin</i></b> for the northsouth direction. For optimum performance, the
+length of spline step should be no less than the distance between observation
+points. Each vector point observation is modeled as a linear function of the
+nonzero splines in the area around the observation. The least squares
+regression predicts the the coefficients of these linear functions.
+Regularization, avoids the need to have one one observation and one coefficient
+for each spline (in order to avoid instability).
+
+<p>
+With regularly distributed data points, a spline step corresponding to the
+maximum distance between two points in both the east and north directions is
+sufficient. But often data points are not regularly distributed and require
+statistial regularization or estimation. In such cases, v.surf.bspline will
+attempt to minimize the gradient of bilinear splines or the curvature of bicubic
+splines in areas lacking point observations. As a general rule, spline step
+length should be greater than the mean distance between observation points
+(twice the distance between points is a good starting point). Separate eastwest
+and northsouth spline step length arguments allows the user to account for some
+degree of anisotropy in the distribution of observation points. Short spline
+step lengthsespecially spline step lengths that are less than the distance
+between observation pointscan greatly increase processing time.
+
+<p>
+Moreover, the maximum number of splines for each direction at each time is
+fixed, regardless of the spline step length. As the total number of splines used
+increases (i.e., with small spline step lengths), the region is automatically
+into subregions for interpolation. Each subregion can contain no more than
+150x150 splines. To avoid subregion boundary problems, subregions are created to
+partially overlap each other. A weighted mean of observations, based on point
+locations, is calculated within each subregion.
+
+<p>
+The Tykhonov regularization parameter ("<b><i>lambda_i</i></b>") acts to smooth
+the interpolation. With a small <b><i>lambda_i</i></b>, the interpolated surface
+closely follows observation points; a larger value will produce a smoother
interpolation.
<br>
<br>
The number of splines has a great influence on two things, mainly. The
first thing is the module's execution time. The second is the RAM use.
The higher the number of splines, the longer the time of execution and
the higher RAM use. A numerical example: 100 splines in each direction
imply 10e4 splines in total, that is, a square LS normal matrix of 10e4
size. Inverting this matrix means inverting 100 millions elements!
To improve this problems a Tcholebsky method with triangulars matrixes
is used in the normal matrix inversion. It has also fixed a maximum number
of splines for each direction. However, it is also possible running the
module with a higher number of splines. For a number of spline higher than
the fixed maximum, the whole region is divided into smaller regions. Each
subregion is 150x150 splines wide. To avoid contour problems, the subregions
are overlaped one to each other. To estimate a single value within the
overlaped zones, a weighted mean considering the point positions into each
subregion is carried out.
<br>
<br>
The required input is a 3d points vector. If nothing is specified zcoordinates
will be used in the interpolation. It could be also possible to consider
an attribute value by specifying "<b><i>layer=</i></b>" and "<b><i>column=</i></b>"
parameters. If a vector map with another type of features is used, only
points will be considered. If the "<b><i>sparse=</i></b>" vector is
used, the "<b><i>input=</i></b>" vector map will be used to create a
reference surface. This surface will be used to make an estimation on the
points within the "<b><i>sparse=</i></b>". In this case a vector output
("<b><i>output=</i></b>") must be specify. If the "<b><i>sparse=</i></b>"
is not supplied, the final interpolation output will be the interpolated
reference surface from the "<b><i>input=</i></b>" vector map. In this case,
one of both the raster or vector output format can be choosen. For raster
format ("<b><i>raster=</i></b>"), the point estimation will be done
on a regular grid with a resolution equal to the GRASS region. For vector
format, the estimation will be done on the sparse points of the
"<b><i>input=</i></b>" vector supplied. Both, vector and raster output,
are not allowed simultaneously.
<br>
<br>
A cross validation method has been implemented. It helps to find the optimal
lambda_i value that fits the data. It shows the <i>mean</i> and <i>rms</i>
of the residuals from the true point value and the estimated from the
interpolation made with all the data without the point itself. This procedure
is done for fixed lambda_i values. The results of the cross validation will
appear in the stdout and no vector nor raster output will be created. The
external input ("<b><i>sparse=</i></b>") will be not considered. Due to
the nature of the algorithm, it is advised the user no to try the cross
validation with more than 100 points at a time because it will take too long.
The execution time could be reduced by considering a lower number of splines.
Although, as seen, it is possible to use a high number of splines, more than
150x150 splines is not recommended.
<br>
<br>
In a raster map output ("<b><i>raster=</i></b>"), region resolution implying
more than 2000x2000 (4 mill) cells are not allowed. If the user tries with a
more than those cells an error message will ask for a lower region resolution.
+<p>
+The input can be a 2D pr 3D vector points map. If "<b><i>layer =</i></b>" 0 the
+zvalue of a 3D map is used for interpolation. If layer > 0, the user must
+specify an attribute column to used for interpolation using the
+"<b><i>column=</i></b>" argument (2D or 3D map).
+
+<p>
+v.surf.bspline can produce a raster OR a vector output (NOT simultaneously).
+However, a vector output cannot be obtained using the default GRASS DBF driver.
+
+<p>
+If output is a vector points map and a "<b><i>sparse=</i></b>" vector points map
+is not specified, the output vector map will contain points at the same
+locations as observation points in the input map, but the values of the output
+points are interpolated values. If a "<b><i>sparse=</i></b>" vector points map
+is specified, the output vector map will contain points at the same locations as
+the sparse vector map points, and values will be those of the interpolated
+raster surface at those points.
+
+<p>
+A cross validation "leaveoneout" analysis is available to help to determine
+the optimal <b><i>lambda_i</i></b> value that produces an interpolation that
+best fits the original observation data. The more points used for
+crossvalidation, the longer the time needed for computation. Empirical testing
+indicates a threshold of a maximum of 100 points is recommended. The
+crossvalidation output reports <i>mean</i> and <i>rms</i> of the residuals from
+the true point value and the estimated from the interpolation for a fixed series
+of <b><i>lambda_i</i></b> values. No vector nor raster output will be created
+when crossvalidation is selected.
+
+<p>
+A raster output map ("<b><i>raster=</i></b>") of more than 2000x2000 (4 mill)
+cells is not allowed. If an output map would exceed this size, an error message
+is generated.
+
+
<h2>EXAMPLES</h2>
<h4>Basic interpolation</h4>
@@ 82,85 +94,90 @@
v.surf.bspline input=point_vector output=interpolate_surface type=bicubic
</pre></div>
In this case, a bicubic spline interpolation will be done and an
estimation on the points of point_vector will be the output.
+A bicubic spline interpolation will be done and a vector points map with estimated
+(i.e., interpolated) values will be created.
<h4>Basic interpolation and raster output with a long spline step</h4>
+<h4>Basic interpolation and raster output with a longer spline step</h4>
<div class="code"><pre>
v.surf.bspline input=point_vector raster=interpolate_surface sie=25 sin=25
</pre></div>
Now, a bilinear spline interpolation will be done on a grid. The spline steps
are set to 25. It doesn't mean that the grid will have a resolution equal to 25,
but that each 25 units there will be a spline.
+A bilinear spline interpolation will be done with a spline step length of 25 map
+units. An interpolated raster map will be created at the current region resolution.
<h4> Estimation of lambda_i parameter with a cross validation proccess</h4>
+<h4>Estimation of <b><i>lambda_i</i></b> parameter with a cross validation proccess</h4>
<div class="code"><pre>
v.surf.bspline c input=point_vector
</pre></div>

<h4>Estimation on sparse points</h4>
<div class="code"><pre>
v.surf.bspline input=point_vector sparse=sparse_points output=interpolate_surface
</pre></div>
In this last case, an estimation on the points of the sparse_points vector
will be done. The reference surface used for this estimation will be that
interpolated using the point_vector vector.
+An output map of vector points will be created, corresponding to the sparse vector map, with interpolated values.
<h4>Using attribute values instead Zcoordinates</h4>
<div class="code"><pre>
v.surf.bspline input=point_vector raster=interpolate_surface layer=1 column=attrib_column
</pre></div>
This last case, the module uses the attribute values in attrib_column
in the table associated to layer 1.
+The interpolation will be done using the values in attrib_column, in the
+table associated with layer 1.
<h2>BUGS</h2>
Known issues:
<br>
<br>
In order to avoid RAM memory problems, an auxiliar table will be needed for
recording some intermediate calculi. Since the "<b>GROUP BY</b>" SQL function is used,
which is not supported by the "<b>dbf</b>" driver, this driver is not
allowed with the vector map output "<b><i>output=</i></b>". There is no problem
with the raster map output.
<br>
<br>
At this time, using the external vector input ("<b><i>sparse=</i></b>") implies
interpoling with Zcoordinates. Updates to allow using attribute values
will be done in a near future (I hope).
<br>
<br>
+<p>
+In order to avoid RAM memory problems, an auxiliary table is needed for
+recording some intermediate calculations. This requires the "<b>GROUP BY</b>"
+SQL function is used, which is not supported by the "<b>dbf</b>" driver. For
+this reason, vector map output "<b><i>output=</i></b>" is not permitted with the
+DBF driver. There are no problems with the raster map output from the DBF
+driver.
+<p>
+At this time, sparse vector input ("<b><i>sparse=</i></b>") can only be used
+with interpolation from 3D vector zcoordinates (<a href="http://trac.osgeo.org/grass/ticket/96">trac #96</a>).
+<p>
+
<h2>SEE ALSO</h2>
<em><a HREF="v.surf.rst.html">v.surf.rst</a></em>
+<em><a
+href="http://grass.osgeo.org/grass64/manuals/html64_user/v.surf.idw.html">v.surf.idw</a>,
+<a
+href="http://grass.osgeo.org/grass64/manuals/html64_user/v.surf.rst.html">v.surf.rst</a></em>
+
<h2>AUTHORS</h2>
+
Original version in GRASS 5.4: (s.bspline.reg)
<BR>
+<br>
Maria Antonia Brovelli, Massimiliano Cannata, Ulisse Longoni, Mirko Reguzzoni
<BR><BR>
+<p>
Update for GRASS 6.X and improvements:
<BR>
+<br>
Roberto Antolin
<h2>REFERENCES</h2>
Brovelli M. A., Cannata M., and Longoni U.M., 2004, LIDAR Data Filtering and DTM Interpolation Within GRASS, Transactions in GIS, April 2004, vol. 8, iss. 2, pp. 155174(20), Blackwell Publishing Ltd
<br>
<br>
Brovelli M. A. and Cannata M., 2004, Digital Terrain model reconstruction in urban areas from airborne laser scanning data: the method and an example for Pavia (Northern Italy). Computers and Geosciences 30, pp.325331
<br>
<br>
Brovelli M. A e Longoni U.M., 2003, Software per il filtraggio di dati LIDAR, Rivista dell'Agenzia del Territorio, n. 32003, pp. 1122 (ISSN 15932192)
<br>
<br>
Brovelli M. A., Cannata M. and Longoni U.M., 2002, DTM LIDAR in area urbana, Bollettino SIFET N.2, 2002, pp. 726
<br>
+Brovelli M. A., Cannata M., and Longoni U.M., 2004, LIDAR Data
+Filtering and DTM Interpolation Within GRASS, Transactions in GIS,
+April 2004, vol. 8, iss. 2, pp. 155174(20), Blackwell Publishing Ltd
+<p>
+Brovelli M. A. and Cannata M., 2004, Digital Terrain model
+reconstruction in urban areas from airborne laser scanning data: the
+method and an example for Pavia (Northern Italy). Computers and
+Geosciences 30, pp.325331
+<p>
+Brovelli M. A e Longoni U.M., 2003, Software per il filtraggio di
+dati LIDAR, Rivista dell'Agenzia del Territorio, n. 32003, pp. 1122
+(ISSN 15932192)
+<p>
+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,
+Girona, España. CD ISBN: 9788469038869 <br>
+
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