Provided by: grass-doc_7.8.2-1build3_all 
NAME
v.surf.bspline - Performs bicubic or bilinear spline interpolation with Tykhonov regularization.
KEYWORDS
vector, surface, interpolation, LIDAR
SYNOPSIS
v.surf.bspline
v.surf.bspline --help
v.surf.bspline [-ce] input=name [layer=string] [column=name] [sparse_input=name] [output=name]
[raster_output=name] [mask=name] [ew_step=float] [ns_step=float] [method=string]
[lambda_i=float] [solver=name] [maxit=integer] [error=float] [memory=integer] [--overwrite]
[--help] [--verbose] [--quiet] [--ui]
Flags:
-c
Find the best Tykhonov regularizing parameter using a "leave-one-out" cross validation method
-e
Estimate point density and distance
Estimate point density and distance in map units for the input vector points within the current
region extents and quit
--overwrite
Allow output files to overwrite existing files
--help
Print usage summary
--verbose
Verbose module output
--quiet
Quiet module output
--ui
Force launching GUI dialog
Parameters:
input=name [required]
Name of input vector point map
Or data source for direct OGR access
layer=string
Layer number or name
Vector features can have category values in different layers. This number determines which layer to
use. When used with direct OGR access this is the layer name.
Default: 1
column=name
Name of the attribute column with values to be used for approximation
If not given and input is 3D vector map then z-coordinates are used.
sparse_input=name
Name of input vector map with sparse points
Or data source for direct OGR access
output=name
Name for output vector map
raster_output=name
Name for output raster map
mask=name
Raster map to use for masking (applies to raster output only)
Only cells that are not NULL and not zero are interpolated
ew_step=float
Length of each spline step in the east-west direction
Default: 4 * east-west resolution
ns_step=float
Length of each spline step in the north-south direction
Default: 4 * north-south resolution
method=string
Spline interpolation algorithm
Options: bilinear, bicubic
Default: bilinear
bilinear: Bilinear interpolation
bicubic: Bicubic interpolation
lambda_i=float
Tykhonov regularization parameter (affects smoothing)
Default: 0.01
solver=name
The type of solver which should solve the symmetric linear equation system
Options: cholesky, cg
Default: cholesky
maxit=integer
Maximum number of iteration used to solve the linear equation system
Default: 10000
error=float
Error break criteria for iterative solver
Default: 0.000001
memory=integer
Maximum memory to be used (in MB)
Cache size for raster rows
Default: 300
DESCRIPTION
v.surf.bspline 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 user-specified attribute column in a 2D or 3D vector map. Output can be a raster (raster_output) or
vector (output) map. Optionally, a "sparse point" vector map can be input which indicates the location
of output vector points.
NOTES
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 piece-wise non-zero polynomial functions calculated
within a limited, 2D area. The length (in mapping units) of each spline step is defined by ew_step for
the east-west direction and ns_step for the north-south direction. For optimal 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 non-zero 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 observation and one coefficient for each spline (in order to avoid instability).
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
east-west and north-south spline step length arguments allows the user to account for some degree of
anisotropy in the distribution of observation points. Short spline step lengths - especially spline step
lengths that are less than the distance between observation points - can greatly increase the processing
time.
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 split 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.
The Tykhonov regularization parameter (lambda_i) acts to smooth the interpolation. With a small lambda_i,
the interpolated surface closely follows observation points; a larger value will produce a smoother
interpolation.
The input can be a 2D or 3D vector points map. If input is 3D and column is not given than z-coordinates
are used for interpolation. Parameter column is required when input is 2D vector map.
v.surf.bspline can produce a raster_output OR a output (but NOT simultaneously). Note that topology is
not build for output vector point map. The topology can be built if required by v.build.
If output is a vector points map and a sparse 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 instead a sparse 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.
A cross validation "leave-one-out" analysis is available to help to determine the optimal lambda_i value
that produces an interpolation that best fits the original observation data. The more points used for
cross-validation, the longer the time needed for computation. Empirical testing indicates a threshold of
a maximum of 100 points is recommended. Note that cross validation can run very slowly if more than 100
observations are used. The cross-validation output reports mean and rms of the residuals from the true
point value and the estimated from the interpolation for a fixed series of lambda_i values. No vector nor
raster output will be created when cross-validation is selected.
EXAMPLES
Basic interpolation
v.surf.bspline input=point_vector output=interpolate_surface method=bicubic
A bicubic spline interpolation will be done and a vector points map with estimated (i.e., interpolated)
values will be created.
Basic interpolation and raster output with a longer spline step
v.surf.bspline input=point_vector raster=interpolate_surface ew_step=25 ns_step=25
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.
Estimation of lambda_i parameter with a cross validation process
v.surf.bspline -c input=point_vector
Estimation on sparse points
v.surf.bspline input=point_vector sparse=sparse_points output=interpolate_surface
An output map of vector points will be created, corresponding to the sparse vector map, with interpolated
values.
Using attribute values instead z-coordinates
v.surf.bspline input=point_vector raster=interpolate_surface layer=1 \
column=attrib_column
The interpolation will be done using the values in attrib_column, in the table associated with layer 1.
North carolina location example using z-coordinates for interpolation
g.region region=rural_1m res=2 -p
v.surf.bspline input=elev_lid792_bepts raster=elev_lid792_rast \
ew_step=5 ns_step=5 method=bicubic lambda_i=0.1
KNOWN ISSUES
Known issues:
In order to avoid RAM memory problems, an auxiliary table is needed for recording some intermediate
calculations. This requires the GROUP BY SQL function is used, which is not supported by the DBF driver.
For this reason, vector map output (output) is not permitted with the DBF driver. There are no problems
with the raster map output from the DBF driver.
REFERENCES
• 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. 155-174(20), Blackwell
Publishing Ltd
• 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.325-331
• Brovelli M. A e Longoni U.M., 2003, Software per il filtraggio di dati LIDAR, Rivista
dell’Agenzia del Territorio, n. 3-2003, pp. 11-22 (ISSN 1593-2192)
• 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:
978-84-690-3886-9
SEE ALSO
v.surf.idw, v.surf.rst
Overview: Interpolation and Resampling in GRASS GIS
AUTHORS
Original version (s.bspline.reg) in GRASS 5.4: Maria Antonia Brovelli, Massimiliano Cannata, Ulisse
Longoni, Mirko Reguzzoni
Update for GRASS 6 and improvements: Roberto Antolin
SOURCE CODE
Available at: v.surf.bspline source code (history)
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© 2003-2019 GRASS Development Team, GRASS GIS 7.8.2 Reference Manual