Provided by: grass-doc_8.4.1-1_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=memory in MB]
[--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=memory in MB
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 point layer. 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 layer. Output can be a raster (raster_output) or
vector (output) layer. Optionally, a "sparse point" vector layer 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, which 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. However, data points are often not regularly
distributed and require statistical 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, the 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.
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 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 point vector layer. 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 layer.
v.surf.bspline can produce raster (raster_output) OR vector output but NOT simultaneously. Note that
topology is not built for output point vector layer. If required, the topology can be built using
v.build.
If output is a point vector layer and sparse is not specified, the output vector layer will contain
points at the same locations as observation points in the input layer but the values of the output points
will be interpolated values. If a sparse point vector layer is specified, the output vector layer will
contain points at the same locations as the sparse vector layer points. The 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 point vector layer 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 layer 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 layer of vector points will be created, corresponding to the sparse vector layer, 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 dataset 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
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. This function is not supported by the DBF
driver. For this reason, vector 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)
Accessed: Friday Apr 04 01:20:35 2025
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GRASS 8.4.1 v.surf.bspline(1grass)