Provided by: grass-doc_8.4.1-1_all 
NAME
r.resamp.bspline - Performs bilinear or bicubic spline interpolation with Tykhonov regularization.
KEYWORDS
raster, surface, resample, interpolation, splines, bilinear, bicubic, no-data filling
SYNOPSIS
r.resamp.bspline
r.resamp.bspline --help
r.resamp.bspline [-nc] input=name output=name [grid=name] [mask=name] [ew_step=float]
[ns_step=float] [method=string] [lambda=float] [memory=memory in MB] [--overwrite] [--help]
[--verbose] [--quiet] [--ui]
Flags:
-n
Only interpolate null cells in input raster map
-c
Find the best Tykhonov regularizing parameter using a "leave-one-out" cross validation method
--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 raster map
output=name [required]
Name for output raster map
grid=name
Name for output vector map with interpolation grid
mask=name
Name of raster map to use for masking
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: 1.5 * ewres.
ns_step=float
Length of each spline step in the north-south direction. Default: 1.5 * nsres.
method=string
Spline interpolation algorithm
Options: bilinear, bicubic
Default: bicubic
bilinear: Bilinear interpolation
bicubic: Bicubic interpolation
lambda=float
Tykhonov regularization parameter (affects smoothing)
Default: 0.01
memory=memory in MB
Maximum memory to be used (in MB)
Cache size for raster rows
Default: 300
DESCRIPTION
r.resamp.bspline performs a bilinear/bicubic spline interpolation with Tykhonov regularization. The input
is a raster surface map, e.g. elevation, temperature, precipitation etc. Output is a raster map.
Optionally, only input NULL cells are interpolated, useful to fill NULL cells, an alternative to
r.fillnulls. Using the -n flag to only interpolate NULL cells will considerably speed up the module.
The input raster map is read at its native resolution, the output raster map will be produced for the
current computational region set with g.region. Any MASK will be respected, masked values will be treated
as NULL cells in both the input and the output map.
Spline step values ew_step for the east-west direction and ns_step for the north-south direction should
not be smaller than the east-west and north-south resolutions of the input map. For a raster map without
NULL cells, 1 * resolution can be used, but check for undershoots and overshoots. For very large areas
with missing values (NULL cells), larger spline step values may be required, but most of the time the
defaults (1.5 x resolution) should be fine.
The Tykhonov regularization parameter (lambda) acts to smooth the interpolation. With a small lambda, the
interpolated surface closely follows observation points; a larger value will produce a smoother
interpolation. Reasonable values are 0.0001, 0.001, 0.005, 0.01, 0.02, 0.05, 0.1 (needs more testing).
For seamless NULL cell interpolation, a small value is required. The default lambda value is set to 0.01.
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; these are 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 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 spline step
values should be no less than the east-west and north-south resolutions of the input map. Each non-NULL
cell 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 one observation and one coefficient for each spline (in order
to avoid instability).
A cross validation "leave-one-out" analysis is available to help to determine the optimal lambda 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 values. No vector nor
raster output will be created when cross-validation is selected.
EXAMPLES
Basic interpolation
r.resamp.bspline input=raster_surface output=interpolated_surface method=bicubic
A bicubic spline interpolation will be done and a raster map with estimated (i.e., interpolated) values
will be created.
Interpolation of NULL cells and patching
General procedure:
# set region to area with NULL cells, align region to input map
g.region n=north s=south e=east w=west align=input -p
# interpolate NULL cells
r.resamp.bspline -n input=input_raster output=interpolated_nulls method=bicubic
# set region to area with NULL cells, align region to input map
g.region raster=input -p
# patch original map and interpolated NULLs
r.patch input=input_raster,interpolated_nulls output=input_raster_gapfilled
Interpolation of NULL cells and patching (NC data)
In this example, the SRTM elevation map in the North Carolina sample dataset is filtered for outlier
elevation values; missing pixels are then re-interpolated to obtain a complete elevation map:
g.region raster=elev_srtm_30m -p
d.mon wx0
d.histogram elev_srtm_30m
r.univar -e elev_srtm_30m
# remove too low elevations (esp. lakes)
# Threshold: thresh = Q1 - 1.5 * (Q3 - Q1)
r.mapcalc "elev_srtm_30m_filt = if(elev_srtm_30m < 50.0, null(), elev_srtm_30m)"
# verify
d.histogram elev_srtm_30m_filt
d.erase
d.rast elev_srtm_30m_filt
r.resamp.bspline -n input=elev_srtm_30m_filt output=elev_srtm_30m_complete \
method=bicubic
d.histogram elev_srtm_30m_complete
d.rast elev_srtm_30m_complete
Estimation of lambda parameter with a cross validation process
A random sample of points should be generated first with r.random, and the current region should not
include more than 100 non-NULL random cells.
r.resamp.bspline -c input=input_raster
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
r.fillnulls, r.resamp.rst, r.resamp.interp, v.surf.bspline
Overview: Interpolation and Resampling in GRASS GIS
AUTHORS
Markus Metz
based on v.surf.bspline by
Maria Antonia Brovelli, Massimiliano Cannata, Ulisse Longoni, Mirko Reguzzoni, Roberto Antolin
SOURCE CODE
Available at: r.resamp.bspline source code (history)
Accessed: Friday Apr 04 01:19:29 2025
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GRASS 8.4.1 r.resamp.bspline(1grass)