r.resamp.bspline(1grass) GRASS GIS User's Manual r.resamp.bspline(1grass)
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. eleva-
tion, temperature, precipitation etc. Output is a raster map. Option-
ally, only input NULL cells are interpolated, useful to fill NULL
cells, an alternative to r.fillnulls. Using the -n flag to only inter-
polate 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 over-
shoots. 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 in-
terpolation. With a small lambda, the interpolated surface closely fol-
lows observation points; a larger value will produce a smoother inter-
polation. 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 interpo-
lated 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 di-
rection. 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 co-
efficient for each spline (in order to avoid instability).
A cross validation "leave-one-out" analysis is available to help to de-
termine 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 recom-
mended. 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 esti-
mated (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 location is filtered for outlier elevation values; missing pix-
els 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 re-
construction 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. Pro-
ceedings 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: unknown
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