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NAME

       r.resamp.bspline   -  Performs  bilinear  or  bicubic  spline  interpolation with Tykhonov
       regularization.

KEYWORDS

       raster, surface, resample, interpolation, splines, 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=integer]    [--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=integer
           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 and default is set to 0.005.

       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  location  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

       Last changed: $Date: 2016-08-03 13:50:26 +0200 (Wed, 03 Aug 2016) $

SOURCE CODE

       Available at: r.resamp.bspline source code (history)

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       © 2003-2019 GRASS Development Team, GRASS GIS 7.6.1 Reference Manual