NAME
s.bspline.reg - Interpolate a site file with
bidimensional spline to produce a surface.
SYNOPSIS
s.bspline.reg
s.bspline.reg help
s.bspline.reg [-g] input=string output=string
Sie=float Sin=float [type=string]
[lambda_i=float]
DESCRIPTION
s.bispline.reg allows a user to create a (binary) GRASS raster
map layer representing a distributed field starting from pointwise
samples.
Sites data are interpolated by bicubic or bilinear spline
functions (Meissl
1982) with Tikhonov regularisation (Vinod and Ullah 1981, Engl et al.
1996) in
a least square approach.
This command
is part of a procedure to filter airbone
laser scanning (LIDAR) data in order to extract Digital Terrain Model.
The procedure involves the execution of the following
commands:
1) s.edgedetection - 2) s.growing - 3) s.correction - 4)
s.bspline.reg
OPTIONS
The user can run this program either interactively
or non- interactively. The program will be run non-interactively if the
user
specifies program arguments and flag settings on the command line using
the
form:
s.bspline.reg [-g] input=string output=string
Sie=float Sin=float [type=string]
[lambda_i=float]
Alternately, the user can simply type s.bispline.reg
on the command
line without program arguments. In this case, the user will be prompted
for parameter values and flag settings using the standard GRASS parser
interface described in the manual entry for parser.
Flags:
- -g
- rast output instead sites list file output
Parameters:
input=string
input observation sites list file name
output=string
output interpolated file name (default
is a sites list)
Sie=float
interpolation spline step value in east
direction
Sin=float
interpolation spline step value in
north direction
type=string
spline type
Options: bilinear,bicubic
Default: bilinear
lambda_i=float
Tikhonov regularization weigth
Default: 1
NOTES
The
spline step (Sie- Sin) choice depends on the
mean planimetric resolution of the raw data: in airbone laser scanning
data
we have chosen 3 to 4 times this
parameter.
The Tikhonov regularisation parameter (lambda_i)
permits (i) to avoid local and global singularity
in the least square approach (in case of missing observations
areas) (ii) to assure the regularity of the surface in empty
areas, minimising
the gradient (in case of type=bilinear)
or the curvature (in case of type=bicubic)
(iii) to produce a surface that feels as
little
as possible the influence of possible outliers.
Imposing a high value for lambda_i a
surface with a behaviour quite
different from an exact interpolator is obtained.
The type parameter selects
the spline function type; is to be noted that
bicubic produces a smoothed
surface while bilinear permits
a more
accurate data fitting. For these reasons, in DTM
extraction, the first type is preferred for outlier detection and the
second one for
surface reconstruction.
Input format example (x|y|z):
513629.21|5403205.11|#0 %291.24
513629.25|5403206.53|#0 %291.28
513629.29|5403208.16|#0 %291.27
513629.33|5403209.69|#0 %291.29
513629.37|5403211.12|#0 %291.32
A bug in analysing very large data set has been reported.
Please report any further bug to massimiliano.cannata@supsi.ch
SEE ALSO
s.correction, s.edgedetection, s.growing, s.to.qrast, s.surf.rst.
AUTHORS
Maria
A. Brovelli, Politecnico di Milano - Campus Como
Massimiliano Cannata, Politecnico
di Milano - Campus Como
Ulisse M.
Longoni, Politecnico
di Milano - Campus Como
REFERENCES
Brovelli M.A.;
Cannata M.; Longoni U.M., LIDAR Data Filtering and DTM Interpolation
Within GRASS
Transactions in GIS, April 2004, vol. 8, no. 2, pp.
155-174(20) - Blackwell Publishing Ltd
Meissl
P
1982 Least Squares Adjustment: a Modern
Approach.
Mitteilungen der Geodätischen Institute der Technischen
Universität Graz,
Folge 43
Vinod
H.
and Ullah A. 1981 Recent advances in
regression methods. Marcel Dekker.