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.