Optimum Weight in Spline for Surface Model

  • Published : 2005.03.01

Abstract

The digital surface model (DSM) is used for several purposes in photogrammetry, remote sensing and laser scanned data such as orthoimage production, contours erivation, extraction of height information. Creation of a surface model from point-clouds (3-D sparse points) that can be derived from stereo imagery and range data (e.g. laser scanned data) can be done with several mathematical interpolation models. In this paper, thin-plate-spline (TPS) is used for digital surface modeling. Determination of suitable weight is an important problem in thin-plate function for a surface. The Voronoi algorithm has been proposed as a method for determination of the weight in thin-plate-spline. In this paper, methods has been tested for different surfaces. The results show that thin-plate-spline can be independent of weight.

Keywords

References

  1. Bazen, A. M. and Gerez, S. H., 2002, Thin-Plate Modelling of Elastic Deformations in Fingewrprints, 3rd IEEE Benelux Signal Processing Symposium, Leuven, Belgium, 21-22
  2. Billings, S. D., Beatsonz, R. K., and Newsam, G. N., 2002, Interpolation of geophysical data using continuous global surfaces, J. GEOPHYSICS, 67, 6
  3. Duchon, J., 1976, Interpolation des fonctions de deux variables suivant le principe de la flexion des plaques minces, RAIRO Analyse Numerique 10, 5-12
  4. Franke, R., 1982, Smooth interpolation of scattered data by local thin plate splines, Computing and Mathematics with Applications 8, 273-281 https://doi.org/10.1016/0898-1221(82)90009-8
  5. Meinguet, K., 1979, Multivariate Interpolation at Arbitrary Points Made Simple, J. Appl. Math. Phys. 30, 292-304 https://doi.org/10.1007/BF01601941
  6. Pedersen, L., 2000, Estimation of thin plate spline WARP Parameters from protein spot positions in 2D, ELECTROPHORESIS GELS
  7. Gousie, M. B., 2004, Converting Elevation Contours to a Grid
  8. Maillet, G., 2004, DSM reconstruction, Manual of photogrammetry
  9. htttp://mathworld.wolfram.com Thin Plate Spline
  10. Jenkins, D. R., 2000, Thin plate spline interpolation in an annulus, ANZIAM J. 42 (E) C819 https://doi.org/10.21914/anziamj.v42i0.623
  11. Boztosun, I.. Chara, A.. Zerroukat, M. and Djidjeli, K. 2002, Thin-Plate Spline Radial Basis Function Scheme for Advection- Diffusion Problemsm, Electronic Journal of Boundary Elements, Vol. BETEQ, 2, 267-282
  12. Goncalves, G., Julien P., Riazanoff, S., and Cervelle, B., 2002, Preserving cartographic quality in DTM interpolation from contour lines, ISPRS 56, 210-220 https://doi.org/10.1016/S0924-2716(02)00044-8
  13. Sjowall, A., 2004, Short Report on OrthoEngine. Vilnius 2001-04-08