Advertisement

Contour Smoothing Based on Weighted Smoothing Splines

  • Leonor Maria
  • Oliveira Malva
Conference paper

Abstract

Here we present a contour-smoothing algorithm based on weighted smoothing splines for contour extraction from a triangular irregular network (TIN) structure based on sides. Weighted smoothing splines are one-variable functions designed for approximating oscillatory data. Here some properties are derived from a small space of functions and working with few knots and special boundary conditions. However, in order to apply these properties to a two variable application such as contour smoothing, local reference frames for direct and inverse transformation are required. The advantage of using weighted smoothing splines as compared to pure geometric constructions such as the approximation by parabolic arcs or other type of spline function is the fact that these functions adjust better to the data and avoid the usual oscillations of spline functions. We note that Bezier and B-spline techniques are result in convenient, alternative representations of the same spline curves. While these techniques could be adapted to the weighted smoothing spline context, there is no advantage as our approach will be simple enough.

Keywords

Smoothing Spline Bezier Curve Special Boundary Condition Local Reference Frame Adjacent Triangle 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Cinquin. P., (1981) Splines Unidimensionells Sous Tension et Bidimensionelles Parametrées: Deux Applications Medicals, Thèse, Université de Saint_Etienne.Google Scholar
  2. Christensen, A. H. J., (2001) Contour Smoothing by an Ecletic Procedure, Photogrametric Engineering & Remote Sensing, 67(4): 511–517.Google Scholar
  3. Malva, L., Salkauskas, K., (2000) Enforced Drainage Terrain Models Using Minimum Norm Networks and Smoothing Splines, Rocky Mountain Journal of Mathematics, 30(3): 1075–1109.Google Scholar
  4. Rahman A. A., 1994, Design and evaluation of TIN interpolation algorithms, EGIS FoundationGoogle Scholar
  5. Salkauskas, K., 1984, C1splines for interpolation of rapidly varying data, Rocky Mountain Journal of Mathematics, 14(1): 239–250.Google Scholar
  6. Wahba. G., (1990) Spline models for observational data, SIAM Stud. Appl. Math. 59.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Leonor Maria
    • 1
  • Oliveira Malva
    • 1
  1. 1.Departamento de MatemáticaF.C.T.U.C.CoimbraPortugal

Personalised recommendations