Minimum-Length Polygons in Approximation Sausages
The paper introduces a new approximation scheme for planar digital curves. This scheme defines an approximating sausage ‘around’ the given digital curve, and calculates a minimum-length polygon in this approximating sausage. The length of this polygon is taken as an estimator for the length of the curve being the (unknown) preimage of the given digital curve. Assuming finer and finer grid resolution it is shown that this estimator converges to the true perimeter of an r-compact polygonal convex bounded set. This theorem provides theoretical evidence for practical convergence of the proposed method towards a ‘correct’ estimation of the length of a curve. The validity of the scheme has been verified through experiments on various convex and non-convex curves. Experimental comparisons with two existing schemes have also been made.
KeywordsDigital geometry digital curves multigrid convergence length estimation
Unable to display preview. Download preview PDF.
- 1.T. Asano, Y. K awamura, R. Klette, and K. Obokata. A new approximation scheme for digital objects and curve length estimations. in Proc. of Image and Vision Computing New Zealand, Hamilton, pages 26–31, 2000.Google Scholar
- 2.T. Buelow and R. Klette. Rubber band algorithm for estimating the length of digitized space-curves. in Proc. IEEE Conf. ICPR, Barcelona, Vol. III, pages 551–555, 2000.Google Scholar
- 4.R. Klette, V. Kovalevsky, and B. Yip. On the length estimation of digital curves. in Proc. Vision Geometry VIII, Denver, SPIE-3811, pages 117–129, 1999.Google Scholar
- 5.R. Klette and Ben Yip. The length of digital curves. Machine GRAPHICS & VISION, 9:673–703, 2000.Google Scholar
- 6.R. Klette and J. Žuni. Multigrid convergence of calculated features in image analysis. J. Mathem. Imaging and Vision, 173–191, 2000.Google Scholar
- 7.V. Kovalevsky and S. Fuchs. Theoretical and experimental analysis of the accuracy of perimeter estimates. in Robust Computer Vision (W. Förstner, S. Ruwiedel, eds.), Wichmann, Karlsruhe, pages 218–242, 1992.Google Scholar
- 9.F. Sloboda, B. Zaťko, and P. Ferianc. Minimum perimeter polygon and its application. in Theoretical Foundations of Computer Visi/-on (R. Klette, W.G. Kropatsch, eds.), Mathematical Research 69, Akademie Verlag, Berlin, pages 59–70, 1992.Google Scholar
- 10.F. Sloboda, B. Zaťko, and J. Stoer. On approximation of planar one-dimensional continua. in Advances in Digital and Computational Geometry, (R. Klette, A. Rosenfeld and F. Sloboda, eds.) Springer, pages 113–160, 1998.Google Scholar