Abstract
We propose a simple approach to evolution of polygonal curves that is specially designed to fit discrete nature of curves in digi- tal images. It leads to simplification of shape complexity with no blur- ring (i.e., shape rounding) effects and no dislocation of relevant features. Moreover, in our approach the problem to determine the size of discrete steps for numerical implementations does not occur, since our evolution method leads in a natural way to a finite number of discrete evolution steps which are just the iterations of a basic procedure of vertex deletion.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
A. Bengtsson and J.-O. Eklundh. Shape representation by mutliscale contour approximation. IEEE Trans. Pattern Analysis and Machine Intelligence, 13:85–93, 1991.
A.M. Bruckstein, G. Shapiro, and C. Shaked. Evolutions of planer polygons. Int. J. of of Pattern Recognition and AI, 9:991–1014, 1995.
A. Brunn, U. Weidner, and W. Förstner. Model-based 2d-shape recovery. In Proc. of 17. DAGM Conf. on Pattern Recognition (Mustererkennung), pages 260–268, Bielefeld, Springer-Verlag, Berlin, 1995.
M.A. Grayson. The heat equation shrinks embedded plane curves to round points. Pattern Recognition, 26:285–314, 1987.
B. B. Kimia and K. Siddiqi. Geometric heat eequation and nonlinear diffusion of shapes and images. Computer Vision and Image Understanding, 64:305–322, 1996.
B. B. Kimia, A. R. Tannenbaum, and S. W. Zucker. Shapes, shocks, and deformations. i: The components of shape and the reaction-diffusion space. Int. J. Computer Vision, 15:189–224, 1995.
L. J. Latecki, R.-R. Ghadially, R. Lakämper, and U. Eckhardt. Continuity of the discrete curve evolution. In SPIE and SIAM Conf. on Vision Geometry VIII, July 1999, to appear.
L. J. Latecki and R. Lakämper. Convexity rule for shape decomposition based on discrete contour evolution. Computer Vision and Image Understanding, 73:441–454, 1999.
L. J. Latecki, R. Lakämper, and U. Eckhardt. http://www.math.uni-hamburg.de/home/lakaemper/shape.
F. Mokhtarian and A. K. Mackworth. A theory of multiscale, curvature-based shape representation for planar curves. IEEE Trans. PAMI, 14:789–805, 1992.
U. Ramer. An iterative procedure for the polygonal approximation of plane curves. Computer Graphics and Image Processing, 1:244–256, 1972.
J.A. Sethian. Level Set Methods. Cambridge University Press, Cambridge, 1996.
C.-H. Teh and R. T. Chin. On the detection of dominant points on digital curves. IEEE Trans. PAMI, 11:859–872, 1989.
N. Ueda and S. Suzuki. Learning visual models from shape contours using multi-scale convex/concave structure matching. IEEE Trans. PAMI, 15:337–352, 1993.
J. Weickert. A review of nonlinear diffusion filtering. In B. M. ter Haar Romeny, L. Florack, J. Koenderink, and M. Viergever, editors, Scale-Space Theory in Computer Vision, pages 3–28. Springer, Berlin, 1997.
A.P. Witkin. Scale-space filtering. In Proc. IJCAI, volume 2, pages 1019–1022, 1983.
www site. http://www.ee.surrey.ac.uk/research/vssp/imagedb/demo.html.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Latecki, L.J., Lakämper, R. (1999). Polygon Evolution by Vertex Deletion. In: Nielsen, M., Johansen, P., Olsen, O.F., Weickert, J. (eds) Scale-Space Theories in Computer Vision. Scale-Space 1999. Lecture Notes in Computer Science, vol 1682. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48236-9_35
Download citation
DOI: https://doi.org/10.1007/3-540-48236-9_35
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-66498-7
Online ISBN: 978-3-540-48236-9
eBook Packages: Springer Book Archive