Advertisement

Abstract

Many methods of a raw vectorization produce lines with redundant vertices. Therefore the results of vectorization usually need to be compressed. Approximating methods based on throwing out inessential vertices are widely disseminated. The result of using any of these methods is a polyline, the vertices of which are a subset of source polyline vertices. When the vertices of the source polyline contain noise, vertices of the result polyline will have the same noise. Reduction of vertices without noise filtering can disfigure the shape of the source polyline. We suggested a new optimal method of the piecewise linear approximation that produces noise filtering. Our method divides the source polyline into clusters and approximates each cluster with a straight line. Our optimal method of dividing polylines into clusters guarantees that the functional, which is the integral square error of approximation plus the penalty for each cluster, will be the minimum one.

Keywords

vectorization polylinecompression polyline approximation shape analysis 

References

  1. 1.
    Douglas, D., Peucker, T.: Algorithm for the reduction of the number of points required to represent a digitized line or its caricature. The Canadian Cartographer 10, #2, 112–122 (1973)Google Scholar
  2. 2.
    Lang, T.: Rules for robot draftsmen. Geographical Magazine 22(1), 50–51 (1969)Google Scholar
  3. 3.
    Ramer, U.: Extraction of Line Structures from Photographs of Curved Objects. Computer Graphics and Image Processing 4, 81–103 (1975)CrossRefGoogle Scholar
  4. 4.
    Sklansky, J., Gonzalez, V.: Fast Polygonal Approximation of Digitized Curves. Pattern Recognition 12, 327–331 (1980)CrossRefGoogle Scholar
  5. 5.
    Lowe, D.G.: Perceptual organization and visual recognition, ch. 4. Kluwer Academic Publishers, Boston (1985)Google Scholar
  6. 6.
    Bodansky, E., Gribov, A., Pilouk, M.: Smoothing and Compression of Lines Obtained by Raster-to-Vector Conversion. In: Blostein, D., Kwon, Y.-B. (eds.) GREC 2001. LNCS, vol. 2390, pp. 256–265. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  7. 7.
    Pavlidis, T., Horwitz, S.L.: Segmentation of Plane Curves. IEEE Transactions on Computers 23(8), 860–870 (1974)zbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Alexander Gribov
    • 1
  • Eugene Bodansky
    • 1
  1. 1.Environmental System Research Institute (ESRI)RedlandsUSA

Personalised recommendations