ACCORD: With Approximate Covering of Convex Orthogonal Decomposition

  • Mousumi Dutt
  • Arindam Biswas
  • Partha Bhowmick
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6607)

Abstract

A fast and efficient algorithm to obtain an orthogonally convex decomposition of a digital object is presented. The algorithm reports a sub-optimal solution and runs in O(nlogn) time for a hole-free object whose boundary consists of n pixels. The approximate/rough decomposition of the object is achieved by partitioning the inner cover (an orthogonal polygon) of the object into a set of orthogonal convex components. A set of rules is formulated based on the combinatorial cases and the decomposition is obtained by applying these rules while considering the concavities of the inner cover. Experimental results on different shapes have been presented to demonstrate the efficacy, elegance, and robustness of the proposed technique.

Keywords

convex component convex decomposition image analysis polygon decomposition rectangular component 

References

  1. 1.
    Aguilera, A., Ayala, D.: Faster ASV Decomposition for Orthogonal Polyhedra, Using the Extreme Vertices Model (EVM). In: WSCG 2000, pp. 60–67 (2000)Google Scholar
  2. 2.
    Asano, T., Asano, T., Imai, H.: Partitioning a Polygonal Region into Trapezoids. JACM 33, 290–312 (1986)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Biswas, A., Bhowmick, P., Bhattacharya, B.B.: TIPS: On finding a tight isothetic polygonal shape covering a 2D object. In: Kalviainen, H., Parkkinen, J., Kaarna, A. (eds.) SCIA 2005. LNCS, vol. 3540, pp. 930–939. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  4. 4.
    Chazelle, B.: Approximation and Decomposition of Shapes. In: Schwartz, J.T., Yap, C.K. (eds.) Advances in Robotics 1: Algorithmic and Geometric Aspects of Robotics, pp. 145–186. Lawrence Erlbaum Associates, Hillsdale (1987)Google Scholar
  5. 5.
    Chazelle, B., Dobkin, D.: Decomposing a polygon into its convex parts. In: Proc. STOC, pp. 38–48 (1979)Google Scholar
  6. 6.
    Feng, H.Y.F., Pavlidis, T.: Decomposition of Polygons Into Simpler Components: Feature Generation for Syntactic Pattern Recognition. IEEE Trans. Computers 24, 636–650 (1975)MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Ferrari, L., Sankar, P.V., Sklansky, J.: Minimal Rectangular Partitions of Digitized Blobs. CVGIP 28, 58–71 (1984)MATHGoogle Scholar
  8. 8.
    Keil, J.M.: Decomposing a Polygon into Simpler Components. PhD thesis, Univ. of Toronto, Canada (1983)Google Scholar
  9. 9.
    Keil, J.M.: Minimally Covering a Horizontally Convex Orthogonal Polygon. In: Proc. SoCG, pp. 43–51 (1986)Google Scholar
  10. 10.
    Keil, J.M., Sack, J.R.: Minimum Decompositions of Polygonal Objects. In: Toussaint, J.T. (ed.) Computational Geometry, Netherlands, pp. 197–216 (1985)Google Scholar
  11. 11.
    Klincsek, G.T.: Minimal Triangulations of Polygonal Domains. Discrete Math. 9, 121–123 (1980)MathSciNetMATHGoogle Scholar
  12. 12.
    Levcopoulos, C., Lingas, A.: Bounds on the Length of Convex Partition of Polygons. In: Joseph, M., Shyamasundar, R.K. (eds.) FSTTCS 1984. LNCS, vol. 181, pp. 279–295. Springer, Heidelberg (1984)CrossRefGoogle Scholar
  13. 13.
    Lien, J.-M., Amato, N.M.: Approximate convex decomposition of polygons. In: Proc. SoCG, pp. 17–26 (2004)Google Scholar
  14. 14.
    Lien, J.-M., Amato, N.M.: Approximate convex decomposition of polygons. CGTA 35, 100–123 (2006)MathSciNetMATHGoogle Scholar
  15. 15.
    Lingas, A.: The power of non-rectilinear holes. In: Proc. ICALP. LNCS, vol. 140, pp. 369–383 (1982)Google Scholar
  16. 16.
    Lingas, A., Pinter, R., Rivest, R., Shamir, A.: Minimum Edge Length Partitioning of Rectilinear Polygons. In: Proc. 20th Allerton Conf. Commun. Control Comput., pp. 53–63 (1982)Google Scholar
  17. 17.
    Lingas, A., Soltan, V.: Minimum Convex Partition of a Polygon with Holes by Cuts in Given Directions. In: Proc. ISAAC, vol. 1178, pp. 315–325 (2006)Google Scholar
  18. 18.
    Nahar, S., Sahni, S.: Fast Algorithm for Polygon Decomposition. IEEE Trans. CAD 7, 473–483 (1988)CrossRefGoogle Scholar
  19. 19.
    Ohtsuki, T.: Minimum Dissection of Rectiliniear Regions. In: Proc. IEEE Intl. Symp. Circuits & Systems, pp. 1210–1213 (1982)Google Scholar
  20. 20.
    O’Rourke, J., Supowit, K.J.: Some NP-Hard Polygon Decomposition Problems. IEEE Trans. Information Theory 29, 181–190 (1983)MathSciNetCrossRefMATHGoogle Scholar
  21. 21.
    Pavlidis, T.: Shape Discrimination. In: Fu, K.S. (ed.) Syntactic Pattern Recognition, NY, pp. 125–145 (1977)Google Scholar
  22. 22.
    Pavlidis, T.: Structural Pattern Recognition. Springer, Berlin (1977)CrossRefMATHGoogle Scholar
  23. 23.
    Pavlidis, T.: Survey: A Review of Algorithms for Shape Analysis. CGIP 7, 243–258 (1978)Google Scholar
  24. 24.
    Reckhow, R.A., Culberson, J.: Covering a Simple Orthogonal Polygon with a Minimum Number of Orthgonally Convex Polygons. In: Proc. SoCG, pp. 43–51 (1986)Google Scholar
  25. 25.
    O’Rourke, J.: Art Gallery Theorems and Applications. Oxford University Press, NY (1987)MATHGoogle Scholar
  26. 26.
    Shermer, T.C.: Recent Results in Art Gallery. Proc. of the IEEE 80(9), 1384–1399 (1992)CrossRefGoogle Scholar
  27. 27.
    Toussaint, G.T.: Pattern Recognition and Geometrical Complexity. In: Proc. ICPR, pp. 1324–1347 (1980)Google Scholar
  28. 28.
    Waco, D.L., Kim, Y.S.: Geometric Reasoning for Matching Features Using Convex Decomposition. In: Proc. ACM Symp. Solid & Physical Modeling, pp. 323–332 (1993)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Mousumi Dutt
    • 1
  • Arindam Biswas
    • 1
  • Partha Bhowmick
    • 2
  1. 1.Department of Information TechnologyBengal Engineering and Science UniversityShibpur, HowrahIndia
  2. 2.Department of Computer Science and EngineeringIndian Institute of TechnologyKharagpurIndia

Personalised recommendations