Representing 2D Digital Objects

  • Vito Gesú Di 
  • Cesare Valenti 
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1953)


The paper describes the combination a multi-views approach to represent connected components of 2D binary images. The approach is based on the Object Connectivity Graph (OCG), which is a sub-graph of the connectivity graph generated by the Discrete Cylindrical Algebraic Decomposition(DCAD) performed in the 2D discrete space. This construction allows us to find the number of connected components, to determine their connectivity degree, and to solve visibility problem. We show that the CAD construction, when performed on two orthogonal views, supply information to avoid ambiguities in the interpretation of each image component. The implementation of the algorithm is outlined and the computational complexities is given.


shape representation shape decomposition shape descrip-tion digital topology 


  1. 1.
    Barcucci, E., Del Lungo, A., Nivat, M., Pinzani, R.: Reconstructing convex polymi-noes from horizontal and vertical projections. Theoretical Computer Science 155 (1996) 321–347. 337zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Herman, G. T.: Image Reconstruction from Projections: The Fundamentals of Computerized Tomography. Academic Press (New York) (1980). 337Google Scholar
  3. 3.
    Chella, A., Di Gesú, V., Infantino, I., Intravaia, D., Valenti, C.: Cooperating Strat-egy for Objects Recognition. in Lecture Notes in Computer Science book “Shape, contour and grouping in computer vision”, Springer Verlag, 1681 (1999) 264–274. 337CrossRefGoogle Scholar
  4. 4.
    Collins, G. E.: Quantifier elimination for real closed fields by cylindrical algebraic decomposition. Proc.of the Second GI Conference on Automata Theory and Formal Languages, Springer Lect.Notes Comp. SCi. 33 (1975) 515–532. 337Google Scholar
  5. 5.
    Di Gesú, V. and Renda, R.: An algorithm to analyse connected components of binary images. Geometrical Problems of Image Processing 4 (1991) 87–93. 337, 338Google Scholar
  6. 6.
    Arnon, D. S., McCallum, S.: A polynomial-time algorithm for the topological type of a real algebraic curve. Journal Symb. Comp. 5 (1988) 213–236. 337MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    Arnborg, S., Feng, H.: Algebraic decomposition of regular curves. Journal Symb. Comp. 5 (1988) 131–140. 337MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Françon, J. M.: Sur la topologie d’un plan arithmétique. Theoretical Computer Science 156 (1996) 31–40. 337Google Scholar
  9. 9.
    Khalimsky, E. D., Kopperman, R., Meyer P. R.: Computer graphics and connected topologies on finite ordered sets. Topology and Applications 36 (1990) 1–17. 337zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Chassery, J. M. and Montanvert, A.: Geómetrie discreète en analyse d’images. Hermeś, Paris (1991). 338Google Scholar
  11. 11.
    Kovalevsky, V. A.: Finite Topology as Applied to Image Analysis. Computer Vi-sion, Graphics, and Image Processing 45 (1989) 141–161. 338CrossRefGoogle Scholar
  12. 12.
    Chiavetta, F., Di Gesú, V., and Renda, R.: A Parallel Algorithm to analyse con-nected components on binary images. International Journal of Pattern Recognition and Artificial Intelligence 6(2,3) (1992) 315–333. 345CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Vito Gesú Di 
    • 1
  • Cesare Valenti 
    • 1
  1. 1.Dipartimento di Matematica ed ApplicazioniUniversity of PalermoPalermoItaly

Personalised recommendations