TIPS: On Finding a Tight Isothetic Polygonal Shape Covering a 2D Object

  • Arindam Biswas
  • Partha Bhowmick
  • Bhargab B. Bhattacharya
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3540)


The problem of constructing a tight isothetic outer (or inner) polygon covering an arbitrarily shaped 2D object on a background grid, is addressed in this paper, and a novel algorithm is proposed. Such covers have many applications to image mining, rough sets, computational geometry, and robotics. Designing efficient algorithms for these cover problems was an open problem in the literature. The elegance of the proposed algorithm lies in utilizing the inherent combinatoral properties of the relative arrangement of the object and the grid lines. The shape and the relative error of the polygonal cover can be controlled by changing the granularity of the grid. Experimental results on various complex objects with variable grid sizes have been reported to demonstrate the versatility, correctness, and speed of the algorithm.


  1. 1.
    Bemporad, A., Filippi, C., Torrisi, F.D.: Inner and outer approximations of polytopes using boxes. Computational Geometry - Theory and Applications 27, 151–178 (2004)zbMATHMathSciNetGoogle Scholar
  2. 2.
    Gatrell, L.: Cad-based grasp synthesis utilizing polygons, edges and vertices. In: Proc. IEEE Intl. Conf. Robotics and Automation, pp. 184–189 (1989)Google Scholar
  3. 3.
    Kamon, Y., Flash, T., Edelman, S.: Learning to grasp using visual information. In: Proc. IEEE Intl. Conf. Robotics and Automation, pp. 2470–2476 (1995)Google Scholar
  4. 4.
    Lengyel, J., Reichert, M., Donald, B.R., Greenberg, D.P.: Real-time Robot Motion Planning Using Rasterizing Computer. Computer Graphics, ACM 24(4), 327–335 (1990)CrossRefGoogle Scholar
  5. 5.
    Liu, M., He, Y., Hu, H., Yu, D.: Dimension Reduction Based on Rough Set in Image Mining. In: Das, G., Gulati, V.P. (eds.) CIT 2004. LNCS, vol. 3356, pp. 39–44. Springer, Heidelberg (2004)Google Scholar
  6. 6.
    Morales, A., Sanz, P.J., del Pobil, Á.P.: Vision-Based Computation of Three-Finger Grasps on Unknown Planar Objects. In: IEEE Intl. Conf. on Intelligent Robots and Systems, pp. 1711–1716 (2002)Google Scholar
  7. 7.
    Nandy, S.C., Bhattacharya, B.B.: Safety Zone Problem. Journal of Algorithms 37, 538–569 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Pal, S.K., Mitra, P.: Case Generation Using Rough Sets with Fuzzy Representation. IEEE Trans. on Knowledge and Data Engg. 16(3), 292–300 (2004)CrossRefGoogle Scholar
  9. 9.
    Pal, S.K., Mitra, P.: Pattern Recognition Algorithms for Data Mining. Chapman and Hall/CRC Press, Boca Raton (2004)zbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Arindam Biswas
    • 1
  • Partha Bhowmick
    • 1
  • Bhargab B. Bhattacharya
    • 2
  1. 1.Computer Science and Technology DepartmentBengal Engineering and Science UniversityShibpur, HowrahIndia
  2. 2.Center for Soft Computing ResearchIndian Statistical InstituteKolkataIndia

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