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Annals of Operations Research

, Volume 12, Issue 1, pp 51–64 | Cite as

Solving jigsaw puzzles by computer

  • Haim Wolfson
  • Edith Schonberg
  • Alan Kalvin
  • Yehezkel Lamdan
Article

Abstract

An algorithm to assemble large jigsaw puzzles using curve matching and combinatorial optimization techniques is presented. The pieces are photographed one by one and then the assembly algorithm, which uses only the puzzle piece shape information, is applied. The algorithm was experimented successfully in the assembly of 104-piece puzzles with many almost similar pieces. It was also extended to solve an intermixed puzzle assembly problem and has successfully solved a 208-piece puzzle consisting of two intermixed 104-piece puzzles. Previous results solved puzzles with about 10 pieces, which were substantially different in shape.

Keywords

Computer vision curve matching jigsaw puzzle assembly traveling salesman assignment pattern recognition 2-D shape 

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References

  1. [1] [B-M]
    M. Belmore and J.C. Malone, Pathology of traveling-salesman subtour-elimination algorithms, Oper. Res. 19(1971)278.Google Scholar
  2. [2] [B-N]
    M. Belmore and G.L. Nemhauser, The traveling-salesman problem: A survey, Oper. Res. 16(1968)538.Google Scholar
  3. [3] [B-W]
    G. Burdea and H. Wolfson, Automated assembly of a jigsaw puzzle using the IBM 7565 Robot, Tech. Rep. No. 188, Comp. Sci. Div., Courant Inst. of Math., NYU (1985).Google Scholar
  4. [4] [C]
    N. Christofides,Graph Theory (Academic Press, 1975).Google Scholar
  5. [5] [F]
    Z. Fencl, Routing problem, CACM Algorithm 456.Google Scholar
  6. [6] [F-G]
    H. Freeman and L. Garder, Apictorial jigsaw puzzles: The computer solution of a problem in pattern recognition, IEEE Trans. on Electronic Comp. EC-13, 2(1964)118.Google Scholar
  7. [7] [G-J]
    M.R. Garey and D.S. Johnson,Computers and Intractability: A Guide to the Theory of NP-Completeness (W.H. Freeman and Co., 1979).Google Scholar
  8. [8] [K-S-S-S]
    A. Kalvin, E. Schonberg, J.T. Schwartz and M. Sharir, Two dimensional model based boundary matching using footprints, Tech. Rep. No. 162, Comp. Sci. Div., Courant Inst. of Math., NYU (1985).Google Scholar
  9. [9] [L]
    E.L. Lawler,Combinatorial Optimization: Networks and Matroids (Holt, Rinehart and Winston, 1976).Google Scholar
  10. [10] [L-L-RK-S]
    E.L. Lawler, J.R. Lenstra, A.H.G. Rinnooy Kan and D.B. Shmoys,The Traveling Salesman Problem: A Guided Tour of Combinatorial Optimization (Wiley, 1985).Google Scholar
  11. [11] [R]
    T.C. Raymond, Heuristic algorithm for the traveling-salesman problem, IBM J. Res. Develop. 13, 4(1969)400.Google Scholar
  12. [12] [R-B]
    G.M. Radack and N.I. Badler, Jigsaw puzzle matching using a boundary-centered polar encoding, Computer Graphics and Image Processing 19(1982)1.Google Scholar
  13. [13] [S-S]
    J.T. Schwartz and M. Sharir, Identification of partially obscured objects in two dimensions by matching of noisy “characteristic curves”, Tech. Rep. No. 165, Comp. Sci. Div., Courant Inst. of Math., NYU (1985).Google Scholar
  14. [14] [W]
    H. Wolfson, On curve matching, Tech. Rep. No. 256, Comp. Sci. Div., Courant Inst. of Math., NYU (1986).Google Scholar

Copyright information

© J.C. Baltzer AG, Scientific Publishing Company 1988

Authors and Affiliations

  • Haim Wolfson
    • 1
  • Edith Schonberg
    • 1
  • Alan Kalvin
    • 1
  • Yehezkel Lamdan
    • 1
  1. 1.Robotics Research Laboratory, Department of Computer Science, Courant Institute of Mathematical SciencesNew York UniversityNew YorkUSA

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