Reconstructing (h,v)-convex 2-dimensional patterns of objects from approximate horizontal and vertical projections

Theoretical Computer Science

Volumn 290, Issue 3, 2003, Pages 1647-1664

  Boufkhad, Yacine ^a   Dubois, Olivier ^b   Nivat, Maurice ^c  

^a UNIVERSITÉ D'ARTOIS   (France)

^b UNIVERSITÉ PARIS DESCARTES   (France)

^c UNIVERSITÉ PARIS DIDEROT   (France)

Author keywords

Discrete tomography; Polymino; Satisfiability

Indexed keywords

FORMAL LOGIC; IMAGE CODING;

DISCRETE TOMOGRAPHY; ORTHOGONAL PROJECTION; POLYMINO; SATISFIABILITY; SATISFIABILITY PROBLEMS; SUM OF ABSOLUTE DIFFERENCES; SUM OF THE ABSOLUTE DIFFERENCES; VERTICAL PROJECTION;

EMBEDDED SYSTEMS;

EID: 85009170433     PISSN: 03043975     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-3975(02)00072-5     Document Type: Article

References (14)

1. [1] Barcucci, E., Del Lungo, A., Nivat, M., Pinzani, R., Reconstructing convex polyominoes from horizontal and vertical projections. Theoret. Comput. Sci. 155 (1996), 321–347.
2. [2] Y. Boufkhad, Aspects probabilities et algorithmiques du problème de satisfiabilité, Ph.D. Thesis, Université Paris 6, 1996.
3. [3] Brunetti, S., Daurat, A., Del Lungo, A., An algorithm for reconstructing special lattice sets from their approximate X-rays. Discrete Geometry for Computer Imagery (DGCI 2000), Lecture Notes in Computer Science, Vol. 1953, 2000, Springer, Berlin, 113–125.
4. [4] Chang, S., The reconstruction of binary patterns from their projections. Commun. ACM 14 (1971), 21–25.
5. [5] Chrobak, M., Dürr, C., Reconstructing hv-convex polyominoes from orthogonal projections. Inform. Process. Lett. 69 (1999), 283–289.
6. [6] Davis, M., Logemann, G., Loveland, D., A machine program for theorem proving. J. Assoc. Comput. Mach. 5 (1962), 267–270.
7. [7] O. Dubois, P. André, Y. Boufkhad, J. Carlier, SAT versus UNSAT, in: D. Johnson, M.A. Trick (Eds.), Second DIMACS Implementation Challenge, Dimacs series, American Mathematical Society, Providence, RI, 1993.
8. [8] E. Freuder, Modeling satisfaction and satisfactory modeling: modeling problems so constraint engines can solve them, Invited Talk, 1998, AAAI’98, Madison, WI.
9. [9] Garey, M., Johnson, D., Computers and Intractability: A Guide to the Theory of NP-Completeness, 1979, Freeman, New York.
10. [10] Kuba, A., The reconstruction of two-directionaly connected binary patterns. Comput. Vision. Graph. Image Process 27 (1984), 249–265.
11. [11] Lungo, A.D., Polyominoes defined by two vectors. Theoret. Comput. Sci. 127 (1994), 187–198.
12. [12] H. Ryser, Combinatorial Mathematics, in: The Carus Mathematical Monographs, Vol. 14, Mathematical Association of America, Rahway, 1963.
13. [13] Wang, Y., Characterization of binary patterns and their projections. IEEE Trans. Comput. C-24 (1975), 1032–1035.
14. [14] G. Woeginger, The reconstruction of polyominoes from their orthogonal projections, Technical Report, TU Graz, 1996.