Polyhedral scene analysis combining parametric propagation with calotte analysis

Lecture Notes in Computer Science

Volumn 3519, Issue , 2005, Pages 383-402

  Li, Hongbo ^a   Zhao, Lina ^b   Chen, Ying ^a  

^a CHINESE ACADEMY OF SCIENCES   (China)

^b BEIJING UNIVERSITY OF CHEMICAL TECHNOLOGY   (China)

Author keywords

Constraint satisfaction; Grassmann Cay ley algebra; Imaging algebra; Polyhedral scene analysis; Projective reconstruction

Indexed keywords

COMPUTATIONAL COMPLEXITY; DRAWING (GRAPHICS); PARAMETER ESTIMATION;

2D LINE DRAWING; BIVECTOR; POLYHEDRAL SCENE ANALYSIS;

ALGEBRA;

EID: 25144462626     PISSN: 03029743     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1007/11499251_27     Document Type: Conference Paper

References (26)

1. J. Bokowski and B. Sturmfels. Computational Synthetic Geometry, LNM 1355, Springer, Berlin, Heidelberg, 1989.
2. H. Crapo and W. Whiteley. Stresses on Frameworks and Motions of Panel Structures: a Projective Geometric Introduction. Structural Topology 6: 42-82, 1982.
3. H. Crapo and J. Ryan. Spatial Realizations of Linear Scenes. Structural Topology 13: 33-68, 1986.
4. H. Crapo. Invariant-Theoretic Methods in Scene Analysis and Structural Mechanics. J. of Symbolic Computation 11: 523-548, 1991.
5. H. Crapo and W. Whiteley. Plane Self Stresses and Projected Polyhedra I: The Basic Pattern. Structural Topology 20: 55-78, 1993.
6. D. Huffman. Realizable Configurations of Lines in Pictures of Polyhedra, Machine Intelligence 8: 493-509, 1977.
7. H. Li. Vectorial Equation-Solving for Mechanical Geometry Theorem Proving. J. Automated Reasoning 25: 83-121, 2000.
8. H. Li and Y. Wu. Automated Short Proof Generation for Projective Geometric Theorems with Cayley and Bracket Algebras, I. Incidence Geometry. To appear in J. of Symbolic Computation.
9. A. Mackworth. Interpreting Pictures of Polyhedral Scenes, Artificial Intelligence 4: 121-137, 1973.
10. J. Richter-Gebert. Realization Spaces of Polytopes. LNM 1643, Springer, Berlin, Heidelberg, 1996.
11. L. Ros and F. Thomas. Analysing Spatial Realizability of Line Drawings through Edge-Concurrence Tests. In: Proc. IEEE Int'l Conf. Robotics and Automation, vol IV, pp. 3559-3566, May 1998.
12. L. Ros. A Kinematic-Geometric Approach to Spatial Interpretation of Line Drawings, Ph. D. Thesis, Polytechnic Univ. of Catalonia, May 2000.
13. L. Ros, F. Thomas. Overcoming Superstrictness in Line Drawing Interpretation. IEEE Trans. PAMI 24(4): 456-466, 2002.
14. B. Sturmfels and W. Whiteley. On the Synthetic Factorization of Projectively Invariant Polynomials. J. of Symbolic Computation 11: 439-453, 1991.
15. K. Sugihara. Mathematical Structures of Line Drawings of Polyhedrons - Towards Man-Machine Communication by Means of Line Drawings. IEEE Trans. PAMI 4: 458-469, 1982.
16. K. Sugihara (1984a). An Algebraic and Combinatorial Approach to the Analysis of Line Drawings of Polyhedra. Discrete Appl. Math. 9: 77-104, 1984.
17. K. Sugihara (1984b). An Algebraic Approach to Shape-from-Image Problems, Artificial Intelligence 23: 59-95, 1984.
18. K. Sugihara. Machine Interpretation of Line Drawings, MIT Press, Cambridge, Mass, 1986.
19. K. Sugihara. Resolvable Representation of Polyhedra. Discrete Computational Geometry 21(2): 243-255, 1999.
20. T. Tay. On the Cayley Factorization of Calotte Conditions. Discrete Computational Geometry 11: 97-109, 1994.
21. N. White and W. Whiteley. The Algebraic Geometry of Stresses in Frameworks, SIAM J. Alg. Discrete Math. 4: 481-511, 1983.
22. N. White. Multilinear Cayley Factorization. J. of Symbolic Computation 11: 421-438, 1991.
23. W. Whiteley. From a Line Drawing to a Polyhedron. J. Math. Psych. 31: 441-448, 1987.
24. W. Whiteley. A Matroid on Hypergraphs with Applications in Scene Analysis and Geometry. Discrete Computational Geometry 4: 75-95, 1989.
25. W. Whiteley. Weavings, Sections and Projections of Spherical Polyhedra. Discrete Appl. Math. 32: 275-294, 1991.
26. W. Whiteley. Matroids and Rigid Structures. In Matroid Applications, N. White ed., Encyclopedia of Mathematics and Its Applications 40, pp. 1-53, Cambridge University Press, Cambridge, 1992.