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Identifying Faces in a 2D Line Drawing Representing a Manifold Object
December 2002 (vol. 24 no. 12)
pp. 1579-1593

Abstract—A straightforward way to illustrate a 3D model is to use a line drawing. Faces in a 2D line drawing provide important information for reconstructing its 3D geometry. Manifold objects belong to a class of common solids and most solid systems are based on manifold geometry. In this paper, a new method is proposed for finding faces from single 2D line drawings representing manifolds. The face identification is formulated based on a property of manifolds: each edge of a manifold is shared exactly by two faces. The two main steps in our method are 1) searching for cycles from a line drawing and 2) searching for faces from the cycles. In order to speed up the face identification procedure, a number of properties, most of which relate to planar manifold geometry in line drawings, are presented to identify most of the cycles that are or are not real faces in a drawing, thus reducing the number of unknown cycles in the second searching. Schemes to deal with manifolds with curved faces and manifolds each represented by two or more disjoint graphs are also proposed. The experimental results show that our method can handle manifolds previous methods can handle, as well as those they cannot.

[1] T. Marill, “Emulating the Human Interpretation of Line-Drawings as Three-Dimensional Objects,” Int'l J. Computer Vision, vol. 6, no. 2, pp. 147-161, 1991.
[2] Y.G. Leclerc and M.A. Fischler, “An Optimization-Based Approach to the Interpretation of Single Line Drawings as 3D Wire Frames,” Int'l J. Computer Vision, vol. 9, no. 2, pp. 113-136, 1992.
[3] H. Lipson and M. Shpitalni, “Optimization-Based Reconstruction of a 3D Object from a Single Freehand Line Drawing,” Computer-Aided Design, vol. 28, no. 8, pp. 651-663, 1996.
[4] K. Sugihara, “A Necessary and Sufficient Condition for a Picture to Represent a Polyhedral Scene,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 6, no. 5, pp. 578-586, 1984.
[5] K. Sugihara, “An Algebraic Approach to Shape-from-Image problem,” Artificial Intelligence, vol. 23, pp. 59-95, 1984.
[6] I. Shimshoni and J. Ponce, “Recovering the Shape of Polyhedra Using Line-Drawing Analysis and Complex Reflectance Models,” Computer Vision and Image Understanding, vol. 65, no. 2, pp. 296-310, 1997.
[7] P.E. Debevec, C.J. Taylor, and J. Malik, “Modeling and Rendering Architecture from Photographs: A Hybrid Geometry- and Image-Based Approach,” Proc. SIGGRAPH '96, pp. 11-20, Aug. 1996.
[8] A. Turner, D. Chapman, and A. Penn, “Sketching Space,” Computers&Graphics, vol. 24, pp. 869-879, 2000.
[9] M. Shpitalni and H. Lipson, “Identification of Faces in a 2D Line Drawing Projection of a Wireframe Object,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 18, no. 10, pp. 1000-1012, Oct. 1996.
[10] S.C. Agarwal and J.W.N. Waggenspack, “Decomposition Method for Extracting Face Topologies from Wireframe Models,” Computer-Aided Design, vol 24, no. 3, pp. 123-140, 1992.
[11] J. Liu and Y.T. Lee, “A Graph-Based Method for Face Identification from a Single 2D Line Drawing,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 23, no. 10, pp. 1106-1119, 2001.
[12] S. Bagali and J.W.N. Waggenspack, “A Shortest Path Approach to Wireframe to Solid Model Conversion,” Proc. Third Symp. Solid Modeling and Applications, pp. 339-349, 1995.
[13] J.S. Hojnicki and P.R. White, “Converting CAD Wireframe Data to Surfaced Representations,” Computer in Mechanical Eng., pp. 19-25, Mar./Apr., 1988.
[14] D.E. LaCourse, Handbook of Solid Modeling. New York: McGraw-Hill, 1995.
[15] G. Chartrand and O.R. Oellermann, Applied and Algorithmic Graph Theory. New York: McGraw-Hill, 1993.
[16] M. Mantyla, An Introduction to Solid Modeling.Rockville, Md., Computer Science Press, 1988.
[17] D.A. Huffman, “Impossible Objects as Nonsense Sentences,” Machine Intelligence, vol. 6, pp. 295-323, B. Meltzer and D. Mitchie, eds. London: Edinburgh Univ. Press, 1971.
[18] M.B. Clowes, “On Seeing Things,” Artificial Intelligence, vol. 2, pp. 79-116, 1971.
[19] D. Waltz, “Understanding Line Drawings of Scenes with Shadows,” Psychology of Computer Vision, pp. 19-91, P.H. Winston, ed. New York: McGraw-Hill, 1975.
[20] R. Haralick and L. Shapira, “The Consistent Labeling Problem: Part 1,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 1, no. 2, pp. 173-184, 1979.
[21] J. Malik, “Interpreting Line Drawings of Curved Objects,” Int'l J. Computer Vision, vol. 1, pp. 73-103, 1987.
[22] M.C. Cooper, “Interpretation of Line Drawings of Complex Objects,” Image and Vision Computing, vol. 11, no. 2, pp. 82-90, 1993.
[23] M.C. Cooper, “The Interpretations of Line Drawings with Contrast Failure and Shadows,” Int'l J. Computer Vision, vol. 43, no. 2, pp. 75-97, 2001.
[24] R. Lequette, “Automatic Construction of Curvilinear Solid from Wireframe Views,” Computer-Aided Design, vol. 20, no. 4, pp. 171-180, 1988.
[25] D. Lysak, “Interpretation of Engineering Drawings of Polyhedral and Nonpolyhedral Objects from Orthographic Projections,” PhD thesis, Dept. of Electrical&Computer Eng., Pennsylvania State Univ. 1991.
[26] S. Ablameyko, V. Bereishik, A. Gorelik, and S. Medvedev, “3D Object Reconstruction from Engineering Drawing Projections,” Computing&Control Eng. J., vol. 10, no. 6, pp. 277-284, 1999.
[27] M.H. Kuo, “Reconstruction of Quadric Surface Solid from Three-View Engineering Drawings,” Computer-Aided Design, vol. 30, no. 7, pp. 517-527, 1998.
[28] G. Markowsky and M.A. Wesley, “Fleshing out Wire-Frames,” IBM J. Research and Development, vol. 24, no. 5, pp. 582-597, 1980.
[29] P.M. Hanrahan, “Creating Volume Models from Edge-Vertex Graphs,” Computer Graphics, vol. 16, no. 3 pp. 77-84, 1982.
[30] R.D. Dutton and R.C. Brigham, “Efficiently Identifying the Faces of a Solid,” Computer and Graphics in Mechanical Eng., vol. 7, no. 2, pp. 143-147, 1983.
[31] M.A. Ganter and J.J. Uicker, “From Wire-Frame to Solid Geometric: Automated Conversion of Data Representations,” Computer in Mechanical Eng., vol. 2, no. 2, pp. 40-45, 1983.
[32] S.M. Courter and J.A. Brewer, “Automated Conversation of Curvilinear Wire-Frame Models to Surface Boundary Models: A Topological Approach,” Computer Graphics, vol. 20, no. 4, pp. 171-178, 1986.
[33] C. Thomasse, “The Graph Genus Problem is NP-Complete,” J. Algorithms, vol. 10, no. 4, pp. 568-576, 1989.
[34] P. Mateti and N. Deo, “On Algorithms for Enumerating all Circuits of a Graph,” SIAM J. Computing, vol. 5, no. 1, pp. 90-99, 1976.
[35] E.M. Reingold, J. Nievergelt, and N. Deo, Combinatorial Algorithms: Theory and Practices. New Jersey: Prentice-Hall, 1977.
[36] R. Sedgewick, Algorithms in C. Reading, Mass.: Addison-Wesley, 1990.

Index Terms:
3D models, face identification, geometry, graphs, line drawings, manifolds.
Jianzhuang Liu, Yong Tsui Lee, Wai-Kuen Cham, "Identifying Faces in a 2D Line Drawing Representing a Manifold Object," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 24, no. 12, pp. 1579-1593, Dec. 2002, doi:10.1109/TPAMI.2002.1114850
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