This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
What the Back of the Object Looks Like: 3D Reconstruction from Line Drawings without Hidden Lines
March 2008 (vol. 30 no. 3)
pp. 507-517
ASCII Text
x 
 
Liangliang Cao, Jianzhuang Liu, Xiaoou Tang, "What the Back of the Object Looks Like: 3D Reconstruction from Line Drawings without Hidden Lines," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 30, no. 3, pp. 507-517, March, 2008.
 
 
BibTex
x
 
@article{ 10.1109/TPAMI.2007.1185,
author = {Liangliang Cao and Jianzhuang Liu and Xiaoou Tang},
title = {What the Back of the Object Looks Like: 3D Reconstruction from Line Drawings without Hidden Lines},
journal ={IEEE Transactions on Pattern Analysis and Machine Intelligence},
volume = {30},
number = {3},
issn = {0162-8828},
year = {2008},
pages = {507-517},
doi = {http://doi.ieeecomputersociety.org/10.1109/TPAMI.2007.1185},
publisher = {IEEE Computer Society},
address = {Los Alamitos, CA, USA},
}
 
 
RefWorks Procite/RefMan/Endnote
x 
 
TY - JOUR
JO - IEEE Transactions on Pattern Analysis and Machine Intelligence
TI - What the Back of the Object Looks Like: 3D Reconstruction from Line Drawings without Hidden Lines
IS - 3
SN - 0162-8828
SP507
EP517
EPD - 507-517
A1 - Liangliang Cao,
A1 - Jianzhuang Liu,
A1 - Xiaoou Tang,
PY - 2008
KW - 3D reconstruction
KW - hidden topology
KW - line drawings
KW - visual perception
VL - 30
JA - IEEE Transactions on Pattern Analysis and Machine Intelligence
ER -
 
The human vision system can interpret a single 2D line drawing as a 3D object without much difficulty even if the hidden lines of the object are invisible. Many reconstruction methods have been proposed to emulate this ability, but they cannot recover the complete object if the hidden lines of the object are not shown. This paper proposes a novel approach to reconstructing a complete 3D object, including the shape of the back of the object, from a line drawing without hidden lines. First, we develop theoretical constraints and an algorithm for the inference of the topology of the invisible edges and vertices of an object. Then we present a reconstruction method based on perceptual symmetry and planarity of the object. We show a number of examples to demonstrate the success of our approach.

[1] S. Ortiz Jr., “3D Searching Starts to Take Shape,” Computer, pp. 24-26, Aug. 2004.
[2] P. Min, J. Chen, and T. Funkhouser, “A 2D Sketch Interface for a 3D Model Search Engine,” Proc. ACM SIGGRAPH '02, p. 138, 2002.
[3] M. Yu, I. Atmosukarto, W.K. Leow, Z. Huang, and R. Xu, “3D Model Retrieval with Morphing-Based Geometric and Topological Feature Maps,” Proc. IEEE Computer Vision and Pattern Recognition, vol. 2, pp. 656-661, 2003.
[4] P. Debevec, C.J. Yaylor, and J. Malik, “Modeling and Rendering Architecture from Photographs: A Hybrid Geometry—and Image-Based Approach,” Proc. ACM SIGGRAPH '96, pp. 11-20, 1996.
[5] A. Turner, D. Chapman, and A. Penn, “Sketching Space,” Computers and Graphics, vol. 24, pp. 869-879, 2000.
[6] P. Sturm and S. Maybank, “A Method for Interactive 3D Reconstruction of Piecewise Planar Objects from Single Images,” Proc. British Machine Vision Conf., pp. 265-274, 1999.
[7] S. Bagali and J. Waggenspack, “A Shortest Path Approach to Wireframe to Solid Model Conversion,” Proc. Third Symp. Solid Modeling and Applications, pp. 339-349, 1995.
[8] T. Syeda-Mahmood, “Indexing of Technical Line Drawing Databases,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 21, no. 8, pp. 737-751, Aug. 1999.
[9] M.Q.J. Marefat, “Hierarchical Bayesian Methods for Recognition and Extraction of 3-D Shape Features from CAD Solid Models,” IEEE Trans. Systems, Man, and Cybernetics, Part A, vol. 27, no. 6, pp.705-727, 1997.
[10] 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.
[11] D. Dori and L. Wenyin, “Automated CAD Conversion with the Machine Drawing Understanding System: Concepts, Algorithms, and Performance,” IEEE Trans. Systems, Man, and Cybernetics, PartA, vol. 29, no. 4, pp. 411-416, 1999.
[12] A. Shesh and B. Chen, “Smartpaper: An Interactive and User Friendly Sketching System,” Computer Graphics Forum, vol. 23, no. 3, pp. 301-310, 2004.
[13] M. Clowes, “On Seeing Things,” Artificial Intelligence, vol. 2, pp.79-116, 1971.
[14] D. Huffman, “Impossible Objects as Nonsense Sentences,” Machine Intelligence, vol. 6, pp. 295-323, 1971.
[15] 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.
[16] J. Malik, “Interpreting Line Drawings of Curved Objects,” Int'l J.Computer Vision, vol. 1, pp. 73-103, 1987.
[17] M.C. Cooper, “Interpretation of Line Drawings of Complex Objects,” Image and Vision Computing, vol. 11, no. 2, pp. 82-90, 1993.
[18] M.C. Cooper, “The Interpretation of Line Drawings with Contrast Failure and Shadows,” Int'l J. Computer Vision, vol. 43, no. 2, pp.75-97, 2001.
[19] L.G. Shapiro and G.C. Stockman, Computer Vision. Prentice Hall, 2001.
[20] R. Lequette, “Automatic Construction of Curvilinear Solid from Wireframe Views,” Computer-Aided Design, vol. 20, no. 4, pp. 171-180, 1988.
[21] S. Ablameyko, V. Bereishik, A. Gorelik, and S. Medvedev, “3D Object Reconstruction from Engineering Drawing Projections,” Computing and Control Eng. J., vol. 10, no. 6, pp. 277-284, 1999.
[22] M.H. Kuo, “Reconstruction of Quadric Surface Solid from Three-View Engineering Drawings,” Computer-Aided Design, vol. 30, no. 7, pp. 517-527, 1998.
[23] K. Sugihara, “Mathematical Structures of Line Drawings of Polyhedrons: Toward Man-Machine Communication by Means of Line Drawings,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 4, no. 5, pp. 458-469, 1982.
[24] 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.
[25] W. Whiteley, “A Matroid on Hypergraphs with Applications in Scene Analysis and Geometry,” Discrete and Computational Geometry, vol. 4, pp. 75-95, 1989.
[26] W. Whiteley, “Weavings, Sections and Projections of Spherical Polyhedra,” Discrete and Computational Geometry, vol. 32, pp. 275-294, 1991.
[27] L. Ros and F. Thomas, “Geometric Methods for Shape Recovery from Line Drawings of Polyhedra,” J. Math. Imaging and Vision, vol. 22, no. 1, pp. 5-18, 2005.
[28] L. Ros and F. Thomas, “Overcoming Superstrictness in Line Drawing Interpretation,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 24, no. 4, pp. 456-466, Apr. 2002.
[29] Y. Leclerc and M. 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.
[30] 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.
[31] J. Liu and Y. 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, Oct. 2001.
[32] J. Liu, Y. Lee, and W.-K. Cham, “Identifying Faces in a 2D Line Drawing Representing a Manifold Object,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 24, no. 12, pp. 1579-1593, Dec. 2002.
[33] J. Liu and X. Tang, “Evolutionary Search for Faces from Line Drawings,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 27, no. 6, pp. 861-872, June 2005.
[34] 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.
[35] L. Baird and P. Wang, “3D Object Perception Using Gradient Descent,” Int'l J. Math. Imaging and Vision, vol. 5, pp. 111-117, 1995.
[36] P.A.C. Varley and R.R. Martin, “Estimating Depth from Line Drawings,” Proc. Seventh ACM Symp. Solid Modeling and Applications, pp. 180-191, 2002.
[37] K. Shoji, K. Kato, and F. Toyama, “3-D Interpretation of Single Line Drawings Based on Entropy Minimization Principle,” Proc. IEEE Computer Vision and Pattern Recognition, vol. 2, pp. 90-95, 2001.
[38] K. Sugihara, “An Algebraic Approach to Shape-from-Image Problem,” Artificial Intelligence, vol. 23, pp. 59-95, 1984.
[39] I. Shimshoni and J. Ponce, “Recovering the Shape of Polyhedra Using Line-Drawing Analysis and Complex Reflectance Models,” Computer Vision and Image Processing, vol. 65, no. 2, pp. 296-310, 1997.
[40] H. Shimodaira, “A Shape-from-Shading Method of Polyhedral Objects Using Prior Information,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 28, no. 4, pp. 612-624, Apr. 2006.
[41] P.A.C. Varley and R.R. Martin, “A System for Constructing Boundary Representation Solid Models from a Two-Dimensional Sketch—Topology of Hidden Parts,” Proc. First UK-Korea Workshop Geometric Modeling and Computer Graphics, pp. 129-144, 2000.
[42] S. Palmer, Vision Science: Photons to Phenomenology. The MIT Press, 1999.
[43] K. Koffka, Principles of Gestalt Psychology. Routledge and K. Paul, 1963.
[44] D. West, Introduction to Graph Theory. Prentice Hall, 1996.
[45] M. Berger, Geometrie. CEDIC/Fernand Nathan, 1977.
[46] L. Cao, “3D Object Reconstruction from Line Drawings,” master's thesis, Dept. of Information Eng., Chinese Univ. of Hong Kong, 2005.
[47] M.D. Berg, M.V. Kreveld, M. Overmars, and O. Schwarzkopf, Computational Geometry: Algorithms and Applications. Springer, 2000.
[48] L. Cao, J. Liu, and X. Tang, “3D Object Reconstruction from a Single 2D Line Drawing without Hidden Lines,” Proc. IEEE Int'l Conf. Computer Vision, vol. 1, pp. 272-277, 2005.

Index Terms:
3D reconstruction, hidden topology, line drawings, visual perception
Citation:
Liangliang Cao, Jianzhuang Liu, Xiaoou Tang, "What the Back of the Object Looks Like: 3D Reconstruction from Line Drawings without Hidden Lines," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 30, no. 3, pp. 507-517, March 2008, doi:10.1109/TPAMI.2007.1185
Usage of this product signifies your acceptance of the Terms of Use.