Identifying Faces in a 2D Line Drawing Representing a Manifold Object

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]  Jr. Daniel Bohdan Lysak.  Interpretation of engineering drawings of polyhedral and non-polyhedral objects from orthographic projections , 1991 .

[2]  Gary Chartrand,et al.  Applied and algorithmic graph theory , 1992 .

[3]  Martin C. Cooper.  The Interpretation of Line Drawings with Contrast Failure and Shadows , 2001, International Journal of Computer Vision.

[4]  Pat Hanrahan,et al.  Creating volume models from edge-vertex graphs , 1982, SIGGRAPH.

[5]  Narsingh Deo,et al.  On Algorithms for Enumerating All Circuits of a Graph , 1976, SIAM J. Comput..

[6]  Réi Lequette,et al.  Automatic construction of curvilinear solids from wireframe views , 1988 .

[7]  David L. Waltz,et al.  Understanding Line drawings of Scenes with Shadows , 1975 .

[8]  M. H. Kuo.  Reconstruction of quadric surface solids from three-view engineering drawings , 1998, Comput. Aided Des..

[9]  Jitendra Malik,et al.  Interpreting line drawings of curved objects , 1986, International Journal of Computer Vision.

[10]  George Markowsky,et al.  Fleshing Out Wire Frames , 1980, IBM J. Res. Dev..

[11]  John A. Brewer,et al.  Automated conversion of curvilinear wire-frame models to surface boundary models; a topological approach , 1986, SIGGRAPH.

[12]  Thomas Marill,et al.  Emulating the human interpretation of line-drawings as three-dimensional objects , 1991, International Journal of Computer Vision.

[13]  Kokichi Sugihara,et al.  A Necessary and Sufficient Condition for a Picture to Represent a Polyhedral Scene , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[14]  Ronald D. Dutton,et al.  Efficiently identifying the faces of a solid , 1983, Comput. Graph..

[15]  R M Haralick,et al.  The consistent labeling problem: part I. , 1979, IEEE transactions on pattern analysis and machine intelligence.

[16]  Jean Ponce,et al.  Recovering the Shape of Polyhedra Using Line-Drawing Analysis and Complex Reflectance Models , 1997, Comput. Vis. Image Underst..

[17]  Jitendra Malik,et al.  Modeling and Rendering Architecture from Photographs: A hybrid geometry- and image-based approach , 1996, SIGGRAPH.

[18]  Hod Lipson,et al.  Identification of Faces in a 2D Line Drawing Projection of a Wireframe Object , 1996, IEEE Trans. Pattern Anal. Mach. Intell..

[19]  Martin C. Cooper.  Interpretation of line drawings of complex objects , 1993, Image Vis. Comput..

[20]  E. Reingold,et al.  Combinatorial Algorithms: Theory and Practice , 1977 .

[21]  Alasdair Turner,et al.  Sketching space , 2000, Comput. Graph..

[22]  S. Sutherland.  Seeing things , 1989, Nature.

[23]  Robert Sedgewick,et al.  Algorithms in C , 1990 .

[24]  Mark A. Ganter,et al.  FROM WIRE-FRAME TO SOLID-GEOMETRIC , 1983 .

[25]  Donald E. LaCourse.  Handbook of solid modeling , 1995 .

[26]  Warren N. Waggenspack,et al.  Decomposition method for extracting face topologies from wireframe models , 1992, Comput. Aided Des..

[27]  Martin A. Fischler,et al.  An optimization-based approach to the interpretation of single line drawings as 3D wire frames , 1992, International Journal of Computer Vision.

[28]  Warren N. Waggenspack,et al.  A shortest path approach to wireframe to solid model conversion , 1995, Symposium on Solid Modeling and Applications.

[29]  Carsten Thomassen,et al.  The Graph Genus Problem is NP-Complete , 1989, J. Algorithms.

[30]  Kokichi Sugihara,et al.  An Algebraic Approach to Shape-from-Image Problems**This work is supported in part by the Grant in Aid for Scientific Research of the Ministry of Education, Science and Culture of Japan (Grant No. 57780035). , 1987 .

[31]  Martti Mäntylä,et al.  Introduction to Solid Modeling , 1988 .

[32]  Sergey Ablameyko,et al.  3D object reconstruction from engineering drawing projections , 1999 .

[33]  Jianzhuang Liu,et al.  A Graph-Based Method for Face Identification from a Single 2D Line Drawing , 2001, IEEE Trans. Pattern Anal. Mach. Intell..