# A FAST ALGORITHM FOR N D POLYHEDRAL SCENE PERCEPTION FROM A SINGLE 2D LINE DRAWING

### Hongbo Li, Lei Huang

#### Abstract

In this paper, we study the problem of reconstructing the polyhedral structures of a general nD polyhedral scene from its single 2D line drawing. With the idea of local construction and propagation, we propose a number of powerful techniques for general face identification. Our reconstruction algorithm, called “nDView”, is tested by all the 3D examples we found in the literature, plus a number of 4D and 5D examples we devised. Our algorithm does not prerequire the dimension n of the object nor the dimension m of its surrounding space be given, and allows the object to be a non-manifold in which neighboring faces can be coplanar. Another striking feature is its efficiency: our algorithm can handle 3D solids of over 10,000 faces, with a speed 100 times as fast as the fastest existing algorithms on 2D polyhedral manifold reconstruction.

#### References

- Agarwel, S. and Waggenspack, C. (1992). Decomposition method for extracting face topologies from wireframe models. In Computer Aided Design. 24(3): 123-140.
- Courter, S. and Brewer, J. (1986). Automated conversion of curvilinear wireframe models to surface boundary models. In Comput. Graph. 20(4): 171-178.
- Ganter, M. and Uicker, J. (1983). From wireframe to solid geometric: Automated conversion of data representations. In Computer in Mechanical Eng. 2(2): 40-45.
- Hanrahan, P. (1982). Creating volume models from edgevertex graphs. In Computer Graphics. 16(3): 77-84.
- Liu, J. and Lee, Y. (2001). A graph-based method for face identification from a single 2d line drawing. In IEEE Trans. on PAMI. 23(10): 1106-1119.
- Liu, J., Lee, Y., and Cham, C. (2002). Identifying faces in a 2d line drawing representing a manifold object. In IEEE Trans. on PAMI. 24(12): 1579-1593.
- Marill, T. (1991). Emulation the human interpretation of line drawings as 3d objects. In International J. of Computer Vision. 6(2): 147-161.
- Miyazaki, K. (1983). An Adventure in Multidimensional Space: The Art and Geometry of Polygons, Polyhedra, and Polytopes. Wileyinterscience Publ.
- Shpitalni, M. and Lipson, H. (1996). Identification of faces in a 2d line drawing projection of a wireframe object. In IEEE Trans. on PAMI. 18(10): 1000-1012.

#### Paper Citation

#### in Harvard Style

Li H. and Huang L. (2006). **A FAST ALGORITHM FOR N D POLYHEDRAL SCENE PERCEPTION FROM A SINGLE 2D LINE DRAWING** . In *Proceedings of the First International Conference on Computer Vision Theory and Applications - Volume 2: VISAPP,* ISBN 972-8865-40-6, pages 69-76. DOI: 10.5220/0001363100690076

#### in Bibtex Style

@conference{visapp06,

author={Hongbo Li and Lei Huang},

title={A FAST ALGORITHM FOR N D POLYHEDRAL SCENE PERCEPTION FROM A SINGLE 2D LINE DRAWING},

booktitle={Proceedings of the First International Conference on Computer Vision Theory and Applications - Volume 2: VISAPP,},

year={2006},

pages={69-76},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0001363100690076},

isbn={972-8865-40-6},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the First International Conference on Computer Vision Theory and Applications - Volume 2: VISAPP,

TI - A FAST ALGORITHM FOR N D POLYHEDRAL SCENE PERCEPTION FROM A SINGLE 2D LINE DRAWING

SN - 972-8865-40-6

AU - Li H.

AU - Huang L.

PY - 2006

SP - 69

EP - 76

DO - 10.5220/0001363100690076