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Sketching of Mirror-Symmetric Shapes
November 2011 (vol. 17 no. 11)
pp. 1650-1662
Frederic Cordier, University of Haute Alsace, Mulhouse
Hyewon Seo, University of Strasbourg, Illkirch
Jinho Park, Namseoul University, Chungnam
Junyong Noh, KAIST, DKAIST GSCT, Daejeon
This paper presents a system to create mirror-symmetric surfaces from free-form sketches. The system takes as input a hand-drawn sketch and generates a surface whose silhouette approximately matches the input sketch. The input sketch typically consists of a set of curves connected at their endpoints, forming T-junctions and cusps. Our system is able to identify the skewed-mirror and translational symmetry between the hand-drawn curves and uses this information to reconstruct the occluded parts of the surface and its 3D shape.

[1] E. Brown and P. Wang, “3D Object Recovery from 2D Images: A New Approach,” Proc. SPIE Robotics and Computer Vision, vol. 2904, pp. 138-145, 1996.
[2] S.-U. Cheon and S. Han, “A Template-Based Reconstruction of Plane-Symmetric 3D Models from Freehand Sketches,” Computer-Aided Design, vol. 40, no. 9, pp. 975-986, 2008.
[3] J. Cohen, L. Markosian, R. Zeleznik, J. Hughes, and R. Barzel, “An Interface for Sketching 3D Curves,” Proc. 1999 Symp. Interactive 3D Graphics (I3D '99), pp. 17-21, 1999.
[4] F. Cordier and H. Seo, “Free-Form Sketching of Self-Occluding Objects,” IEEE Computer Graphics and Applications, vol. 27, no. 1, pp. 50-59, Jan./Feb. 2007.
[5] A. Francois, G. Medioni, and R. Waupotitsch, “Reconstructing Mirror Symmetric Scenes from a Single View Using 2-View Stereo Geometry,” Proc. Int'l Conf. Pattern Recognition (ICPR), 2002.
[6] Y. Gingold, T. Igarashi, and D. Zorin, “Structured Annotations for 2D-to-3D Modeling,” Proc. ACM SIGGRAPH Asia '09 Papers, Dec. 2009.
[7] D.A. Huffman, “Impossible Objects as Nonsense Sentences,” Machine Intelligence 6, B. Meltzer and D. Michie, eds., Am. Elsevier Publishing Co., 1971.
[8] T. Igarashi, S. Matsuoka, and H. Tanaka, “Teddy: A Sketching Interface for 3D Freeform Design,” Proc. SIGGRAPH '99 Conf., pp. 409-416, 1999.
[9] N. Jiang, P. Tan, and L.-F. Cheong, “Symmetric Architecture Modeling with a Single Image,” Proc. ACM SIGGRAPH Asia '09 Papers, 2009.
[10] T. Kanade, “Recovery of the Three-Dimensional Shape of an Object from a Single View,” Artificial Intelligence, vol. 17, pp. 409-460, 1981.
[11] O. Karpenko and J. Hughes, “SmoothSketch: 3D Free-Form Shapes from Complex Sketches,” ACM Trans. Graphics, vol. 25, no. 3, pp. 589-598, 2006.
[12] B. Kerautret, X. Granier, and A. Braquelaire, “Intuitive Shape Modeling by Shading Design,” Proc. Int'l Symp. Smart Graphics, pp. 163-174, 2005.
[13] Y. Kho and M. Garland, “Sketching Mesh Deformations,” Proc. Symp. Interactive 3D Graphics and Games (I3D), pp. 147-154, 2005.
[14] 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.
[15] Y. Li, Z. Pizlo, and R.M. Steinman, “A Computational Model that Recovers the 3D Shape of an Object from a Single 2D Retinal Representation,” Vision Research, vol. 49, no. 9, pp. 979-991, May 2009.
[16] J. Liu, L. Cao, Z. Li, and X. Tang, “Plane-Based Optimization for 3D Object Reconstruction from Single Line Drawings,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 30, no. 2, pp. 315-327, Feb. 2008.
[17] 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.
[18] 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.
[19] A. Nealen, O. Sorkine, M. Alexa, and D. Cohen-Or, “A Sketch-Based Interface for Detail-Preserving Mesh Editing,” ACM Trans. Graphics, vol. 24, no. 3, pp. 1142-1147, 2005.
[20] A. Nealen, T. Igarashi, O. Sorkine, and M. Alexa, “FiberMesh: Designing Freeform Surfaces with 3D Curves,” Proc. ACM SIGGRAPH '07 Papers, 2007.
[21] S. Posch, “Detecting Skewed Symmetries,” Proc. Int'l Conf. Pattern Recognition, pp. 602-606, Aug. 1992.
[22] R. Schmidt, A. Khan, K. Singh, and G. Kurtenbach, “Analytic Drawing of 3D Scaffolds,” ACM Trans. Graphics, vol. 28, no. 5, 2009.
[23] O. Tolba, J. Dorsey, and L. McMillan, “A Projective Drawing System,” Proc. I3D Symp. Interactive 3D Graphics, 2001.
[24] L.R. Williams, “Topological Reconstruction of a Smooth Manifold-Solid from Its Occluding Contour,” Int'l J. Computer Vision, vol. 23, no. 1, pp. 93-108, 1997.
[25] L.R. Williams, “Perceptual Completion of Occluded Surfaces,” PhD dissertation, Dept. of Computer Science, Univ. of Massachusetts, 1994.
[26] R.C. Zeleznik, K.P. Herndon, and J.F. Hughes, “SKETCH: An Interface for Sketching 3D Scenes,” Proc. ACM SIGGRAPH, vol. 96, pp. 163-170, 1996.

Index Terms:
Sketching interface, 3D modeling, and mirror-symmetric shape.
Frederic Cordier, Hyewon Seo, Jinho Park, Junyong Noh, "Sketching of Mirror-Symmetric Shapes," IEEE Transactions on Visualization and Computer Graphics, vol. 17, no. 11, pp. 1650-1662, Nov. 2011, doi:10.1109/TVCG.2010.258
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