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Stroke-Based Surface Reconstruction

Published online by Cambridge University Press:  28 May 2015

Jooyoung Hahn ,
Jie Qiu ,
Eiji Sugisaki ,
Lei Jia ,
Xue-Cheng Tai  and
Hock Soon Seah
Jooyoung Hahn*
Affiliation:
Institute of Mathematics and Scientific Computing, University of Graz, Austria
Jie Qiu*
Affiliation:
School of Computer Engineering, Nanyang Technological University, Singapore
Eiji Sugisaki*
Affiliation:
N-Design Inc., Japan
Lei Jia*
Affiliation:
School of Computer Engineering, Nanyang Technological University, Singapore
Xue-Cheng Tai*
Affiliation:
Mathematics Institute, University of Bergen, Norway
Hock Soon Seah*
Affiliation:
School of Computer Engineering, Nanyang Technological University, Singapore
*
Corresponding author.Email address:JooyoungHahn@gmail.com
Corresponding author.Email address:JQiu@ntu.edu.sg
Corresponding author.Email address:eiji@ndesign.co.jp
Corresponding author.Email address:JIALEI@ntu.edu.sg
Corresponding author.Email address:tai@math.uib.no
Corresponding author.Email address:A@HSSEAH@ntu.edu.sg
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Abstract

In this paper, we present a surface reconstruction via 2D strokes and a vector field on the strokes based on a two-step method. In the first step, from sparse strokes drawn by artists and a given vector field on the strokes, we propose a nonlinear vector interpolation combining total variation (TV) and H 1 regularization with a curl-free constraint for obtaining a dense vector field. In the second step, a height map is obtained by integrating the dense vector field in the first step. Jump discontinuities in surface and discontinuities of surface gradients can be well reconstructed without any surface distortion. We also provide a fast and efficient algorithm for solving the proposed functionals. Since vectors on the strokes are interpreted as a projection of surface gradients onto the plane, different types of strokes are easily devised to generate geometrically crucial structures such as ridge, valley, jump, bump, and dip on the surface. The stroke types help users to create a surface which they intuitively imagine from 2D strokes. We compare our results with conventional methods via many examples.

Keywords

65K1065D1865D17Surface reconstruction from a sparse vector fieldaugmented Lagrangian methodtwo-step methodcurl-free constrainttotal variation regularizationpreservation of discontinuities in surface normal vectors

Information

Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 6 , Issue 1 , February 2013 , pp. 297 - 324
Copyright
Copyright © Global Science Press Limited 2013

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References

[1] Zeleznik, R. C., Herndon, K. P., and Hughes, J. F., “Sketch: an interface for sketching 3d scenes,” in Proceedings of the 23rd annual conference on Computer graphics and interactive techniques, Aug. 1996, pp. 163–170.CrossRefGoogle Scholar
[2] Igarashi, T., Matsuoka, S., and Tanaka, H., “Teddy: a sketching interface for 3d freeform design,” in Proceedings of the 26th annual conference on Computer graphics and interactive techniques (Siggraph 1999), 1999, pp. 409–416.Google Scholar
[3] Karpenko, O. A. and Hughes, J. F., “SmoothSketch: 3D free-form shapes from complex sketches,” in Proceedings of the 33th annual conference on Computer graphics and interactive techniques (Siggraph 2006), 2006, pp. 589–598.Google Scholar
[4] Nealen, A., Igarashi, T., Sorkine, O., and Alexa, M., “FiberMesh: designing freeform surfaces with 3D curves,” ACM Transactions on Graphics (Siggraph 2007), vol. 26, no. 3, p. Article No. 41, July 2007.Google Scholar
[5] Olsen, L., Samavati, F. F., Sousa, M. C., and Jorge, J. A., “Sketch-based modeling: A survey,” Computers & Graphics, vol. 33, no. 1, pp. 88–103, Feb 2009.Google Scholar
[6] Woodham, R. J., “Photometric method for determining surface orientation from multiple images,” Shape from shading, vol. 27, pp. 513–531, 1989.Google Scholar
[7] Hertzmann, A. and Seitz, S. M., “Example-based photometric stereo: Shape reconstruction with general, varying brdfs,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 27, pp. 1254–1264, 2005.Google Scholar
[8] Wu, T.-P. and Tang, C.-K., “Dense photometric stereo by expectation maximization,” Computer Vision - ECCV2006, vol. 3954/2006, pp. 159–172, 2006.Google Scholar
[9] Zhang, R., Tsai, P.-S., Cryer, J. E., and Shah, M., “Shape-from-shading: a survey,” IEEE Transcations on Pattern Analysis and Machine Intelligence, vol. 21, no. 8, pp. 690–706, Aug 1999.Google Scholar
[10] Parados, E. and Faugeras, O., Shape from shading. Springer, 2006.CrossRefGoogle Scholar
[11] Morigi, S. and Rucci, M., “Reconstructing surfaces from sketched 3d irregular curve networks,” in Proceedings of the 8th Eurographics workshop on Sketch-based interfaces and modeling (SBIM), 2011, pp. 39–46.CrossRefGoogle Scholar
[12] C. öztireli, Uyumaz, U., Popa, T., Sheffer, A., and Gross, M., “3d modeling with a symmetric sketch,” in Proceedings of the 8th Eurographics workshop on Sketch-based interfaces and modeling (SBIM), 2011, pp. 23–30.Google Scholar
[13] Gingold, Y., Igarashi, T., and Zorin, D., “Structured annotations for 2d-to-3d modeling,” ACM Transactions on Graphics (Siggraph Asia 2009), vol. 28, no. 5, p. Article No. 148, Dec 2009.Google Scholar
[14] Olsen, L., Samavati, F. F., Sousa, M. C., and Jorge, J. A., “Sketch-based mesh augmentation,” in Proceedings of the 2nd eurographics workshop on sketch-based interfaces and modeling (SBIM), 2005.Google Scholar
[15] Agrawal, A., Raskar, R., and Chellappa, R., “What is the Range of Surface Reconstructions from a Gradient Field?” Computer Vision ĺlC ECCV 2006, pp. 578–591, 2006.Google Scholar
[16] Frankot, R. T., Chellappa, R., and Member, S., “A Method for enforcing integrability in shape from shading algorithms,” IEEE Transactions on Pattern Analysis and Machine Intelligence, pp. 118–128, 1987.Google Scholar
[17] Petrovic, N., Cohen, I., Frey, B. J., Koetter, R., and Huang, T. S., “Enforcing integrability for surface reconstruction algorithms using belief propagation in graphical models,” Computer Vision and Pattern Recognition, IEEE Computer Society Conference on, vol. 1, p. 743, 2001.Google Scholar
[18] Simchony, T., Chellappa, R., and Shao, M., “Direct analytical methods for solving poisson equations in computer vision problems,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 12, pp. 435–446, 1990.CrossRefGoogle Scholar
[19] Zhang, L., Dugas-Phocion, G., and Samson, J.-S., “Single-view modeling of free-form scenes,” The Journal of Visualization and Computer Animation, vol. 13, pp. 225–235, 2002.Google Scholar
[20] Wu, T.-P., Tang, C.-K., Brown, M., and Shum, H.-Y., “Shapepalettes: Interactive normal transfer via sketching,” ACM Transactions on Graphics, vol. 26, no. 307, p. Article No.44, 2007.Google Scholar
[21] Prasad, M. and Fitzgibbon, A., “Single view reconstruction of curved surfaces,” in Proceedings of the 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition - Volume 2, 2006, pp. 1345–1354.Google Scholar
[22] Ng, H.-S., Wu, T.-P., and Tang, C.-K., “Surface-From-Gradients Without Discrete Integrability Enforcement: A Gaussian Kernel Approach,” IEEE Transactions on Pattern Analysis and Machine Intelligence, pp. 2085–2099, 2009.Google Scholar
[23] Tai, X.-C. and Wu, C., “Augmented lagrangian method, dual methods and split bregman iteration for rof model.” in SSVM, ser. Lecture Notes in Computer Science, Tai, X.-C., Ml’łrken, K., Lysaker, M., and Lie, K.-A., Eds., vol. 5567. Springer, 2009, pp. 502–513.Google Scholar
[24] Koenderink, J. J., “Pictorial relief,” Philosophical Transactions: Mathematical, Physical and Engineering Sciences, vol. 256, no. 1740, pp. 1071–1086, May 1998.Google Scholar
[25] Johnston, S. F., “Lumo: illumination for cel animation,” in NPAR ‘02: Proceedings of the 2nd international symposium on Non-photorealistic animation and rendering. New York, NY, USA: ACM, 2002, pp. 45–52.Google Scholar
[26] Terzopoulos, D., “The computation of visible-surface representations,” IEEE Trans. Pattern Anal. Mach. Intell., vol. 10, no. 4, pp. 417–438, 1988.Google Scholar
[27] Rudin, L. I., Osher, S., and Fatemi, E., “Nonlinear total variation based noise removal algorithms,” Physica D, vol. 60, pp. 259–268, 1992.Google Scholar
[28] Wu, C., Zhang, J., and Tai, X.-C., “Augmented lagrangian method for total variation restoration with non-quadratic fidelity,” UCLA CAM Report 09-82, Tech. Rep., 2009.Google Scholar
[29] Cole, F., Golovinskiy, A., Limpaecher, A., Barros, H. S., Finkelstein, A., Funkhouser, T., and Rusinkiewicz, S., “Where do people draw lines?” in Proceedings of the 35th annual conference on Computer graphics and interactive techniques (Siggraph 2008), 2008.Google Scholar
[30] Hahn, J., Wu, C., and Tai, X.-C., “Augmented Lagrangian method for generalized TV-Stokes model,” UCLA CAM Report, Tech. Rep., 2010.Google Scholar
[31] Hahn, J., “Augmented Lagrangian method for generalized TV-Stokes models,” J. Sci. Comput, vol. 50, no. 2, pp. 235–264, 2012.Google Scholar
[32] Chambolle, A., “An algorithm for total variational minimization and applications,” J. Math. Imaging Vis., vol. 20, pp. 89–97, 2004.Google Scholar
[33] Chan, T., Golub, G., and Mulet, P., “A nonlinear primal-dual method for total variation-based image restoration,” SIAM J. Sci. Comput., vol. 20, pp. 1964–1977, 1999.Google Scholar
[34] Goldstein, T. and Osher, S., “The split Bregman method for L1-regularized problems,” SIAM J. Img. Sci., vol. 2, pp. 323–343, 2009.Google Scholar
[35] Steidl, G. and Teuber, T., “Removing multiplicative noise by douglas-rachford splitting methods,” J. Math. Imaging Vision, vol. 36, no. 2, pp. 168–184, 2010.Google Scholar
[36] Winnemoller, H., Orzan, A., Boissieux, L., and Thollot, J., “Texture design and draping in 2d images,” in Eurographics Symposium on Rendering, no. 4, 2009, pp. 1091–1099.Google Scholar
[37] Anjyo, K.-I. and Hiramitsu, K., “Stylized highlights for cartoon rendering and animation,” IEEE Computer Graphics and Applications, vol. 23, no. 4, pp. 54–61, 2003.Google Scholar
[38] Anjyo, K.-I., Wemler, S., and Baxter, W., “Tweakable light and shade for cartoon animation,” in Proceedings of NPAR 2006, 2006, pp. 133–139.Google Scholar
[39] Todo, H., Anjyo, K.-I., Baxter, W., and Igarashi, T., “Locally controllable stylized shading,” ACM Transactions on Graphics (Siggraph 2007), vol. 26, no. 3, p. Article No. 17, August 2007.Google Scholar
[40] Tao, J., “Fixing geometric errors on polygonal models: A survey,” Journal of Computer Science and Technology, vol. 24, pp. 19–29, 2009.Google Scholar