A Convex Framework for High Resolution 3D Reconstruction

Min Li, Changyu Diao, Song Lv, Dongming Lu

Abstract

We present a convex framework to acquire high resolution surfaces. It is typical to couple a structure-light setup and a photometric method to reconstruct a high resolution 3D surface. Previous methods often get stuck in a local minima for the appearance of occasional outliers. To address this issue, we develop a convex variational model by incorporating a total variation (TV) regularization term with a data term to generate the surface. Through relaxing the model to an equivalent high dimensional variational problem, we obtain a global minimizer of the proposed problem. Results on both synthetic and real-world data show an excellent performance by utilizing our convex variational model.

References

  1. Agrawal, A., Raskar, R., and Chellappa, R. (2006). What is the range of surface reconstructions from a gradient field? In ECCV, pages 578-591. Springer.
  2. Aliaga, D. G. and Xu, Y. (2010). A self-calibrating method for photogeometric acquisition of 3d objects. IEEE Transactions. Pattern Analysis and Machine Intelligence, 32(4):747-754.
  3. Banerjee, S., Sastry, P., and Venkatesh, Y. (1992). Surface reconstruction from disparate shading: An integration of shape-from-shading and stereopsis. IAPR, 1:141- 144.
  4. Bernardini, F., Rushmeier, H., Martin, I. M., Mittleman, J., and Taubin, G. (2002). Building a digital model of michelangelo's florentine pieta. IEEE Transactions. Computer Graphics and Applications, 22(1):59-67.
  5. Birkbeck, N., Cobzas, D., Sturm, P., and Jagersand, M. (2006). Variational shape and reflectance estimation under changing light and viewpoints. In ECCV, pages 536-549. Springer.
  6. Herbort, S. and Wöhler, C. (2011). An introduction to image-based 3d surface reconstruction and a survey of photometric stereo methods. 3D Research, 2(3):1-17.
  7. Hernández, C., Vogiatzis, G., and Cipolla, R. (2008). Multiview photometric stereo. IEEE Transactions. Pattern Analysis and Machine Intelligence, 30(3):548-554.
  8. Higo, T., Matsushita, Y., Joshi, N., and Ikeuchi, K. (2009). A hand-held photometric stereo camera for 3-d modeling. In ICCV, pages 1234-1241. IEEE.
  9. Horn, B. K. (1990). Height and gradient from shading. International Journal of Computer Vision, 5(1):37-75.
  10. Horn, B. K. and Brooks, M. J. (1989). Shape from shading. MIT press.
  11. Hornung, A. and Kobbelt, L. (2006). Hierarchical volumetric multi-view stereo reconstruction of manifold surfaces based on dual graph embedding. In CVPR, volume 1, pages 503-510. IEEE.
  12. Ishikawa, H. (2003). Exact optimization for markov random fields with convex priors. IEEE Transactions. Pattern Analysis and Machine Intelligence, 25(10):1333- 1336.
  13. Kolev, K., Pock, T., and Cremers, D. (2010). Anisotropic minimal surfaces integrating photoconsistency and normal information for multiview stereo. In ECCV, pages 538-551. Springer.
  14. Ladikos, A., Benhimane, S., and Navab, N. (2008). Multiview reconstruction using narrow-band graph-cuts and surface normal optimization. In BMVC, pages 1- 10.
  15. Lange, H. (1999). Advances in the cooperation of shape from shading and stereo vision. In Second International Conference on 3-D Digital Imaging and Modeling, pages 46-58. IEEE.
  16. Lu, Z., Tai, Y.-W., Ben-Ezra, M., and Brown, M. S. (2010). A framework for ultra high resolution 3d imaging. In CVPR, pages 1205-1212. IEEE.
  17. Nehab, D., Rusinkiewicz, S., Davis, J., and Ramamoorthi, R. (2005). Efficiently combining positions and normals for precise 3d geometry. ACM Transactions. Graphics, 24(3):536-543.
  18. Pock, T., Schoenemann, T., Graber, G., Bischof, H., and Cremers, D. (2008). A convex formulation of continuous multi-label problems. In ECCV, pages 792-805. Springer.
  19. Salvi, J., Fernandez, S., Pribanic, T., and Llado, X. (2010). A state of the art in structured light patterns for surface profilometry. Pattern recognition, 43(8):2666-2680.
  20. Scharstein, D. and Szeliski, R. (2002). A taxonomy and evaluation of dense two-frame stereo correspondence algorithms. International Journal of Computer Vision, 47(1-3):7-42.
  21. Seitz, S. M., Curless, B., Diebel, J., Scharstein, D., and Szeliski, R. (2006). A comparison and evaluation of multi-view stereo reconstruction algorithms. In CVPR, volume 1, pages 519-528. IEEE.
  22. Sinha, S. N. and Pollefeys, M. (2005). Multi-view reconstruction using photo-consistency and exact silhouette constraints: A maximum-flow formulation. In ICCV, volume 1, pages 349-356. IEEE.
  23. Vogiatzis, G., Hernández, C., Torr, P. H., and Cipolla, R. (2007). Multiview stereo via volumetric graph-cuts and occlusion robust photo-consistency. IEEE Transactions. Pattern Analysis and Machine Intelligence, 29(12):2241-2246.
  24. Woodham, R. J. (1980). Photometric method for determining surface orientation from multiple images. Optical engineering, 19(1):191139-191139.
  25. Wu, C., Liu, Y., Dai, Q., and Wilburn, B. (2011). Fusing multiview and photometric stereo for 3d reconstruction under uncalibrated illumination. IEEE Transactions. Visualization and Computer Graphics, 17(8):1082-1095.
  26. Yu, T., Ahuja, N., and Chen, W.-C. (2006). Sdg cut: 3d reconstruction of non-lambertian objects using graph cuts on surface distance grid. In CVPR, volume 2, pages 2269-2276. IEEE.
  27. Yuan, J., Bae, E., and Tai, X.-C. (2010). A study on continuous max-flow and min-cut approaches. In CVPR, pages 2217-2224. IEEE.
Download


Paper Citation


in Harvard Style

Li M., Diao C., Lv S. and Lu D. (2015). A Convex Framework for High Resolution 3D Reconstruction . In Proceedings of the 10th International Conference on Computer Vision Theory and Applications - Volume 3: VISAPP, (VISIGRAPP 2015) ISBN 978-989-758-091-8, pages 317-324. DOI: 10.5220/0005306503170324


in Bibtex Style

@conference{visapp15,
author={Min Li and Changyu Diao and Song Lv and Dongming Lu},
title={A Convex Framework for High Resolution 3D Reconstruction},
booktitle={Proceedings of the 10th International Conference on Computer Vision Theory and Applications - Volume 3: VISAPP, (VISIGRAPP 2015)},
year={2015},
pages={317-324},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0005306503170324},
isbn={978-989-758-091-8},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 10th International Conference on Computer Vision Theory and Applications - Volume 3: VISAPP, (VISIGRAPP 2015)
TI - A Convex Framework for High Resolution 3D Reconstruction
SN - 978-989-758-091-8
AU - Li M.
AU - Diao C.
AU - Lv S.
AU - Lu D.
PY - 2015
SP - 317
EP - 324
DO - 10.5220/0005306503170324