Discrete Optimal View Path Planning

Sebastian Haner, Anders Heyden

Abstract

This paper presents a discrete model of a sensor path planning problem, with a long-term planning horizon. The goal is to minimize the covariance of the reconstructed structures while meeting constraints on the length of the traversed path of the sensor. The sensor is restricted to move on a graph representing a discrete set of configurations, and additional constraints can be incorporated by altering the graph connectivity. This combinatorial problem is formulated as an integer semi-definite program, the relaxation of which provides both a lower bound on the objective cost and input to a proposed genetic algorithm for solving the original problem. An evaluation on synthetic data indicates good performance.

References

  1. Blaer, P. and Allen, P. (2007). Data acquisition and view planning for 3-d modeling tasks. In Intelligent Robots and Systems, 2007. IROS 2007. IEEE/RSJ International Conference on, pages 417-422.
  2. Boyd, S. and Vandenberghe, L. (2004). Convex Optimization. Cambridge University Press, New York, NY, USA.
  3. Choi, I.-C., Kim, S.-I., and Kim, H.-S. (2003). A genetic algorithm with a mixed region search for the asymmetric traveling salesman problem. Computers & Operations Research, 30(5):773 - 786.
  4. Dahl, J. (2012). Semidefinite optimization using MOSEK. In 21st International Symposium on Mathematical Programming.
  5. Davoodi, M., Panahi, F., Mohades, A., and Hashemi, S. N. (2013). Multi-objective path planning in discrete space. Applied Soft Computing, 13(1):709 - 720.
  6. Dunn, E., Olague, G., and Lutton, E. (2006). Parisian camera placement for vision metrology. Pattern Recognition Letters, 27(11):1209-1219.
  7. Dunn, E., van den Berg, J., and Frahm, J.-M. (2009). Developing visual sensing strategies through next best view planning. In Intelligent Robots and Systems, 2009. IROS 2009. IEEE/RSJ International Conference on, pages 4001-4008.
  8. Englot, B. and Hover, F. (2010). Inspection planning for sensor coverage of 3d marine structures. In IROS, pages 4412-4417. IEEE.
  9. Foix, S., Kriegel, S., Fuchs, S., Aleny, G., and Torras, C. (2012). Information-gain view planning for free-form object reconstruction with a 3d tof camera. In Advanced Concepts for Intelligent Vision Systems, volume 7517 of Lecture Notes in Computer Science, pages 36-47. Springer Berlin Heidelberg.
  10. Fraser, C. S. (1984). Network Design Considerations for Non-Topographic Photogrammetry. Photo Eng. and Remote Sensing, 50(8):1115-1126.
  11. Golovin, D. and Krause, A. (2010). Adaptive submodularity: A new approach to active learning and stochastic optimization. In 23rd Annual Conference on Learning Theory, pages 333-345.
  12. Haner, S. and Heyden, A. (2011). Optimal view path planning for visual SLAM. In Heyden, A. and Kahl, F., editors, Image Analysis, volume 6688 of Lecture Notes in Computer Science, pages 370-380. Springer Berlin / Heidelberg.
  13. Hollinger, G. A., Englot, B., Hover, F., Mitra, U., and Sukhatme, G. S. (2012). Uncertainty-driven view planning for underwater inspection. In ICRA, pages 4884-4891. IEEE.
  14. Lawler, G. (2012). Intersections of Random Walks. Modern Birkhäuser Classics. Springer-Verlag New York.
  15. L öfberg, J. (2004). Yalmip : A toolbox for modeling and optimization in MATLAB. In Proceedings of the CACSD Conference, Taipei, Taiwan.
  16. Low, K.-L. and Lastra, A. (2006). An adaptive hierarchical next-best-view algorithm for 3d reconstruction of indoor scenes. 14th Pacific Conference on Computer Graphics and Applications, Taipei, Taiwan.
  17. Montgomery, D. C. (2000). Design and Analysis of Experiments. John Wiley & Sons Canada, Ltd., 5th edition.
  18. Papadimitriou, C. H. and Steiglitz, K. (1998). Combinatorial Optimization: Algorithms and Complexity. Dover Publications.
  19. Schmitt, L. J. and Amini, M. M. (1998). Performance characteristics of alternative genetic algorithmic approaches to the traveling salesman problem using path representation: An empirical study. European Journal of Operational Research, 108(3):551 - 570.
  20. Schrijver, A. (2004). Combinatorial Optimization : Polyhedra and Efficiency (Algorithms and Combinatorics). Springer.
  21. Singh, A., Krause, A., Guestrin, C., and Kaiser, W. J. (2009). Efficient informative sensing using multiple robots. J. Artif. Intell. Res. (JAIR), 34:707-755.
  22. Trummer, M., Munkelt, C., and Denzler, J. (2010). Online Next-Best-View Planning for Accuracy Optimization Using an Extended E-Criterion. In Proc. International Conference on Pattern Recognition (ICPR'10), volume 0, pages 1642-1645. IEEE Computer Society.
  23. Vasquez-Gomez, J. I., Sucar, L. E., and Murrieta-Cid, R. (2013). Hierarchical ray tracing for fast volumetric next-best-view planning. 2013 International Conference on Computer and Robot Vision, 0:181-187.
  24. Wenhardt, S., Deutsch, B., Hornegger, J., Niemann, H., and Denzler, J. (2006). An Information Theoretic Approach for Next Best View Planning in 3-D Reconstruction. In Proc. International Conference on Pattern Recognition (ICPR'06), volume 1, pages 103- 106. IEEE Computer Society.
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Paper Citation


in Harvard Style

Haner S. and Heyden A. (2015). Discrete Optimal View Path Planning . 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 411-419. DOI: 10.5220/0005252104110419


in Bibtex Style

@conference{visapp15,
author={Sebastian Haner and Anders Heyden},
title={Discrete Optimal View Path Planning},
booktitle={Proceedings of the 10th International Conference on Computer Vision Theory and Applications - Volume 3: VISAPP, (VISIGRAPP 2015)},
year={2015},
pages={411-419},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0005252104110419},
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 - Discrete Optimal View Path Planning
SN - 978-989-758-091-8
AU - Haner S.
AU - Heyden A.
PY - 2015
SP - 411
EP - 419
DO - 10.5220/0005252104110419