Nonparametric Bayesian Line Detection - Towards Proper Priors for Robotic Computer Vision

Anne C. van Rossum, Hai Xiang Lin, Johan Dubbeldam, H. Jaap van den Herik

2016

Abstract

In computer vision there are many sophisticated methods to perform inference over multiple lines, however they are quite ad-hoc. In this paper a fully Bayesian approach is used to fit multiple lines to a point cloud simultaneously. Our model extends a linear Bayesian regression model to an infinite mixture model and uses a Dirichlet process as a prior for the partition. We perform Gibbs sampling over non-unique parameters as well as over clusters to fit lines of a fixed length, a variety of orientations, and a variable number of data points. The performance is measured using the Rand Index, the Adjusted Rand Index, and two other clustering performance indicators. This paper is mainly meant to demonstrate that general Bayesian methods can be used for line estimation. Bayesian methods, namely, given a model and noise, perform optimal inference over the data. Moreover, rather than only demonstrating the concept as such, the first results are promising with respect to the described clustering performance indicators. Further research is required to extend the method to inference over multiple line segments and multiple volumetric objects that will need to be built on the mathematical foundation that has been laid down in this paper.

References

  1. Antoniak, C. E. (1974). Mixtures of Dirichlet processes with applications to Bayesian nonparametric problems. The annals of statistics, pages 1152-1174.
  2. Bolles, R. C. and Fischler, M. A. (1981). A RANSAC-based approach to model fitting and its application to finding cylinders in range data. In IJCAI, volume 1981, pages 637-643.
  3. Bonci, A., Leo, T., and Longhi, S. (2005). A bayesian approach to the hough transform for line detection. Systems, Man and Cybernetics, Part A: Systems and Humans, IEEE Transactions on, 35(6):945-955.
  4. Box, G. E. and Tiao, G. C. (2011). Bayesian inference in statistical analysis, volume 40. John Wiley & Sons.
  5. Buntine, W. L. (1994). Operations for learning with graphical models. JAIR, 2:159-225.
  6. Chen, H., Meer, P., and Tyler, D. E. (2001). Robust regression for data with multiple structures. In Computer Vision and Pattern Recognition, 2001. CVPR 2001. Proceedings of the 2001 IEEE Computer Society Conference on, volume 1, pages I-1069. IEEE.
  7. Dahyot, R. (2009). Statistical hough transform. Pattern Analysis and Machine Intelligence, IEEE Transactions on, 31(8):1502-1509.
  8. de Finetti, B. (1992). Foresight: Its logical laws, its subjective sources. In Breakthroughs in statistics, pages 134-174. Springer.
  9. Escobar, M. D. and West, M. (1995). Bayesian density estimation and inference using mixtures. Journal of the american statistical association, 90(430):577-588.
  10. Fienberg, S. E. et al. (2006). When did Bayesian inference become “Bayesian”? Bayesian analysis, 1(1):1-40.
  11. Gael, J. V., Teh, Y. W., and Ghahramani, Z. (2009). The infinite factorial hidden markov model. InAdvances in Neural Information Processing Systems, pages 1697- 1704.
  12. Gallo, O., Manduchi, R., and Rafii, A. (2011). CCRANSAC: Fitting planes in the presence of multiple surfaces in range data. Pattern Recognition Letters, 32(3):403-410.
  13. Geman, S. and Geman, D. (1984). Stochastic relaxation, gibbs distributions, and the bayesian restoration of images. Pattern Analysis and Machine Intelligence, IEEE Transactions on, (6):721-741.
  14. Ghahramani, Z. and Griffiths, T. L. (2005). Infinite latent feature models and the indian buffet process. In Advances in neural information processing systems, pages 475-482.
  15. Hough, P. V. (1962). Method and means for recognizing complex patterns. Technical report.
  16. Jain, S. and Neal, R. M. (2004). A split-merge markov chain monte carlo procedure for the dirichlet process mixture model. Journal of Computational and Graphical Statistics, 13(1).
  17. Kwon, S.-W., Bosche, F., Kim, C., Haas, C. T., and Liapi, K. A. (2004). Fitting range data to primitives for rapid local 3D modeling using sparse range point clouds. Automation in Construction, 13(1):67-81.
  18. MacEachern, S. N. and Müller, P. (1998). Estimating mixture of Dirichlet process models. Journal of Computational and Graphical Statistics, 7(2):223-238.
  19. Minka, T. (2000). Bayesian linear regression. Technical report, Citeseer.
  20. Neal, R. M. (2000). Markov chain sampling methods for Dirichlet process mixture models. Journal of computational and graphical statistics, 9(2):249-265.
  21. Rand, W. M. (1971). Objective criteria for the evaluation of clustering methods. Journal of the American Statistical Association, 66(336):846-850.
  22. Rasmussen, C. E. (1999). The infinite gaussian mixture model. In NIPS, volume 12, pages 554-560.
  23. Sudderth, E. B. and Jordan, M. I. (2009). Shared segmentation of natural scenes using dependent Pitman-Yor processes. In Advances in Neural Information Processing Systems, pages 1585-1592.
  24. Vasudevan, S., Gächter, S., Nguyen, V., and Siegwart, R. (2007). Cognitive maps for mobile robots - an object based approach. Robotics and Autonomous Systems, 55(5):359-371.
  25. Zellner, A. (1988). Optimal information processing and Bayes's theorem. The American Statistician, 42(4):278-280.
  26. Zhang, W. and Ksecká, J. (2007). Nonparametric estimation of multiple structures with outliers. In Dynamical Vision, pages 60-74. Springer.
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Paper Citation


in Harvard Style

Rossum A., Lin H., Dubbeldam J. and Herik H. (2016). Nonparametric Bayesian Line Detection - Towards Proper Priors for Robotic Computer Vision . In Proceedings of the 5th International Conference on Pattern Recognition Applications and Methods - Volume 1: ICPRAM, ISBN 978-989-758-173-1, pages 119-127. DOI: 10.5220/0005673301190127


in Bibtex Style

@conference{icpram16,
author={Anne C. van Rossum and Hai Xiang Lin and Johan Dubbeldam and H. Jaap van den Herik},
title={Nonparametric Bayesian Line Detection - Towards Proper Priors for Robotic Computer Vision},
booktitle={Proceedings of the 5th International Conference on Pattern Recognition Applications and Methods - Volume 1: ICPRAM,},
year={2016},
pages={119-127},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0005673301190127},
isbn={978-989-758-173-1},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 5th International Conference on Pattern Recognition Applications and Methods - Volume 1: ICPRAM,
TI - Nonparametric Bayesian Line Detection - Towards Proper Priors for Robotic Computer Vision
SN - 978-989-758-173-1
AU - Rossum A.
AU - Lin H.
AU - Dubbeldam J.
AU - Herik H.
PY - 2016
SP - 119
EP - 127
DO - 10.5220/0005673301190127