# 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

#### 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.

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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