Nonparametric Bayesian Line Detection

Towards Proper Priors for Robotic Computer Vision

Conference paper (2016)

Authors

Anne C. van Rossum Almende BV, Universiteit Leiden, Distributed Organisms B.V.
H.X. Lin Universiteit Leiden, Mathematical Physics - EEMCS
J.L.A. Dubbeldam Mathematical Physics - EEMCS
Jaap Van Den Herik Universiteit Leiden
Research Group
Mathematical Physics (EEMCS) (TU Delft)
More Info
expand_more

Published Date

2016

Language

English

Reuse Rights

Other than for strictly personal use, it is not permitted to download, forward or distribute the text or part of it, without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license such as Creative Commons.

Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Mathematical Physics

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.