Fundamentals of Nonparametric Bayesian Line Detection

Line detection is a fundamental problem in the world of computer vision. Many sophisticated methods have been proposed for performing inference over multiple lines; however, they are quite ad-hoc. Our fully Bayesian model extends a linear Bayesian regression model to an infinite mixture model and uses a Dirichlet Process as a prior. Gibbs sampling over non-unique parameters as well as over clusters is performed to fit lines of a fixed length, a variety of orientations, and a variable number of data points. Bayesian inference over data is optimal given a model and noise definition. Initial computer experiments show promising results with respect to clustering performance indicators such as the Rand Index, the Adjusted Rand Index, the Mirvin metric, and the Hubert metric. In future work, this mathematical foundation can be used to extend the algorithms to inference over multiple line segments and multiple volumetric objects.