Bayesian estimation of edge orientations in junctions

Abstract Junctions, defined as those points of an image where two or more edges meet, play a significant role in many computer vision applications. Junction detection is a widely treated problem, and some detectors can provide even the directions of the edges that meet in a junction. The main objective of this paper is the precise estimation of such directions. It is supposed that the junction point has been previously found by some detector. Also, it is assumed that samples, possibly noisy, of orientations of the edges found in a circular window surrounding the point are available. A mixture of von Mises distributions is assumed for these data, and then a Bayesian methodology is applied to estimate its parameters, some of which are precisely the searched edge orientations. The Bayesian methodology requires the calculation of the mean value of expectation of a posterior distribution which is too complicated to be analytically solved; consequently, a Markov Chain Monte Carlo Method is used for this purpose. Tests have been performed on both a synthetic and a real image. They show that the procedure converges to the expected value for the orientations, and moreover, can provide reliable confidence intervals for these quantities. Since computational cost is high, this method should be used when precision is preferred to speed.