Bayesian estimation of edge orientations in junctions

Junctions, defined as those points of an image where two or more edges meet , play a significant role in many computer vision applications. Junction de tection is a widely treated problem, and some detectors can provide even th e directions of the edges that meet in a junction. The main objective of th is 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 Mi ses distributions is assumed for these data, and then a Bayesian methodolog y is applied to estimate its parameters, some of which are precisely the se arched 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 C arlo Method is used for this purpose. Tests have been performed on both a s ynthetic and a real image. They show that the procedure converges to the ex pected value for the orientations, and moreover, can provide reliable confi dence intervals for these quantities. Since computational cost is high, thi s method should be used when precision is preferred to speed. (C) 1999 Else vier Science B.V. All rights reserved.