We describe a method for inferring vascular (tree-like) structures from 2D and 3D imagery. A Bayesian formulation is used to make effective use of prior knowledge of likely tree structures with the observed being modelled locally with intensity profiles as being Gaussian. The local feature models are estimated by combination of a multiresolution, windowed Fourier approach followed by an iterative, minimum meansquare estimation, which is both computationally efficient and robust. A Markov Chain Monte Carlo (MCMC) algorithm is employed to produce approximate samples from the posterior distribution given the feature model estimates. We present results of the multiresolution parameter estimation on representative 2D and 3D data, and show preliminary results of our implementation of the MCMC algorithm 1.