Boundary detection in noisy vector fields

In this paper we propose a novel method for boundary detection of vector fields. The derivation is based on the assumption that the observed vector fields are realizations of a spatially quasi-stationary process and that the vector observations at each pixel site are generated by a parametric probability distribution function. The form of the function is known but its parameters are not. To detect and estimate the locations of the boundaries, we use Bayesian theory and adopt the maximum a posteriori probability (MAP) criterion. It is shown that the criterion is a penalized maximum likelihood, which is composed of two terms. One is a data term that monotonically decreases as the number of hypothesized boundaries increases. The other term is a penalty that penalizes for the complexity of the model used to describe the data. The MAP solution is the one that minimizes the criterion. Simulation results are provided that show the performance of the proposed method. The results on synthesized magnetic resonance (MR) images demonstrate that this technique yields highly accurate estimates of the number of boundaries and their locations even for low contrast-to-noise ratios.