Robust quadrature filters

We deal with the relation between two well-known topics in signal processing and computational vision: quadrature filters (QF’s) and Bayesian estimation with Markov random fields (MRF’s) as prior models. We present a new class of complex-valued MRF models such that the optimal estimators obtained with them correspond to the output of QF’s tuned at particular frequencies. It is shown that the machinery that has proven to be effective in classical (real-valued) MRF modeling may be generalized to the complex case in a straightforward way. To illustrate the power of this technique, we present complex MRF models that implement robust QF’s that exhibit good performance in situations in which ordinary linear, shift-invariant filters fail. These include robust filters that are relatively insensitive to edge effects and missing data and that can reliably estimate the local phase in singularity neighborhoods; we also present models for the specification of piecewise-smooth QF’s. Examples of applications to fringe pattern analysis, phase-based stereo reconstruction, and texture segmentation are presented as well.