ROBUST QUADRATURE FILTERS

We deal with the relation between two well-known topics in signal proc essing and computational vision: quadrature filters (QF's) and Bayesia n estimation with Markov random fields (MRF's) as prior models. We pre sent a new class of complex-valued MRF models such that the optimal es timators 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 genera lized 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 ordin ary 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 neighborhood s; we also present models for the specification of piecewise-smooth QF 's. Examples of applications to fringe pattern analysis, phase-based s tereo reconstruction, and texture segmentation are presented as well. (C) 1997 Optical Society of America.