ADAPTIVE QUADRATURE FILTERS AND THE RECOVERY OF PHASE FROM FRINGE PATTERN IMAGES

A principled approach, based on Bayesian estimation theory and complex -valued Markov random-field prior models, is introduced for the design of a new class of adaptive quadrature filters. These filters are capa ble of adapting their tuning frequency to the local dominant spatial f requency of the input image while maintaining an arbitrarily narrow lo cal frequency response; therefore they may be effectively used for the accurate recovery of the phase of broadband spatial-carrier fringe pa tterns, even when they are corrupted by a significant amount of noise. Also, by constraining the spatial variation of the adaptive frequency to be smooth, they permit the completely automatic recovery of local phase from single closed fringe pattern images, since the spurious dis continuities and sign reversals that one obtains from the classical Fo urier-based methods are avoided in this case. Although the application s discussed here come from fringe pattern analysis in optics, these fi lters may also be useful in the solution of other problems, such as te xture characterization and segmentation and the recovery of depth from stereoscopic pairs of images. (C) 1997 Optical Society of America.