Curve and surface reconstruction by using sequential Markov random fields (MRFs)

The statistical approach using the coupled Markov random field (MRF) and the maximum a posteriori (MAP) estimate has been proposed in order to satisfy both the preservation of local discontinuities and the smoothing of continuous regions for reconstruction of derivative feature measurements and range data. However, this data reconstruction method has some very difficult problems that it is hard to obtain proper results by finding the global optimal solution correctly. Especially, if the ordinary iteration solutions are used for the noisy and rugged data, is it likely that the convergence happens to be at a local optimal solution depending upon the initial value, and the noise smoothing is insufficient or the edge parts are overslurred. To cope with the difficulties, we propose a recovery method that regards the MAP estimation itself as the basic process and do the computation iteratively while controlling smoothing by changing values of the MRF parameters according to some scheduling. The presented algorithm reduces failures because of the local optimization, and is respected to give better results of reconstruction. The applicability of the method has been verified by several reconstruction experiments.