Incorporation of derivative priors in adaptive Bayesian color image segmentation

In this study, we attempt to incorporate derivative measures into the scheme of adaptive Bayesian color image segmentation, and provide a unified perspective of region-based and edge-based statistical forces in segmentation. The standard Gibbs random field (GRF) is extended from being determined only by intensity (color) values, i.e., the zero-order derivatives, to also incorporating the first- and second-order derivatives. In particular, a significant first-order derivative accounts for discontinuities to help (1) obtain precise definition of region boundaries, and (2) overcome undesirable under-segmentation caused by the over-smoothing effect often introduced by a standard GRF; an insignificant second-order derivative necessitates stronger homogeneity constraints to help (1) further eliminate small segments caused by noise variations in statistically coherent regions, and (2) overcome undesirable over-segmentation of statistically ramp-like regions. Through balancing the three statistical forces derived from the zero-, first- and second-order derivatives, one can achieve physically and psychophysically more coherent image segmentation