Contour Relaxation

The initial segmentation obtained using region growing is refined by contour relaxation. Contour relaxation consists of changing a boundary pixel if such an alteration results in a local maximum of the joint likelihood function, p(Y,Q) = p(Q)P(Y/Q), where Y is the original image data and p(Q) is the probability of a realization Q of the GMRF, and p(Y/Q) is modeled by Gaussian distribution.

Given the initial segmentation, then, boundaries are refined by examining each boundary pixel iteratively. The ratio of the likelihood function p(Y,Q) for the 3x3x3 neighborhood of each boundary pixel is computed. The label of the boundary pixel is changed, if necessary, to the label of the neighbor that maximizes the ratio. The algorithm is stopped when the number of boundary labels altered is less than a threshold.