A Statistical Overlap Prior for Variational Image Segmentation

This study investigates variational image segmentation with an original data term, referred to as statistical overlap prior, which measures the conformity of overlap between the nonparametric distributions of image data within the segmentation regions to a learned statistical description. This leads to image segmentation and distribution tracking algorithms that relax the assumption of minimal overlap and, as such, are more widely applicable than existing algorithms. We propose to minimize active curve functionals containing the proposed overlap prior, compute the corresponding Euler-Lagrange curve evolution equations, and give an interpretation of how the overlap prior controls such evolution. We model the overlap, measured via the Bhattacharyya coefficient, with a Gaussian prior whose parameters are estimated from a set of relevant training images. Quantitative and comparative performance evaluations of the proposed algorithms over several experiments demonstrate the positive effects of the overlap prior in regard to segmentation accuracy and convergence speed.