Level set image segmentation with a statistical overlap constraint.

This study investigates active curve image segmentation with a statistical overlap constraint, which biases the overlap between the nonparametric (kernel-based) distributions of image data within the segmentation regions a foreground and a background-to a statistical description learned a priori. We model the overlap, measured via the Bhattacharyya coefficient, with a Gaussian prior whose parameters are estimated from a set of relevant training images. This can be viewed as a generalization of current intensity-driven constraints for difficult situations where a significant overlap exists between the distributions of the segmentation regions. We propose to minimize a functional containing the overlap constraint and classic regularization terms, compute the corresponding Euler-Lagrange curve evolution equation, and give a simple interpretation of how the statistical overlap constraint influences such evolution. A representative number of statistical, quantitative, and comparative experiments with Magnetic Resonance (MR) cardiac images and Computed Tomography (CT) liver images demonstrate the desirable properties of the statistical overlap constraint. First, it outperforms significantly the likelihood prior commonly used in level set segmentation. Second, it is easy-to-learn; we demonstrate experimentally that the Gaussian assumption is sufficient for cardiac images. Third, it can relax the need of both complex geometric training and accurate learning of the background distribution, thereby allowing more flexibility in clinical use.