Level Set Image Segmentation with a Statistical Overlap Constraint Ismail Ben Ayed 1 , Shuo Li 1 , and Ian Ross 2 1 GE Healthcare, London, ON, Canada 2 London Health Sciences Centre, London, ON, Canada Abstract. This study investigates active curve image segmentation with a statistical overlap constraint, which biases the overlap between the non- parametric (kernel-based) distributions of image data within the segmen- tation 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 generaliza- tion of current intensity-driven constraints for difficult situations where a significant overlap exists between the distributions of the segmenta- tion 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 interpreta- tion 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 Com- puted Tomography (CT) liver images demonstrate the desirable prop- erties of the statistical overlap constraint. First, it outperforms signifi- cantly the likelihood prior commonly used in level set segmentation. Sec- ond, 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 back- ground distribution, thereby allowing more flexibility in clinical use. 1 Introduction Image segmentation is a fundamental task in medical image analysis [2]–[9], [23]–[25]. It consists of partitioning an image into two regions: a target object (foreground), for instance a specific organ, and a background. Level set functional minimization, which uses an active curve to delineate the target object, has resulted in the most effective and flexible segmentation algorithms [10]–[20], mainly because it allows introducing a wide range of photometric and geometric constraints on the solution. It has become very popular in medical image analysis [2]–[9], [23]–[25] because there are several applications where anatomical entities can be enclosed within a closed contour. Furthermore, the level set representation of curve evolution extends readily to higher dimensions, and allows to compute easily the geometric characteristics of objects. J.L. Prince, D.L. Pham, and K.J. Myers (Eds.): IPMI 2009, LNCS 5636, pp. 589–601, 2009. c  Springer-Verlag Berlin Heidelberg 2009