This study investigates an efficient algorithm for image segmentation with a global constraint based on the Bhattacharyya measure. The problem consists of finding a region consistent with an image distribution learned a priori. We derive an original upper bound of the Bhattacharyya measure by introducing an auxiliary labeling. From this upper bound, we reformulate the problem as an optimization of an auxiliary function by graph cuts. Then, we demonstrate that the proposed procedure converges and give a statistical interpretation of the upper bound. The algorithm requires very few iterations to converge, and finds nearly global optima. Quantitative evaluations and comparisons with state-of-the-art methods on the Microsoft GrabCut segmentation database demonstrated that the proposed algorithm brings improvements in regard to segmentation accuracy, computational efficiency, and optimality. We further demonstrate the flexibility of the algorithm in object tracking.

We present an original information theoretic measure of heart motion based on the Shannon's differential entropy (SDE), which allows heart wall motion abnormality detection. Based on functional images, which are subject to noise and segmentation inaccuracies, heart wall motion analysis is acknowledged as a difficult problem, and as such, incorporation of prior knowledge is crucial for improving accuracy. Given incomplete, noisy data and a dynamic model, the Kalman filter, a well-known recursive Bayesian filter, is devised in this study to the estimation of the left ventricular (LV) cavity points. However, due to similarity between the statistical information of normal and abnormal heart motions, detecting and classifying abnormality is a challenging problem, which we investigate with a global measure based on the SDE. We further derive two other possible information theoretic abnormality detection criteria, one is based on Rényi entropy and the other on Fisher information. The proposed methods analyze wall motion quantitatively by constructing distributions of the normalized radial distance estimates of the LV cavity. Using 269 x 20 segmented LV cavities of short-axis MRI obtained from 30 subjects, the experimental analysis demonstrates that the proposed SDE criterion can lead to a significant improvement over other features that are prevalent in the literature related to the LV cavity, namely, mean radial displacement and mean radial velocity.

We propose to embed overlap priors in variational tracking of the left ventricle (LV) in cardiac magnetic resonance (MR) sequences. The method consists of evolving two curves toward the LV endo- and epicardium boundaries. We derive the curve evolution equations by minimizing two functionals each containing an original overlap prior constraint. The latter measures the conformity of the overlap between the nonparametric (kernel-based) intensity distributions within the three target regions--LV cavity, myocardium and background-to a prior learned from a given segmentation of the first frame. The Bhattacharyya coefficient is used as an overlap measure. Different from existing intensity-driven constraints, the proposed priors do not assume implicitly that the overlap between the intensity distributions within different regions has to be minimal. This prevents both the papillary muscles from being included erroneously in the myocardium and the curves from spilling into the background. Although neither geometric training nor preprocessing were used, quantitative evaluation of the similarities between automatic and independent manual segmentations showed that the proposed method yields a competitive score in comparison with existing methods. This allows more flexibility in clinical use because our solution is based only on the current intensity data, and consequently, the results are not bounded to the characteristics, variability, and mathematical description of a finite training set. We also demonstrate experimentally that the overlap measures are approximately constant over a cardiac sequence, which allows to learn the overlap priors from a single frame.

Recent studies have shown that embedding similarity/dissimilarity measures between distributions in the variational level set framework can lead to effective object segmentation/tracking algorithms. In this connection, existing methods assume implicitly that the overlap between the distributions of image data within the object and its background has to be minimal. Unfortunately, such assumption may not be valid in many important applications. This study investigates an overlap prior, which embeds knowledge about the overlap between the distributions of the object and the background in level set tracking. It consists of evolving a curve to delineate the target object in the current frame. The level set curve evolution equation is sought following the maximization of a functional containing three terms: (1) an original overlap prior which measures the conformity of overlap between the nonparametric (kernel-based) distributions within the object and the background to a learned description, (2) a term which measures the similarity between a model distribution of the object and the sample distribution inside the curve, and (3) a regularization term for smooth segmentation boundaries. The Bhattacharyya coefficient is used as an overlap measure. Apart from leading to a method which is more versatile than current ones, the overlap prior speeds up significantly the curve evolution. Comparisons and results demonstrate the advantages of the proposed prior over related methods, and its usefulness in important applications such as the left ventricle tracking in magnetic resonance (MR) images.