Embedding Overlap Priors in Variational Left Ventricle Tracking

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.