Right Ventricle Segmentation with Probability Product Kernel Constraints

We propose a fast algorithm for 3D segmentation of the right ventricle (RV) in MRI using shape and appearance constraints based on probability product kernels (PPK). The proposed constraints remove the need for large, manually-segmented training sets and costly pose estimation (or registration) procedures, as is the case of the existing algorithms. We report comprehensive experiments, which demonstrate that the proposed algorithm (i) requires only a single subject for training; and (ii) yields a performance that is not significantly affected by the choice of the training data. Our PPK constraints are non-linear (high-order) functionals, which are not directly amenable to standard optimizers. We split the problem into several surrogate-functional optimizations, each solved via an efficient convex relaxation that is amenable to parallel implementations. We further introduce a scale variable that we optimize with fast fixed-point computations, thereby achieving pose invariance in real-time. Our parallelized implementation on a graphics processing unit (GPU) demonstrates that the proposed algorithm can yield a real-time solution for typical cardiac MRI volumes, with a speed-up of more than 20 times compared to the CPU version. We report a comprehensive experimental validations over 400 volumes acquired from 20 subjects, and demonstrate that the obtained 3D surfaces correlate with independent manual delineations.