title: Left ventricle segmentation in MRI via convex relaxed distribution matching.
abstract: A fundamental step in the diagnosis of cardiovascular diseases, automatic left ventricle (LV) segmentation in cardiac magnetic resonance images (MRIs) is still acknowledged to be a difficult problem. Most of the existing algorithms require either extensive training or intensive user inputs. This study investigates fast detection of the left ventricle (LV) endo- and epicardium surfaces in cardiac MRI via convex relaxation and distribution matching. The algorithm requires a single subject for training and a very simple user input, which amounts to a single point (mouse click) per target region (cavity or myocardium). It seeks cavity and myocardium regions within each 3D phase by optimizing two functionals, each containing two distribution-matching constraints: (1) a distance-based shape prior and (2) an intensity prior. Based on a global measure of similarity between distributions, the shape prior is intrinsically invariant with respect to translation and rotation. We further introduce a scale variable from which we derive a fixed-point equation (FPE), thereby achieving scale-invariance with only few fast computations. The proposed algorithm relaxes the need for costly pose estimation (or registration) procedures and large training sets, and can tolerate shape deformations, unlike template (or atlas) based priors. Our formulation leads to a challenging problem, which is not directly amenable to convex-optimization techniques. For each functional, we split the problem into a sequence of sub-problems, each of which can be solved exactly and globally via a convex relaxation and the augmented Lagrangian method. Unlike related graph-cut approaches, the proposed convex-relaxation solution can be parallelized to reduce substantially the computational time for 3D domains (or higher), extends directly to high dimensions, and does not have the grid-bias problem. Our parallelized implementation on a graphics processing unit (GPU) demonstrates that the proposed algorithm requires about 3.87 s for a typical cardiac MRI volume, a speed-up of about five times compared to a standard implementation. We report a performance evaluation over 400 volumes acquired from 20 subjects, which shows that the obtained 3D surfaces correlate with independent manual delineations. We further demonstrate experimentally that (1) the performance of the algorithm is not significantly affected by the choice of the training subject and (2) the shape description we use does not change significantly from one subject to another. These results support the fact that a single subject is sufficient for training the proposed algorithm.
authors.affiliation: Western University, London, Ontario, Canada; Robarts Research Institute, London, ON, Canada. Electronic address: msnambakhsh2011@gmail.com.
authors.forename: Cyrus M S
authors.initials: CM
authors.lastname: Nambakhsh
authors.forename: Jing
authors.initials: J
authors.lastname: Yuan
authors.forename: Kumaradevan
authors.initials: K
authors.lastname: Punithakumar
authors.forename: Aashish
authors.initials: A
authors.lastname: Goela
authors.forename: Martin
authors.initials: M
authors.lastname: Rajchl
authors.forename: Terry M
authors.initials: TM
authors.lastname: Peters
authors.forename: Ismail Ben
authors.initials: IB
authors.lastname: Ayed
mesh_terms: D000465:Algorithms; D006352:Heart Ventricles / Q000033:anatomy & histology*; D006801:Humans; D007089:Image Enhancement / Q000379:methods; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D021621:Imaging, Three-Dimensional / Q000379:methods*; D008279:Magnetic Resonance Imaging; D019028:Magnetic Resonance Imaging, Cine / Q000379:methods*; D010363:Pattern Recognition, Automated / Q000379:methods*; D010496:Pericardium / Q000033:anatomy & histology*; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity
keywords: 3D segmentation; Cardiac MRI; Convex-relaxation optimization; Fixed-point optimization; Graphics processing unit