Browsing by Author "Du Preez, Johan A."

Now showing 1 - 2 of 2
  • Thumbnail Image
    Item
    Left ventricular segmentation from MRI datasets with edge modelling conditional random fields
    (BioMed Central, 2013-07) Dreijer, Janto F.; Herbst, Ben M.; Du Preez, Johan A.
    Background: This paper considers automatic segmentation of the left cardiac ventricle in short axis magnetic resonance images. Various aspects, such as the presence of papillary muscles near the endocardium border, makes simple threshold based segmentation difficult. Methods: The endo- and epicardium are modelled as two series of radii which are inter-related using features describing shape and motion. Image features are derived from edge information from human annotated images. The features are combined within a discriminatively trained Conditional Random Field (CRF). Loopy belief propagation is used to infer segmentations when an unsegmented video sequence is given. Powell’s method is applied to find CRF parameters by minimizing the difference between ground truth annotations and the inferred contours. We also describe how the endocardium centre points are calculated from a single human-provided centre point in the first frame, through minimization of frame alignment error. Results: We present and analyse the results of segmentation. The algorithm exhibits robustness against inclusion of the papillary muscles by integrating shape and motion information. Possible future improvements are identified. Conclusions: The presented model integrates shape and motion information to segment the inner and outer contours in the presence of papillary muscles. On the Sunnybrook dataset we find an average Dice metric of 0.91 ± 0.02 and 0.93 ± 0.02 for the inner and outer segmentations, respectively. Particularly problematic are patients with hypertrophy where the blood pool disappears from view at end-systole.
  • Thumbnail Image
    Item
    On the convergence of gaussian belief propagation with nodes of arbitrary size
    (Journal of Machine Learning Research, 2019) Kamper, Francois; Steel, Sarel J.; Du Preez, Johan A.
    This paper is concerned with a multivariate extension of Gaussian message passing applied to pairwise Markov graphs (MGs). Gaussian message passing applied to pairwise MGs is often labeled Gaussian belief propagation (GaBP) and can be used to approximate the marginal of each variable contained in the pairwise MG. We propose a multivariate extension of GaBP (we label this GaBP-m) that can be used to estimate higher-dimensional marginals. Beyond the ability to estimate higher-dimensional marginals, GaBP-m exhibits better convergence behavior than GaBP, and can also provide more accurate univariate marginals. The theoretical results of this paper are based on an extension of the computation tree analysis conducted on univariate nodes to the multivariate case. The main contribution of this paper is the development of a convergence condition for GaBP-m that moves beyond the walk-summability of the precision matrix. Based on this convergence condition, we derived an upper bound for the number of iterations required for convergence of the GaBP-m algorithm. An upper bound on the dissimilarity between the approximate and exact marginal covariance matrices was established. We argue that GaBP-m is robust towards a certain change in variables, a property not shared by iterative solvers of linear systems, such as the conjugate gradient (CG) and preconditioned conjugate gradient (PCG) methods. The advantages of using GaBP-m over GaBP are also illustrated empirically.