Graph Based Lymphatic Vessel Wall Localisation and Tracking. In: Liu C, Luo B, Kropatsch WG, Cheng J, editors. Graph-Based Representations in Pattern Recognition. Cham: Springer International Publishing; 2015. pp. 345-54. [DOI: 10.1007/978-3-319-18224-7_34]

Coupled s-excess HMM for vessel border tracking and segmentation

In this paper, we present a novel image segmentation technique, based on hidden Markov model (HMM), which we then apply to simultaneously segment interior and exterior walls of fluorescent confocal images of lymphatic vessels. Our proposed method achieves this by tracking hidden states, which are used to indicate the locations of both the inner and outer wall borders throughout the sequence of images. We parameterize these vessel borders using radial basis functions (RBFs), thus enabling us to minimize the number of points we need to track as we progress through multiple layers and therefore reduce computational complexity. Information about each border is detected using patch-wise convolutional neural networks (CNN). We use the softmax function to infer the emission probability and use a proposed new training algorithm based on s-excess optimization to learn the transition probability. We also introduce a new optimization method to determine the optimum sequence of the hidden states. Thus, we transform the segmentation problem into one that minimizes an s-excess graph cut, where each hidden state is represented as a graph node and the weight of these nodes are defined by their emission probabilities. The transition probabilities are used to define relationships between neighboring nodes in the constructed graph. We compare our proposed method to the Viterbi and Baum-Welch algorithms. Both qualitative and quantitative analysis show superior performance of the proposed methods.

Energy minimization in medical image analysis: Methodologies and applications

Energy minimization is of particular interest in medical image analysis. In the past two decades, a variety of optimization schemes have been developed. In this paper, we present a comprehensive survey of the state-of-the-art optimization approaches. These algorithms are mainly classified into two categories: continuous method and discrete method. The former includes Newton-Raphson method, gradient descent method, conjugate gradient method, proximal gradient method, coordinate descent method, and genetic algorithm-based method, while the latter covers graph cuts method, belief propagation method, tree-reweighted message passing method, linear programming method, maximum margin learning method, simulated annealing method, and iterated conditional modes method. We also discuss the minimal surface method, primal-dual method, and the multi-objective optimization method. In addition, we review several comparative studies that evaluate the performance of different minimization techniques in terms of accuracy, efficiency, or complexity. These optimization techniques are widely used in many medical applications, for example, image segmentation, registration, reconstruction, motion tracking, and compressed sensing. We thus give an overview on those applications as well.