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.