Geometrically induced force interaction for three-dimensional deformable models

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.

User Interaction in Semi-Automatic Segmentation of Organs at Risk: a Case Study in Radiotherapy

Accurate segmentation of organs at risk is an important step in radiotherapy planning. Manual segmentation being a tedious procedure and prone to inter- and intra-observer variability, there is a growing interest in automated segmentation methods. However, automatic methods frequently fail to provide satisfactory result, and post-processing corrections are often needed. Semi-automatic segmentation methods are designed to overcome these problems by combining physicians' expertise and computers' potential. This study evaluates two semi-automatic segmentation methods with different types of user interactions, named the "strokes" and the "contour", to provide insights into the role and impact of human-computer interaction. Two physicians participated in the experiment. In total, 42 case studies were carried out on five different types of organs at risk. For each case study, both the human-computer interaction process and quality of the segmentation results were measured subjectively and objectively. Furthermore, different measures of the process and the results were correlated. A total of 36 quantifiable and ten non-quantifiable correlations were identified for each type of interaction. Among those pairs of measures, 20 of the contour method and 22 of the strokes method were strongly or moderately correlated, either directly or inversely. Based on those correlated measures, it is concluded that: (1) in the design of semi-automatic segmentation methods, user interactions need to be less cognitively challenging; (2) based on the observed workflows and preferences of physicians, there is a need for flexibility in the interface design; (3) the correlated measures provide insights that can be used in improving user interaction design.

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.

Divergence of Gradient Convolution: Deformable Segmentation With Arbitrary Initializations

In this paper, we propose a unified approach to deformable model-based segmentation. The fundamental force field of the proposed method is based on computing the divergence of a gradient convolution field (GCF), which makes the full use of directional information of the image gradient vectors and their interactions across image domain. However, instead of directly using such a vector field for deformable segmentation as in the conventional approaches, we derive a more salient representation for contour evolution, and very importantly, we demonstrate that this representation of image force field not only leads to global minimum through convex relaxation but also can achieve the same result using the conventional gradient descent with an intrinsic regularization. Thus, the proposed method can handle arbitrary initializations. The proposed external force field for deformable segmentation has both edge-based properties in that the GCF is computed from image gradients, and the region-based attributes since its divergence can be treated as a region indication function. Moreover, nonlinear diffusion can be conveniently applied to GCF to improve its performance in dealing with noise interference. We also show the extension of GCF from 2D to 3D. In comparison to the state-of-the-art deformable segmentation techniques, the proposed method shows greater flexibility in model initialization and optimization realization, as well as better performance toward noise interference and appearance variation.

Processing the image gradient field using a topographic primal sketch approach

The spatial derivatives of the image intensity provide topographic information that may be used to identify and segment objects. The accurate computation of the derivatives is often hampered in medical images by the presence of noise and a limited resolution. This paper focuses on accurate computation of spatial derivatives and their subsequent use to process an image gradient field directly, from which an image with improved characteristics can be reconstructed. The improvements include noise reduction, contrast enhancement, thinning object contours and the preservation of edges. Processing the gradient field directly instead of the image is shown to have numerous benefits. The approach is developed such that the steps are modular, allowing the overall method to be improved and possibly tailored to different applications. As presented, the approach relies on a topographic representation and primal sketch of an image. Comparisons with existing image processing methods on a synthetic image and different medical images show improved results and accuracy in segmentation. Here, the focus is on objects with low spatial resolution, which is often the case in medical images. The methods developed show the importance of improved accuracy in derivative calculation and the potential in processing the image gradient field directly. Copyright © 2015 John Wiley & Sons, Ltd.

Segmentation of biomedical images using active contour model with robust image feature and shape prior

In this article, a new level set model is proposed for the segmentation of biomedical images. The image energy of the proposed model is derived from a robust image gradient feature which gives the active contour a global representation of the geometric configuration, making it more robust in dealing with image noise, weak edges, and initial configurations. Statistical shape information is incorporated using nonparametric shape density distribution, which allows the shape model to handle relatively large shape variations. The segmentation of various shapes from both synthetic and real images depict the robustness and efficiency of the proposed method.

Semi-automatic surface and volume mesh generation for subject-specific biomedical geometries

An overview of surface and volume mesh generation techniques for creating valid meshes to carry out biomedical flows is provided. The methods presented are designed for robust numerical modelling of biofluid flow through subject-specific geometries. The applications of interest are haemodynamics in blood vessels and air flow in upper human respiratory tract. The methods described are designed to minimize distortion to a given domain boundary. They are also designed to generate a triangular surface mesh first and then volume mesh (tetrahedrons) with high quality surface and volume elements. For blood flow applications, a simple procedure to generate a boundary layer mesh is also described. The methods described here are semi-automatic in nature because of the fact that the geometries are complex, and automation of the procedures may be possible if high quality scans are used.