State of the Art of Level Set Methods in Segmentation and Registration of Medical Imaging Modalities

Segmentation of medical images is an important step in various applications such as visualization, quantitative analysis and image-guided surgery. Numerous segmentation methods have been developed in the past two decades for extraction of organ contours on medical images. Low-level segmentation methods, such as pixel-based clustering, region growing, and filter-based edge detection, require additional pre-processing and post-processing as well as considerable amounts of expert intervention or information of the objects of interest. Furthermore the subsequent analysis of segmented objects is hampered by the primitive, pixel or voxel level representations from those region-based segmentation. Deformable models, on the other hand, provide an explicit representation of the boundary and the shape of the object. They combine several desirable features such as inherent connectivity and smoothness, which counteract noise and boundary irregularities, as well as the ability to incorporate knowledge about the object of interest. However, parametric deformable models have two main limitations. First, in situations where the initial model and desired object boundary differ greatly in size and shape, the model must be re-parameterized dynamically to faithfully recover the object boundary. The second limitation is that it has difficulty dealing with topological adaptation such as splitting or merging model parts, a useful property for recovering either multiple objects or objects with unknown topology. This difficulty is caused by the fact that a new parameterization must be constructed whenever topology change occurs, which requires sophisticated schemes. Level set deformable models, also referred to as geometric deformable models, provide an elegant solution to address the primary limitations of parametric deformable models. These methods have drawn a great deal of attention since their introduction in 1988. Advantages of the contour implicit formulation of the deformable model over parametric formulation include: (1) no parameterization of the contour, (2) topological flexibility, (3) good numerical stability, (4) straightforward extension of the 2D formulation to n-D. Recent reviews on the subject include papers from Suri. In this chapter we give a general overview of the level set segmentation methods with emphasize on new frameworks recently introduced in the context of medical imaging problems. We then introduce novel approaches that aim at combining segmentation and registration in a level set formulation. Finally we review a selective set of clinical works with detailed validation of the level set methods for several clinical applications

Segmentation of the left ventricle of the heart in 3-D+t MRI data using an optimized nonrigid temporal model

Modern medical imaging modalities provide large amounts of information in both the spatial and temporal domains and the incorporation of this information in a coherent algorithmic framework is a significant challenge. In this paper, we present a novel and intuitive approach to combine 3-D spatial and temporal (3-D + time) magnetic resonance imaging (MRI) data in an integrated segmentation algorithm to extract the myocardium of the left ventricle. A novel level-set segmentation process is developed that simultaneously delineates and tracks the boundaries of the left ventricle muscle. By encoding prior knowledge about cardiac temporal evolution in a parametric framework, an expectation-maximization algorithm optimally tracks the myocardial deformation over the cardiac cycle. The expectation step deforms the level-set function while the maximization step updates the prior temporal model parameters to perform the segmentation in a nonrigid sense

Image based approach for early assessment of heart failure.

In diagnosing heart diseases, the estimation of cardiac performance indices requires accurate segmentation of the left ventricle (LV) wall from cine cardiac magnetic resonance (CMR) images. MR imaging is noninvasive and generates clear images; however, it is impractical to manually process the huge number of images generated to calculate the performance indices. In this dissertation, we introduce a novel, fast, robust, bi-directional coupled parametric deformable models that are capable of segmenting the LV wall borders using first- and second-order visual appearance features. These features are embedded in a new stochastic external force that preserves the topology of the LV wall to track the evolution of the parametric deformable models control points. We tested the proposed segmentation approach on 15 data sets in 6 infarction patients using the Dice similarity coefficient (DSC) and the average distance (AD) between the ground truth and automated segmentation contours. Our approach achieves a mean DSC value of 0.926±0.022 and mean AD value of 2.16±0.60 mm compared to two other level set methods that achieve mean DSC values of 0.904±0.033 and 0.885±0.02; and mean AD values of 2.86±1.35 mm and 5.72±4.70 mm, respectively. Also, a novel framework for assessing both 3D functional strain and wall thickening from 4D cine cardiac magnetic resonance imaging (CCMR) is introduced. The introduced approach is primarily based on using geometrical features to track the LV wall during the cardiac cycle. The 4D tracking approach consists of the following two main steps: (i) Initially, the surface points on the LV wall are tracked by solving a 3D Laplace equation between two subsequent LV surfaces; and (ii) Secondly, the locations of the tracked LV surface points are iteratively adjusted through an energy minimization cost function using a generalized Gauss-Markov random field (GGMRF) image model in order to remove inconsistencies and preserve the anatomy of the heart wall during the tracking process. Then the circumferential strains are straight forward calculated from the location of the tracked LV surface points. In addition, myocardial wall thickening is estimated by co-allocation of the corresponding points, or matches between the endocardium and epicardium surfaces of the LV wall using the solution of the 3D laplace equation. Experimental results on in vivo data confirm the accuracy and robustness of our method. Moreover, the comparison results demonstrate that our approach outperforms 2D wall thickening estimation approaches

A novel model-based 3D+time left ventricular segmentation technique

A common approach to model-based segmentation is to assume a top-down modelling strategy. However, this is not feasible for complex 3D+time structures such as the cardiac left ventricle due to increased training requirements, aligning difficulties and local minima in resulting models. As our main contribution, we present an alternate bottom-up modelling approach. By combining the variation captured in multiple dimensionally-targeted models at segmentation-time we create a scalable segmentation framework that does not suffer from the ’curse of dimensionality’. Our second contribution involves a flexible contour coupling technique that allows our segmentation method to adapt to unseen contour configurations outside the training set. This is used to identify the endo- and epi-cardium contours of the left ventricle by coupling them at segmentationtime, instead of at model-time. We apply our approach to 33 3D+time MRI cardiac datasets and perform comprehensive evaluation against several state-of-the-art works. Quantitative evaluation illustrates that our method requires significantly less training than state-of-the-art model-based methods, while maintaining or improving segmentation accuracy

Automatic segmentation of wall structures from cardiac images

One important topic in medical image analysis is segmenting wall structures from different cardiac medical imaging modalities such as computed tomography (CT) and magnetic resonance imaging (MRI). This task is typically done by radiologists either manually or semi-automatically, which is a very time-consuming process. To reduce the laborious human efforts, automatic methods have become popular in this research. In this thesis, features insensitive to data variations are explored to segment the ventricles from CT images and extract the left atrium from MR images. As applications, the segmentation results are used to facilitate cardiac disease analysis. Specifically, 1. An automatic method is proposed to extract the ventricles from CT images by integrating surface decomposition with contour evolution techniques. In particular, the ventricles are first identified on a surface extracted from patient-specific image data. Then, the contour evolution is employed to refine the identified ventricles. The proposed method is robust to variations of ventricle shapes, volume coverages, and image quality. 2. A variational region-growing method is proposed to segment the left atrium from MR images. Because of the localized property of this formulation, the proposed method is insensitive to data variabilities that are hard to handle by globalized methods. 3. In applications, a geometrical computational framework is proposed to estimate the myocardial mass at risk caused by stenoses. In addition, the segmentation of the left atrium is used to identify scars for MR images of post-ablation.PhDCommittee Chair: Yezzi, Anthony; Committee Co-Chair: Tannenbaum, Allen; Committee Member: Egerstedt, Magnus ; Committee Member: Fedele, Francesco ; Committee Member: Stillman, Arthur; Committee Member: Vela,Patrici

Estimation of vector fields in unconstrained and inequality constrained variational problems for segmentation and registration

Vector fields arise in many problems of computer vision, particularly in non-rigid registration. In this paper, we develop coupled partial differential equations (PDEs) to estimate vector fields that define the deformation between objects, and the contour or surface that defines the segmentation of the objects as well.We also explore the utility of inequality constraints applied to variational problems in vision such as estimation of deformation fields in non-rigid registration and tracking. To solve inequality constrained vector field estimation problems, we apply tools from the Kuhn-Tucker theorem in optimization theory. Our technique differs from recently popular joint segmentation and registration algorithms, particularly in its coupled set of PDEs derived from the same set of energy terms for registration and segmentation. We present both the theory and results that demonstrate our approach

Active contour driven by scalable local regional information on expandable kernel

An active contour that uses the pixel’s intensity on a set of expandable kernels along the propagating contour for image segmentation is presented in this paper. The objective is this study is to employ the scalable kernels to attract the contour to meet the desired boundary. The key characteristics of this scheme is that the kernels gradually expand to find an object’s boundary. So this scheme could penetrate to the concave boundary more effective and efficient than some other schemes. If a Gaussian kernel is applied, it could trace the object with a blurred or smooth boundary. Moreover, the directional selectivity feature enables in capturing two edge’s types with just one initial position. Its performance showed more desirable segmentation outcomes compared to the other existing active contours using regional information when segmenting the noisy image and the non-uniform (or heterogeneous) textures. Meanwhile, the level set implementation enables topological flexibility to our active contour scheme