Segmentation of diffusion weighted MRI using the level set framework

Medical imaging is a rapidly growing field in which diffusion imaging is a recently developed modality. This novel imaging contrast permits in-vivo measurement of the diffusion of water molecules. This is particularly interesting in brain imaging where the diffusion reveals an amazing insight into the neuronal organization and cerebral cytoarchitecture. Diffusion images contain from six up to hundreds of values in each voxel and are represented as tensor fields (Diffusion Tensor Imaging (DTI)) or as fields of functions (High Angular Resolution Diffusion (HARD) imaging). To fully extract the large amount of data contained within these images new processing and analysis tools are needed. The aim of this thesis is the development of such tools. The method we have been mainly focusing on for this purpose is the level set method. The level set method is a numerical and theoretical tool for propagating interfaces. In image processing it is used for propagating curves in 2D or surfaces in 3D for delineation of objects or for regularization purposes. In this thesis we have explored some of the numerous aspects of the level set frame work to see how the diffusion properties can be used for segmentation. For segmentation of tensor fields we have considered similarity measures for comparison of tensors. From these similarity measures several applications of the level set method have been developed for the segmentation of different structures. Different measures of similarity have been used dependent on the application. When segmenting white matter regions in DTI, the similarity measure emphasizes anisotropic regions. The segmentation algorithm itself has a very local dependence since white matter, in general fiber tracts, experiences different diffusion in different parts of the structure. The presented results show segmentations of the major fiber tracts in the brain. Other structures, such as the deep cerebral nuclei, that are mainly composed of gray matter, have more homogenous diffusion properties than white matter structures. Therefore, in these structures we maximize the internal coherence within the entire structure by using a region based approach to the segmentation problem. Segmentations of the thalamus and its nuclei as well as on tensor fields from fluid mechanics are presented. For High Angular Resolution Diffusion (HARD) images, two methods for fiber tract segmentation are presented based on different types of coherence. The coherence is either measured as the similarity between fibers obtained from a tractography algorithm, or the similarity of scalar values in a five-dimensional non-Euclidean space. The similarity between two fibers is determined by a counting strategy and is equal to the number of voxels they have in common. A spectral clustering algorithm is then used for grouping fibers with a high inter-resemblance. When segmenting white matter with the level set method, we propose to expand the space we are working in from a three-dimensional space of Orientation Distribution Functions (ODF) to a five-dimensional space of position and orientation. By a careful definition of this space and an adaptation of the level set to five dimensions the fibers tracts can be segmented as separated structures. We show some preliminary results from segmentations in this 5D space. The approaches proposed in this thesis permit a consideration of the fiber tracts and gray matter structures as an entity, allowing quantitative measures of the diffusion without losing information by simplifying the images to scalar representations.

An Efficient Algorithm for Level Set Method Preserving Distance Function

Xavier Bresson, Virginia Estellers Casas, Jean-Philippe Thiran, Dominique Zosso

The level set method is a popular technique for tracking moving interfaces in several disciplines including computer vision and fluid dynamics. However, despite its high flexibility, the original level set method is limited by two important numerical issues. Firstly, the level set method does not implicitly preserve the level set function as a distance function, which is necessary to estimate accurately geometric features s.a. the curvature or the contour normal. Secondly, the level set algorithm is slow because the time step is limited by the standard CFL condition, which is also essential to the numerical stability of the iterative scheme. Recent advances with graph cut methods and continuous convex relaxation methods provide powerful alternatives to the level set method for image processing problems because they are fast, accurate and guaranteed to find the global minimizer independently to the initialization. These recent techniques use binary functions to represent the contour rather than distance functions, which are usually considered for the level set method. However, the binary function cannot provide the distance information, which can be essential for some applications s.a. the surface reconstruction problem from scattered points and the cortex segmentation problem in medical imaging. In this paper, we propose a fast algorithm to preserve distance functions in level set methods. Our algorithm is inspired by recent efficient

\ell^1

optimization techniques, which will provide an efficient and easy to implement algorithm. It is interesting to note that our algorithm is not limited by the CFL condition and it naturally preserves the level set function as a distance function during the evolution, which avoids the classical re-distancing problem in level set methods. We apply the proposed algorithm to carry out image segmentation, where our methods proves to be 5 to 6 times faster than standard distance preserving level set techniques. We also present two applications where preserving a distance function is essential. Nonetheless, our method stays generic and can be applied to any level set methods that require the distance information.

Institute of Electrical and Electronics Engineers2012

Convex Formulation of Region-based Image Registration

Shima Sepehri

Medical Imaging is a necessary component of many applications, such as clinical diagnosis, event tracking and decision making. Segmentation of anatomical organs in a medical image is a helpful processing of medical images for clinical purposes. Accurate manual segmentation requires considerable efforts and time, due to some challenges such as the invisibility of some organs in an image, for example. Here, image processing techniques are used to facilitate and improve the accuracy of such a segmentation.

2011

Spline Shape Processing

Daniel Andreas Schmitter

In this thesis, we present a novel generic and unifying framework for data-adaptive shape modeling. Our work is motivated by the raising need for powerful geometric modeling kernels that are required for shape characterization in biomedical imaging. The ongoing development of faster and more precise hardware in biomedicine creates new demands regarding the characterization, processing, and analysis of shapes in medical and biological data such as MRI, CT or microscopy. We develop a novel mathematical framework to construct a geometric kernel that is capable to represent deformable shapes in the contexts of segmentation, visualization, and deformation, while also enabling user-interaction, fast optimization as well as the construction of shape dictionaries for shape encoding. Our approach relies on spline-based concepts for shape representation in computer graphics combined with spline-theoretical fundamentals from signal and image processing. This thesis is organized in two main parts. In the first part, our main contribution is the development of a novel generic framework to encode shapes, learn dictionaries and construct shape projectors onto functional vector spaces defined by spline shapes. Our construction is formulated in the continuous domain and we propose solutions based on L2-methods as well as sparsity-promoting l1-based methods. Our contribution is generic in the sense that it is applicable to any spline-based generator that forms a Riesz Basis. We apply our solution to classify shapes in medical ultrasound images, to learn dictionaries of brain structures and to construct robust shape priors for segmentation algorithms. In the second part of this thesis, our contribution is a novel data-adaptive framework to construct deformable shapes with different kinds of topology that are used in a broad spectrum of applications such as the semi-automatic segmentation of biomedical structures, user-interactive shape modeling, shape deformation and morphing, shape reconstruction from samples as well as the visualization and animation of shapes. We construct novel families of spline-generators that facilitate intuitive user-interaction, shape modeling, and shape characterization, and we provide specific examples and validations of the use of our framework in practice. The two parts of this thesis together build a unifying theory for the construction of a novel flexible geometric modeling kernel with a wide range of use and applications as we illustrate throughout this thesis with a vast amount of experiments.

EPFL2017