Medical imaging is an important part of the clinical workflow. With the increasing amount and complexity of image data comes the need for automatic (or semi-automatic) analysis methods which aid the physician in the exploration of the data. One specific imaging technique is angiography, in which the blood vessels are imaged using an injected contrast agent which increases the contrast between blood and surrounding tissue. In these images, the blood vessels can be viewed as tubular structures with varying diameters. Deviations from this structure are signs of disease, such as stenoses introducing reduced blood flow, or aneurysms with a risk of rupture. This thesis focuses on segmentation and visualization of blood vessels, consituting the vascular tree, in angiography images. Segmentation is the problem of partitioning an image into separate regions. There is no general segmentation method which achieves good results for all possible applications. Instead, algorithms use prior knowledge and data models adapted to the problem at hand for good performance. We study blood vessel segmentation based on a two-step approach. First, we model the vessels as a collection of linear structures which are detected using multi-scale filtering techniques. Second, we develop machine-learning based level set segmentation methods to separate the vessels from the background, based on the output of the filtering. In many applications the three-dimensional structure of the vascular tree has to be presented to a radiologist or a member of the medical staff. For this, a visualization technique such as direct volume rendering is often used. In the case of computed tomography angiography one has to take into account that the image depends on both the geometrical structure of the vascular tree and the varying concentration of the injected contrast agent. The visualization should have an easy to understand interpretation for the user, to make diagnostical interpretations reliable. The mapping from the image data to the visualization should therefore closely follow routines that are commonly used by the radiologist. We developed an automatic method which adapts the visualization locally to the contrast agent, revealing a larger portion of the vascular tree while minimizing the manual intervention required from the radiologist. The effectiveness of this method is evaluated in a user study involving radiologists as domain experts.

First of all, the PDE form of the classical level set function phi is parameterized with an analytical form of Radial Basis Function (RBF), which is real-valued and continuously differentiable. Such that the upwind scheme, extension velocity and reinitialization algorithms in solving the discrete Hamilton-Jacobi equation can be waived in the numerical process, the whole framework is transformed into a standard mathematical programming problem in which the linear objective function can be directly optimized by a gradient algorithm - shape sensitivity. The minimization of the mean compliance is studied and presented to demonstrate the advantages of the parametrical method. / Parametrization substantially reduces the complexity of the original discrete PDE level set method. However, the result shows that the high number of RBF knots leads to dense coefficient matrices. Thus, it induces numerical instabilities, slow convergence and less accuracy in the process. Consequently, we then study the distribution of knots density for faster computation. By updating the movement of the knot, the knot moves towards the position where the change is directly determined by the shape sensitivity. In such case, we may use lesser number of knots to describe the properties of the system while the smoothness of the implicit function is satisfied. The sensitivity study is evaluated carefully and discussed in detail. Results show a significant improvement in the computational speed and stability. / The study found significant improvement obtained in the structural optimization with the parametric level set method, both the stability and efficiency were given as the benefits of using the method of the parametrization. / Traditional structural optimization approaches can be referred to as sizing optimization, since their design variables are the proportions of the structure or material. A major restriction in the sizing problem is that the shape and the topology of the structure are fixed a priori. Undoubtedly, changes in shape (e.g., curved boundary) and topology (e.g., holes in a member) could produce more significant improvement in dynamic performance than modifications in size alone. A recent development of shape and topology optimization based on the implicit moving boundaries with the use of the renowned level set method is regarded as one of the most sophisticated methods in handling the change of the structural topology. In this thesis, we study the parametrization of the classical level set method for the structural optimization and the associated computational methodology. / Usually, a large-scale model will lead to bulk coefficient matrices in the RBF optimization and the linear function normally require O (N3) flops and O (N2) memory while processing. It is becoming impractical to solve as N goes over 10,000. In fact, the dense system equation matrix frequently leads to the numerical instabilities and the failure of the optimization. Finally, we introduce the method of Partition of Unity (POU) to deal with this problem. POU is often used in 3D reconstruction of implicit surfaces from scattered point sets. It breaks the global domain into smaller overlapping subdomains such that the implicit functions can be more efficiently interpolated. Meanwhile, the global solution is obtained by blending all the local solutions with a set of weighting functions. The algorithm of POU is presented here, and we analyze and discuss the numerical results accordingly. / Ho, Hon Shan. / Adviser: Michael Y. Wang. / Source: Dissertation Abstracts International, Volume: 73-03, Section: B, page: . / Thesis (Ph.D.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leaves 106-119). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [201-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese.

One outstanding challenge to understanding the behaviors of organisms and other complexities found in nature through the use of computational fluid dynamics simulations lies in the ability to accurately model the highly tortuous geometries and motions they generally exhibit. Descriptions must be created in a manner that is amenable to definition within some operative computational domain, while at the same time remaining fidelitous to the essence of what is desired to be understood. Typically models are created using functional approximations, so that complex objects are reduced to mathematically tractable representations. Such reductions can certainly lead to a great deal of insight, revealing trends by assigning parameterized motions and tracking their influence on a virtual surrounding environment. However, simplicity sometimes comes at the expense of fidelity; pared down to such a degree, simplified geometries evolving in prescribed fashions may fail to identify some of the essential physical mechanisms that make studying a system interesting to begin with. In this thesis, and alternative route to modeling complex geometries and behaviors is offered, basing its methodology on the coupling of image analysis and level set treatments. First a semi-Lagrangian method is explored, whereby images are utilized as a means for creating a set of surface points that describe a moving object. Later, points are dispensed with altogether, giving in the end a fully Eulerian representation of complex moving geometries that requires no surface meshing and that translates imaged objects directly to level sets without unnecessary tedium. The final framework outlined here represents a completely novel approach to modeling that combines image denoising, segmentation, optical flow, and morphing with level set- based embedded sharp interface methods to produce models that would be difficult to generate any other way.

<p>The Particle Level set method is a successful extension to Level set methods to improve thevolume preservation in fluid simulations. This thesis will analyze how sparse volume data structures can be used to store both the signed distance function and the particles in order to improve access speed and memory efficiency. This Particle Level set implementation will be evaluated against Digital Domains current Particle Level set implementation. Different degrees of quantization will be used to implement particle representations with varying accuracy. These particles will be tested and both visual results and error measurments will be presented. The sparse volume data structures DB-Grid and Field3D will be evaluated in terms of speed and memory efficiency.</p>

<p>Locating and segmenting objects such as bones or internal organs is a common problem in medical imaging. Existing segmentation methods are often cumbersome to use for medical staff, since they require a close initial guess and a range of different parameters to be set appropriately. For this work, we present a two-stage segmentation framework which relies on an initial isosurface interactively extracted by topological analysis. The initial isosurface seldom provides a correct segmentation, so we refine the surface using an iterative level set method to better match the desired object boundary. We present applications and improvements to both the flexible isosurface interface and level set segmentation without edges.</p>

This thesis introduces geometric dynamic active contours in the context of visual tracking, augmenting geometric curve evolution with physically motivated dynamics. Adding additional state information to an evolving curve lifts the curve evolution problem to space dimensions larger than two and thus forbids the use of classical level set techniques. This thesis therefore develops and explores level set methods for problems of higher codimension, putting an emphasis on the vector distance function based approach. This formalism is very general, it is interesting in its own right and still a challenging topic. Two different implementations for geometric dynamic active contours are explored: the full level set approach as well as a simpler partial level set approach. The full level set approach results in full topological flexibility and can deal with curve intersections in the image plane. However, it is computationally expensive. On the other hand the partial level set approach gives up the topological flexibility (intersecting curves cannot be represented) for increased computational efficiency. Contours colliding with different dynamic information (e.g., objects crossing in the image plane) will be merged in the partial level set approach whereas they will correctly traverse each other in the full level set approach. Both implementations are illustrated on synthetic and real examples. Compared to the traditional static curve evolution case, fundamentally different evolution behaviors can be obtained by propagating additional information along with every point on a curve.

Piracy is still a significant threat to ships in a maritime environment. Areas such as the coast of Somalia and the Strait of Malacca are still plagued by pirates, and the total international cost of piracy numbers in the billions of dollars. The first line of defence against these threats is early detection and thus maritime surveillance has become an increasingly important task over the years. While surveillance has traditionally been a manual task using crew members in lookout positions on parts of the ship, much work is being done to automate this task using digital cameras equipped with computer vision software. While these systems are beneficial in that they do not grow tired like their human counterparts, the maritime environment is a challenging task for computer vision systems. This dissertation aims to address some of these challenges by presenting a system that is able to use prior knowledge of an object’s shape to aid in detection and tracking of the object. Additionally, it aims to test this system under various environmental conditions (such as weather). The system is based around the segmentation technique known as the level set method, which uses a contour in the image that is evolved to separate regions of interest. The system is split into two parts, comprising of an object detection stage that initially finds objects in a scene, and an object tracking stage that tracks detected objects for the rest of the sequence. The object detection stage uses a kernel density estimation-based background subtraction and a binary image level set filter, while the object tracker makes use of a tracking level set algorithm for its functionality. The object detector was tested using a group of 4 sequences, of which it was able to find a prior-known object in 3. The object tracker was tested on a group of 10 sequences for 300 frames a sequence. In 6 of these sequences the object tracker was able to successfully track the object in every single frame. It is shown that the developed video tracking system outperforms level set–based systems that don’t use prior shape knowledge, working well even where these systems fail. / Thesis (M.Sc.Eng.)-University of KwaZulu-Natal, Durban, 2012.

This thesis proposes a probabilistic level set method to be used in segmentation of tumors with heterogeneous intensities. It models the intensities of the tumor and surrounding tissue using Gaussian mixture models. Through a contour based initialization procedure samples are gathered to be used in expectation maximization of the mixture model parameters. The proposed method is compared against a threshold-based segmentation method using MRI images retrieved from The Cancer Imaging Archive. The cases are manually segmented and an automated testing procedure is used to find optimal parameters for the proposed method and then it is tested against the threshold-based method. Segmentation times, dice coefficients, and volume errors are compared. The evaluation reveals that the proposed method has a comparable mean segmentation time to the threshold-based method, and performs faster in cases where the volume error does not exceed 40%. The mean dice coefficient and volume error are also improved while achieving lower deviation.

Locating and segmenting objects such as bones or internal organs is a common problem in medical imaging. Existing segmentation methods are often cumbersome to use for medical staff, since they require a close initial guess and a range of different parameters to be set appropriately. For this work, we present a two-stage segmentation framework which relies on an initial isosurface interactively extracted by topological analysis. The initial isosurface seldom provides a correct segmentation, so we refine the surface using an iterative level set method to better match the desired object boundary. We present applications and improvements to both the flexible isosurface interface and level set segmentation without edges.

The Particle Level set method is a successful extension to Level set methods to improve thevolume preservation in fluid simulations. This thesis will analyze how sparse volume data structures can be used to store both the signed distance function and the particles in order to improve access speed and memory efficiency. This Particle Level set implementation will be evaluated against Digital Domains current Particle Level set implementation. Different degrees of quantization will be used to implement particle representations with varying accuracy. These particles will be tested and both visual results and error measurments will be presented. The sparse volume data structures DB-Grid and Field3D will be evaluated in terms of speed and memory efficiency.