Level set (data structures)

Abstract: This paper proposes a novel semiautomatic method to extract the pancreas from abdominal CT images. Traditional level set and region growing methods that request locating initial contour near the final boundary of object have problem of leakage to nearby tissues of pancreas region. The proposed method consists of a customized fast-marching level set method which generates an optimal initial pancreas region to solve the problem that the level set method is sensitive to the initial contour location and a modified distance regularized level set method which extracts accurate pancreas. The novelty in our method is the proper selection and combination of level set methods, furthermore an energy-decrement algorithm and an energy-tune algorithm are proposed to reduce the negative impact of bonding force caused by connected tissue whose intensity is similar with pancreas. As a result, our method overcomes the shortages of oversegmentation at weak boundary and can accurately extract pancreas from CT images. The proposed method is compared to other five state-of-the-art medical image segmentation methods based on a CT image dataset which contains abdominal images from 10 patients. The evaluated results demonstrate that our method outperforms other methods by achieving higher accuracy and making less false segmentation in pancreas extraction.

Abstract: In this paper, an improved variational level set method for the Chan-Vese model is proposed to drive level set function to become fast and stably close to signed distance function. A restriction item that is a nonlinear heat equation with balanced diffusion rate is added to the traditional Chan-Vese model, and therefore the costly re-initialization procedure is completely eliminated. The proposed variational level set formulation is implemented by numerical scheme with spatial rotation-invariance gradient and divergence operator. Consequently it computes more efficiently. The proposed algorithm has been applied to medical images with desired results.

Abstract: In this paper, we propose a novel scheme for cell nucleus segmentation which is multi-scale space level set method. Under this scheme, all nuclei of interest in a microscopic image can be segmented simultaneously. The procedure includes three stages. Firstly, the mathematical morphology method is used to search seed points to localize interested nuclei. Secondly, based on the distribution of these seed points, a level set function is initialized. Finally, the level set function evolves and eventually stops zero level set contours at the boundaries of nuclei labeled by seed points. The evolution in the last stage is a three phase evolution. In each phase, information of different scale spaces is employed. This method was tested by truthful microscope images of lymphocyte, which proved its robustness and efficiency.

Abstract: In sampled data systems the controller receives periodically sampled state feedback about the evolution of a continuous time plant, and must choose a constant control signal to apply between these updates; however, unlike purely discrete time models the evolution of the plant between updates is important. In contrast, for systems with nonlinear dynamics existing reachability algorithms|based on Hamilton-Jacobi equations or viability theory|assume continuous time state feedback and the ability to instantaneously adjust the input signal. In this paper we describe an algorithm for determining an implicit surface representation of minimal backwards reach tubes for nonlinear sampled data systems, and then construct switched, set-valued feedback controllers which are permissive but ensure safety for such systems. The reachability algorithm is adapted from the Hamilton-Jacobi formulation proposed in Ding and Tomlin (2010). We show that this formulation is conservative for sampled data systems. We implement the algorithm using approximation schemes from level set methods, and demonstrate it on a modied double integrator.