Level Set Formulation Research Articles

Segmentation of Intima Media Complex ofCommon Carotid Artery

Atherosclerosis is a disease of blood vessels caused by the formation of plaques in artery walls. Its diagnosis is one of the most important medical examinations for the prevention of cardiovascular events, like myocardial infarction and stroke. The segmentation of the intima-media complex (IMC) of the common carotid artery (CCA) wall is important for the evaluation of the intima media thickness (IMT) on B-mode ultrasound (US) images. IMT is considered an important marker in the evaluation of the risk for the development of atherosclerosis. Carotid intima media thickness (IMT), which is the distance between the lumen-intima and the media-adventitia interfaces, is a measure of early atherosclerosis. segmentation algorithm is based on active contours and active contours without edges and provides information to achieve accurate segmentation. The level set formulation by Chan and Vese model provides a segmentation of the CCA US images into different distinct regions, one of which corresponds to the carotid wall region below the lumen and includes the far wall IMC.

A local level-set method for 3D inversion of gravity-gradient data

We have developed a local level-set method for inverting 3D gravity-gradient data. To alleviate the inherent nonuniqueness of the inverse gradiometry problem, we assumed that a homogeneous density contrast distribution with the value of the density contrast specified a priori was supported on an unknown bounded domain [Formula: see text] so that we may convert the original inverse problem into a domain inverse problem. Because the unknown domain [Formula: see text] may take a variety of shapes, we parametrized the domain [Formula: see text] by a level-set function implicitly so that the domain inverse problem was reduced to a nonlinear optimization problem for the level-set function. Because the convergence of the level-set algorithm relied heavily on initializing the level-set function to enclose the gravity center of a source body, we applied a weighted [Formula: see text]-regularization method to locate such a gravity center so that the level-set function can be properly initialized. To rapidly compute the gradient of the nonlinear functional arising in the level-set formulation, we made use of the fact that the Laplacian kernel in the gravity force relation decayed rapidly off the diagonal so that matrix-vector multiplications for evaluating the gradient can be accelerated significantly. We conducted extensive numerical experiments to test the performance and effectiveness of the new method.

Segmentation of MR image using local and global region based geodesic model.

BackgroundSegmentation of the magnetic resonance (MR) images is fundamentally important in medical image analysis. Intensity inhomogeneity due to the unknown noise and weak boundary makes it a difficult problem.MethodThe paper presents a novel level set geodesic model which integrates the local and the global intensity information in the signed pressure force (SPF) function to suppress the intensity inhomogeneity and implement the segmentation. First, a new local and global region based SPF function is proposed to extract the local and global image information in order to ensure a flexible initialization of the object contours. Second, the global SPF is adaptively balanced by the weight calculated by using the local image contrast. Third, two-phase level set formulation is extended to a multi-phase formulation to successfully segment brain MR images.ResultsExperimental results on the synthetic images and MR images demonstrate that the proposed method is very robust and efficient. Compared with the related methods, our method is much more computationally efficient and much less sensitive to the initial contour. Furthermore, the validation on 18 T1-weighted brain MR images (International Brain Segmentation Repository) shows that our method can produce very promising results.ConclusionsA novel segmentation model by incorporating the local and global information into the original GAC model is proposed. The proposed model is suitable for the segmentation of the inhomogeneous MR images and allows flexible initialization.

Local and Global Region-Based Curve Evolutions for Image Segmentation

In this paper, we propose a novel region-based active contour model in a variational level set formulation. The energy functional for the proposed model consists of two terms, i.e., global term, local term. Therefore, the combination of these two forces allows for flexible initialization of the contours. This energy is then incorporated into a level set for- mulation with a level set regularization term that is necessary for accurate computation in the corresponding level set method. The proposed model is first presented as a two-phase level set formulation and then extended to a multi-phase formulation. Finally, experiments on some synthetic and real images have demonstrated the efficiency and robustness of our model. Moreover, comparisons with recent popular local image fitting (LIF) model also show that our model is less sensitive to the location of initial contour.

Simulation of Premixed Turbulent Combustion in a Gas Engine using the Immersed Boundary Method and a Level Set Flame Model

AbstractAn efficient simulation approach for turbulent flame brush propagation is a level set formulation closed by the turbulent flame speed. A formulation of the level set equation with the corresponding treatment of the turbulent mass burning rate that is compatible with standard Finite Volume discretization schemes available in computational fluid dynamics codes is employed. In order to simplify and to speed up the meshing process in complicated geometries (here in gas engines) the immersed boundary method in a continuous formulation, where the forces replacing the boundaries are introduced in the momentum conservation equations before discretization, is employed. In our contribution, aspects of the numerical implementation of the level set flame model combined with the immersed boundary formulation in OpenFOAM are presented. First representative simulation results of a homogeneous methane/air mixture combustion in a simplified engine geometry are shown. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

3D vasculature segmentation using localized hybrid level-set method.

BackgroundIntensity inhomogeneity occurs in many medical images, especially in vessel images. Overcoming the difficulty due to image inhomogeneity is crucial for the segmentation of vessel image.MethodsThis paper proposes a localized hybrid level-set method for the segmentation of 3D vessel image. The proposed method integrates both local region information and boundary information for vessel segmentation, which is essential for the accurate extraction of tiny vessel structures. The local intensity information is firstly embedded into a region-based contour model, and then incorporated into the level-set formulation of the geodesic active contour model. Compared with the preset global threshold based method, the use of automatically calculated local thresholds enables the extraction of the local image information, which is essential for the segmentation of vessel images.ResultsExperiments carried out on the segmentation of 3D vessel images demonstrate the strengths of using locally specified dynamic thresholds in our level-set method. Furthermore, both qualitative comparison and quantitative validations have been performed to evaluate the effectiveness of our proposed model.ConclusionsExperimental results and validations demonstrate that our proposed model can achieve more promising segmentation results than the original hybrid method does.

Numerical Modeling and Experimental Validation of Free Surface Flow Problems

In this paper we present a summary of numerical methods for solving free surface and two fluid flow problems. We will focus the attention on level set formulations extensively used in the context of the finite element method. In particular, numerical developments to achieve accurate solutions are described. Specific topics of the algorithms, like mass preservation and interface redefinition, are evaluated. To illustrate these aspects, numerical strategies previously developed are applied to the solution of a sloshing and a water column collapse problems. To assess the capabilities of these techniques, the numerical results are compared against each other and with experimental data. Considering these aspects, the present work is aimed to outline some well reported aspects of level set-like formulations.

Selective invocation of shape priors for deformable segmentation and morphologic classification of prostate cancer tissue microarrays

Shape based active contours have emerged as a natural solution to overlap resolution. However, most of these shape-based methods are computationally expensive. There are instances in an image where no overlapping objects are present and applying these schemes results in significant computational overhead without any accompanying, additional benefit. In this paper we present a novel adaptive active contour scheme (AdACM) that combines boundary and region based energy terms with a shape prior in a multi level set formulation. To reduce the computational overhead, the shape prior term in the variational formulation is only invoked for those instances in the image where overlaps between objects are identified; these overlaps being identified via a contour concavity detection scheme. By not having to invoke all three terms (shape, boundary, region) for segmenting every object in the scene, the computational expense of the integrated active contour model is dramatically reduced, a particularly relevant consideration when multiple objects have to be segmented on very large histopathological images. The AdACM was employed for the task of segmenting nuclei on 80 prostate cancer tissue microarray images from 40 patient studies. Nuclear shape based, architectural and textural features extracted from these segmentations were extracted and found to able to discriminate different Gleason grade patterns with a classification accuracy of 86% via a quadratic discriminant analysis (QDA) classifier. On average the AdACM model provided 60% savings in computational times compared to a non-optimized hybrid active contour model involving a shape prior.

A Modified Level Set Approach for Segmentation of Multiband Polarimetric SAR Images

This paper investigates the application of a level set method for the automated multiphase segmentation of multiband and polarimetric synthetic aperture radar (SAR) images. The level set formulation is used to form an energy functional that includes the image statistical information defined on active contours. In addition to the classical Wishart/Gaussian distribution for locating region boundaries, edge information is incorporated into the energy functional to improve the performance of polarimetric data segmentation. An active contour model with an edge indicator is proposed by assuming that the image boundary term follows a Gibbs prior. An empirical parameter setting criterion is developed to ensure that the components of the energy functional are in proper proportion. We then investigate the multiphase extension for energy minimization, and we use a piecewise constant model to embed the proposed active contour model. Synthetic and real multiband polarimetric SAR data are used for verification. The experiments show that our method is superior to another level set method based on the Wishart/Gaussian distribution, in which SAR edge information is not included, particularly for discriminating among low-contrast regions. Furthermore, results also show that segmentation is improved when multiband data are used in the level set framework.

An adaptive level set approach for modeling damage due to galvanic corrosion

This article presents an approach to solving problems related to galvanic corrosion that involve moving boundaries (due to preferential corrosion of one of the metals in the system). The method incorporates an adaptive (node based, finite difference) grid technique for the treatment of boundary-related singularities that arise in the calculation of the electric potential. Simulation of the time evolution of the damage done by the corroding interface is performed using of a level set formulation. An analysis of the convergence of the method and a comparison with experimental data from the literature are included.

Influence of anisotropic grain boundary properties on the evolution of grain boundary character distribution during grain growth—a 2D level set study

The present study elaborates on a 2D level set model of polycrystal microstructures that was recently established by adding the influence of anisotropic grain boundary energy and mobility on microstructure evolution. The new model is used to trace the evolution of grain boundary character distribution during grain growth. The employed level set formulation conveniently allows the grain boundary characteristics to be quantified in terms of coincidence site lattice (CSL) type per unit of grain boundary length, providing a measure of the distribution of such boundaries. In the model, both the mobility and energy of the grain boundaries are allowed to vary with misorientation. In addition, the influence of initial polycrystal texture is studied by comparing results obtained from a polycrystal with random initial texture against results from a polycrystal that initially has a cube texture. It is shown that the proposed level set formulation can readily incorporate anisotropic grain boundary properties and the simulation results further show that anisotropic grain boundary properties only have a minor influence on the evolution of CSL boundary distribution during grain growth. As anisotropic boundary properties are considered, the most prominent changes in the CSL distributions are an increase of general low-angle Σ1 boundaries as well as a more stable presence of Σ3 boundaries. The observations also hold for the case of an initially cube-textured polycrystal. The presence of this kind of texture has little influence over the evolution of the CSL distribution. Taking into consideration the anisotropy of grain boundary properties, grain growth alone does not seem to be sufficient to promote any significantly increased overall presence of CSL boundaries.

A Level-Set Method for Analysis of Particle Motion in an Evaporating Microdroplet

A sharp-interface level-set (LS) method is presented for computing particle motion in an evaporating microdroplet. The LS formulation for incompressible two-phase flow is extended to include the effects of evaporation, mass transfer, heat transfer, and dynamic contact angles. A numerical technique for the conservation of particle concentration is incorporated into the LS method, and calculation procedures are also developed and tested for reducing the numerical errors caused in the computation of interface curvature and liquid–gas velocity jump. The improved LS method is applied to the simulation of particle distribution in microdroplet evaporation on a solid surface.

A novel active contour model driven by local and global intensity fitting energies

In this paper, we propose a novel hybrid active contour model for image segmentation. In our model, we define a new region-scalable fitting (RSF) energy functional which combines the local and the global image information. The RSF energy functional can not only attract the contour toward object boundaries, but also improve the robustness to initialization of the contours. In order to segment the image fast and accurately, the length term and regularization term is incorporated into the variational level set formulation. Finally, by adopting gradient descent method, the minimization of the energy equation can be given. Due to the new kernel function we defined, our model can cope with intensity inhomogeneity images and less sensitive to the initialization of the contour when compared with the other models. Experimental results demonstrated that the proposed model can also segment both the real and medical images accurately.

Canny based DRLSE Algorithm for Segmentation

Image segmentation is typically used to locate objects and boundaries in images. The objective of this application is the segmentation of different medical images. Edge detection significantly reduces the amount of data and filters out useless information, while preserving the important structural properties in an image. Medical image segmentation is one of the most important parts of clinical diagnostic tools. However, the process of accurate segmentation of these images is very important and crucial for a correct diagnosis by clinical tools. In this paper canny operator based Distance Regularization Level Set Evolution Algorithm (DRLSE) is used. The distance regularization effect eliminates the need for reinitialization and thereby avoids its induced numerical errors. First canny operator is used to determine the edges and edge directions. Then a new variation level set formulation is used in which the regularity of the level set function is intrinsically maintained during the level set evolution. The level set evolution is derived as the gradient flow that minimizes energy functional with a distance regularization term and an external energy that drives the motion of the zero level set toward desired locations. The distance regularization term is defined with a potential function such that the derived level set evolution has a unique forward-and-backward (FAB) diffusion effect, which is able to maintain a desired shape of the level set function, particularly a signed distance profile near the zero level set. Proposed algorithm is used for database of different medical images such as Brain, Eye & Comparison of the same algorithm for those images by using different parameters is done.

Nonlinear PDE based numerical methods for cell tracking in zebrafish embryogenesis

The paper presents numerical algorithms leading to an automated cell tracking and reconstruction of the cell lineage tree during the first hours of animal embryogenesis. We present results obtained for large-scale 3D+time two-photon laser scanning microscopy images of early stages of zebrafish (Danio rerio) embryo development. Our approach consists of three basic steps – the image filtering, the cell centers detection and the cell trajectories extraction yielding the lineage tree reconstruction. In all three steps we use nonlinear partial differential equations. For the filtering the geodesic mean curvature flow in level set formulation is used, for the cell center detection the motion of level sets by a constant speed regularized by mean curvature flow is used and the solution of the eikonal equation is essential for the cell trajectories extraction. The core of our new tracking method is an original approach to cell trajectories extraction based on finding a continuous centered paths inside the spatio-temporal tree structures representing cell movement and divisions. Such paths are found by using a suitably designed distance function from cell centers detected in all time steps of the 3D+time image sequence and by a backtracking in the steepest descent direction of a potential field based on this distance function. We also present efficient and naturally parallelizable discretizations of the aforementioned nonlinear PDEs and discuss properties and results of our new tracking method on artificial and real 4D data.

A sharp-interface level-set method for analysis of Marangoni effect on microdroplet evaporation

A level-set method is presented for computation of microdroplet evaporation including not only the effects of heat and mass transfer, phase change and contact line dynamics but also the Marangoni effect, which is a key parameter affecting the internal flow of the droplet and the particle deposition pattern. A sharp-interface formulation of the Marangoni force is derived and tested for two-phase Marangoni convection in a cavity. The computed results show good convergence in both the liquid and gas regions and are in excellent agreement with the analytical solutions. The level-set formulation is applied to microdroplet evaporation on a solid surface to investigate the Marangoni effect.

A convex variational level set model for image segmentation

In this paper, we propose a strictly convex energy functional in a level set formulation for the purpose of two-phase image segmentation. We prove that the value of the unique global minimizer for the energy functional is within the interval [−1, 1] for any image, and equals to 1 in the object and −1 in the background for an ideal binary image. A pointwise convergent numerical scheme is presented to solve the gradient descent flow equation. The proposed model is allowed for flexible initialization and can set a reasonable termination criterion on the algorithm. The proposed model has been successfully applied to some synthesized and real images with promising results.

Split Bregman Method for Minimization of Fast Multiphase Image Segmentation Model for Inhomogeneous Images

In this paper, we present a fast multiphase image segmentation model in a variational level set formulation. The proposed model is mainly used for images with inhomogeneity. The newly defined energy functional combines the local intensity information, the global intensity information, and the edge information to deal with the inhomogeneity. We use a weight function varying with locations to control the force of the local and global information dynamically. The special structure of the new energy functional ensures that the split Bregman method can be used for fast minimization. We apply the split Bregman method to minimize the new energy functional and summarize important results in several theorems. Theoretical evidences for these results are given. Several numerical results are also presented.

Coupled fluid-structure interaction simulation of floating offshore wind turbines and waves: a large eddy simulation approach

We develop a computational framework for simulating the coupled interaction of complex floating structures with large-scale ocean waves and atmospheric turbulent winds. The near-field approach features a partitioned fluid-structure interaction model (FSI) combining the curvilinear immersed boundary (CURVIB) method of Borazjani and Sotiropoulos (J. Comput. Phys. 2008) and the two-phase flow level set formulation of Kang and Sotiropoulos (Adv. in Water Res. 2012) and is capable of solving complex free-surface flows interacting non-linearly with complex real life floating structures. The near-field solver is coupled with a large-scale wave and wind model based on the two-fluid approach of Yang and Shen (J. Comput. Phys. 2011) which integrates a viscous Navier-Stokes solver with undulatory boundaries for the motion of the air and an efficient potential-flow based wave solver. The large-scale turbulent wind is incorporated from the far-field solver to the near-field solver by feeding into the latter inlet boundary conditions. The wave field is incorporated to the near-field solver by using the pressure-forcing method of Guo and Shen (J. Comput. Phys. 2009) which has been appropriately adapted to the level set method. The algorithm for coupling the two codes has been validated for a variety of wave cases including a broadband spectrum showing excellent agreement when compared to theoretical results. Finally, the capabilities of the numerical framework are demonstrated by carrying out large eddy simulation (LES) of a floating wind turbine interacting with realistic ocean wind and wave conditions.

Improving level set method for fast auroral oval segmentation.

Auroral oval segmentation from ultraviolet imager images is of significance in the field of spatial physics. Compared with various existing image segmentation methods, level set is a promising auroral oval segmentation method with satisfactory precision. However, the traditional level set methods are time consuming, which is not suitable for the processing of large aurora image database. For this purpose, an improving level set method is proposed for fast auroral oval segmentation. The proposed algorithm combines four strategies to solve the four problems leading to the high-time complexity. The first two strategies, including our shape knowledge-based initial evolving curve and neighbor embedded level set formulation, can not only accelerate the segmentation process but also improve the segmentation accuracy. And then, the latter two strategies, including the universal lattice Boltzmann method and sparse field method, can further reduce the time cost with an unlimited time step and narrow band computation. Experimental results illustrate that the proposed algorithm achieves satisfactory performance for auroral oval segmentation within a very short processing time.