Narrow Band Level Set Method Research Articles

Analysis of Interaction of Multiple Cracks Based on Tip Stress Field Using Extended Finite Element Method

A new method is presented to study the interaction of multiple cracks, especially for the areas near crack tips by using the extended finite element method. In order to track the cracks, a new geometric tracking technique is proposed to track enriched elements and nodes along the crack instead of using the narrow band level set method. This allows to accurately determine enriched elements and nodes and calculate enrichment values. A method is proposed for constructing a multicrack matrix, which involves numbering enriched nodes of multiple cracks and solving the global stiffness matrix. In this approach, the stress fields around multiple cracks can be studied. The interaction integral method is employed to study the crack propagation and its direction by calculating the stress intensify factor. The developed model has been coded in MATLAB environment and validated against analytical solutions. The application of the model in the crack interaction study is demonstrated through a number of examples. The results illustrate the influence of the interaction of multiple cracks as they approach each other.

Learning-based prediction of wildfire spread with real-time rate of spread measurement

A learning-based wildfire spread model was developed in this study to predict short-term wildfire spread. Real-time rate of spread (RoS) measurement was first conducted by calculating normal movements of fire fronts. Subsequently, machine learning was employed to correlate the local RoS and environmental parameters and predict the RoS in the unburnt area. After that, a narrow-band level-set method was utilized to simulate the evolution of fire front. RoS measurement, machine learning, and level-set method were individually verified with numerically generated fire fronts, and applied in a real scale shrubland fire scenario. Results show that the proposed learning-based method is capable of predicting short-term fire spread without employing an empirical RoS model, which is beneficial for modeling spreading of a real wildfire.

Shape-appearance constrained segmentation and separation of vein and artery in pulsatile tinnitus patients based on MR angiography and flow MRI

This study reports on the development and evaluation of a novel segmentation method for extracting the internal jugular vein and the adjacent carotid artery from magnetic resonance (MR) images of patients with pulsatile tinnitus. A narrow band level set method with combined shape and appearance constraints was developed and applied to high-resolution MR images from 17 pulsatile tinnitus patients (age 52 ± 23 years, 10 females). The proposed method was validated by comparing with the manual segmentation as well as by identifying the jugular vein and carotid artery based on 4D flow MRI in which the two types of vessels have opposing flow. Our study showed that the vein and artery are in contact with each other on 30.2% of all the slices. Dice value, Peak signal-to-noise ratio (PSNR), Hausdorff distance and mean sum of square distance (MSSD) between automatic and manual segmentation were 89.13 ± 2.84%, 27.36 ± 2.39%, 17.2 ± 6.9 mm, 7.4 ± 5.5 mm, demonstrating good segmentation accuracy. The average Dice similarity coefficient and the coefficient of variation compared with 4D flow MRI was 91.42 ± 1.63% and 89.28 ± 4.54% for the internal jugular vein and the carotid artery. The present pipeline for automatic internal jugular vein quantification holds promise for efficient image interpretation in large-scale cohort studies.

Multiplayer Pursuit-Evasion Games in Three-Dimensional Flow Fields

In this paper, we deal with a pursuit-evasion differential game between multiple pursuers and multiple evaders in the three-dimensional space under dynamic environmental disturbances (e.g., winds, underwater currents). We first recast the problem in terms of partitioning the pursuer set and assign each pursuer to an evader. We present two algorithms to partition the pursuer set from either the pursuer’s perspective or the evader’s perspective. Within each partition, the problem is reduced into a multi-pursuer/single-evader game. This problem is then addressed through a reachability-based approach. We give conditions for the game to terminate in terms of reachable set inclusions. The reachable sets of the pursuers and the evader are obtained by solving their corresponding level set equations through the narrow band level set method. We further demonstrate why fast marching or fast sweeping schemes are not applicable to this problem for a general class of disturbances. The time-optimal trajectories and the corresponding optimal strategies can be retrieved afterward by traversing these level sets. The proposed scheme is implemented on problems with both simple and realistic flow fields.

Lithographic source and mask optimization with narrow-band level-set method.

Source and mask optimization (SMO) remains a key technique to improve the wafer image printability for technology nodes of 22 nm and beyond, enabling the continuation of the immersion lithography. In this paper, we propose a distance level-set regularized reformulation of the SMO maintaining the desired signed distance property, which secures stable curve evolution and accurate computation with a simpler and more efficient numerical implementation. Consequently, computation load caused by convolution operations and memory requirements of the electric-field caching technique (EFCT) is significantly eased by performing computation only in the narrow band; moreover, the convergence of the updating process is further improved by applying larger Euler time steps of the Courant-Friedrichs-Lewy (CFL) condition with reduced optimization dimensionality. Simulation results of the proposed narrow-band level-set based SMO prove to improve the computation efficiency, memory usage and imaging performance of the full domain methods.

Three-Dimensional Simulation of DRIE Process Based on the Narrow Band Level Set and Monte Carlo Method.

A three-dimensional topography simulation of deep reactive ion etching (DRIE) is developed based on the narrow band level set method for surface evolution and Monte Carlo method for flux distribution. The advanced level set method is implemented to simulate the time-related movements of etched surface. In the meanwhile, accelerated by ray tracing algorithm, the Monte Carlo method incorporates all dominant physical and chemical mechanisms such as ion-enhanced etching, ballistic transport, ion scattering, and sidewall passivation. The modified models of charged particles and neutral particles are epitomized to determine the contributions of etching rate. The effects such as scalloping effect and lag effect are investigated in simulations and experiments. Besides, the quantitative analyses are conducted to measure the simulation error. Finally, this simulator will be served as an accurate prediction tool for some MEMS fabrications.

A Framework for Segmentation of Inhomogeneous Live Cell Images using Fractional Derivatives and Level Set Method

Cell segmentation has gained significant importance in modern biological image processing applications. The commonly used image segmentation algorithms are region based and depend on the homogeneity of the intensities of the pixels in the region of interest. But due to the highly inhomogeneous behavior of cell nuclei and background, feature overlapping between the two regions lead to misclassification and poor segmentation results. This paper proposes a method to segment the cell images taking into consideration the intensity inhomogeneity issue. A fractional differential term has been introduced in the clustering criteria for bias correction for improving the homogeneity of the cell images. A method to optimize the fractional order for images has also been proposed. Further an improved narrow band level set method using Chan Vese model has been proposed to improve the computational speed of the algorithm. The proposed method is evaluated on datasets of 2D microscopy images and images with improved homogeneity have been obtained. The results also show improved segmentation results and the time efficient bahaviour of the proposed method.

The Research of Image Segmentation Algorithm Based on Narrowband Level Set Method

The Research of Image Segmentation Algorithm Based on Narrowband Level Set Method

Multi-phase flow monitoring with electrical impedance tomography using level set based method

In this paper, a level set-based reconstruction scheme is applied to multi-phase flow monitoring using electrical impedance tomography (EIT). The proposed scheme involves applying a narrowband level set method to solve the inverse problem of finding the interface between the regions having different conductivity values. The multi-phase level set model for the conductivity distribution inside the domain is represented by two level set functions. The key principle of the level set-based method is to implicitly represent the shape of interface as the zero level set of higher dimensional function and then solve a set of partial differential equations. The level set-based scheme handles topological merging and breaking naturally during the evolution process. It also offers several advantages compared to traditional pixel-based approach. Level set-based method for multi-phase flow is tested with numerical and experimental data. It is found that level set-based method has better reconstruction performance when compared to pixel-based method.

Three-dimensional simulation of surface topography evolution in the Bosch process by a level set method

A deep reactive ion etching (DRIE) process (Bosch process) is used extensively in the fabrication of microelectromechanical systems (MEMS). Modeling and simulation studies have helped improve our understanding and process design. The Bosch process consists of multiple cycles of alternating etching and deposition steps. Based on a narrow band level set method, by integrating etching simulation and deposition simulation modules, a simulation system is proposed for three-dimensional (3-D) simulation of the Bosch process with arbitrarily complex mask shapes. To verify the simulation system, a series of simulations and experiments have been performed. The simulation results are in good agreement with the experiments. The method may be used to optimize the practical Bosch process and to design and control the profile of high-aspect ratio microstructures.

A composite Level Set and Extended-Domain-Eigenfunction Method for simulating 2D Stokes flow involving a free surface

In this paper, the Extended-Domain-Eigenfunction-Method (EDEM) is combined with the Level Set Method in a composite numerical scheme for simulating a moving boundary problem. The liquid velocity is obtained by formulating the problem in terms of the EDEM methodology and solved using a least square approach. The propagation of the free surface is effected by a narrow band Level Set Method. The two methods both pass information to each other via a bridging process, which allows the position of the interface to be updated. The numerical scheme is applied to a series of problems involving a gas bubble submerged in a viscous liquid moving subject to both an externally generated flow and the influence of surface tension.

A level set methodology for predicting the surface evolution of inclined masked micro-channels resulting from abrasive jet micro-machining at oblique incidence

A novel implementation of narrow band level set methods (LSM) was used to predict the surface evolution of inclined masked micro-channels in glass and poly-methyl-methacrylate (PMMA) made using abrasive jet micro-machining (AJM) at oblique incidence. The resulting inclined PMMA channels had straight walls and rectangular bottoms, while the glass profiles had curved walls and rounded bottoms. The inclined micro-channels rapidly become multi-valued, and the Hamilton–Jacobi type partial differential equation describing their evolution cannot be solved using traditional analytical or numerical techniques. To predict the decrease in particle flux at the mask edge, a previously developed analytical model was generalized from the normal to the oblique incidence case. The local surface velocity function was non-convex, necessitating the development of a modified extension velocity methodology to address the problem of grid ‘visibility’ of the particle flux. The agreement between LSM-predicted and measured surface evolution was fair. Since in its current form the model ignores particle ‘second-strike effects’ and mask wear, it is best suited to predict AJM surface evolution in ductile targets where mask wear is minimal, and not for brittle targets (e.g. glass). Since AJM at oblique incidence can be used to machine three-dimensional suspended micro-structures, the work has important implications for the micro-fabrication of novel MEMS and microfluidic devices.

The Piecewise Smooth Mumford–Shah Functional on an Arbitrary Graph

The Mumford-Shah functional has had a major impact on a variety of image analysis problems, including image segmentation and filtering, and, despite being introduced over two decades ago, it is still in widespread use. Present day optimization of the Mumford-Shah functional is predominated by active contour methods. Until recently, these formulations necessitated optimization of the contour by evolving via gradient descent, which is known for its overdependence on initialization and the tendency to produce undesirable local minima. In order to reduce these problems, we reformulate the corresponding Mumford-Shah functional on an arbitrary graph and apply the techniques of combinatorial optimization to produce a fast, low-energy solution. In contrast to traditional optimization methods, use of these combinatorial techniques necessitates consideration of the reconstructed image outside of its usual boundary, requiring additionally the inclusion of regularization for generating these values. The energy of the solution provided by this graph formulation is compared with the energy of the solution computed via traditional gradient descent-based narrow-band level set methods. This comparison demonstrates that our graph formulation and optimization produces lower energy solutions than the traditional gradient descent based contour evolution methods in significantly less time. Finally, we demonstrate the usefulness of the graph formulation to apply the Mumford-Shah functional to new applications such as point clustering and filtering of nonuniformly sampled images.

Level-Set Method Applied to Magnetic Induction Tomography Using Experimental Data

Magnetic induction tomography (MIT) can be used to probe electrical conductivity variation of an object. It offers a nondestructive and contactless means of imaging the internal conductivity distribution of the object. The forward problem in MIT is a general eddy current problem, which is required to estimate the measured data for a given conductivity distribution. The edge finite-element method with a formulation using a magnetic vector potential has been implemented to solve the forward problem. Conductivity reconstruction in MIT is a nonlinear and ill-posed inverse problem. The regularization techniques are required to incorporate a priori knowledge of the conductivity distribution for a stable solution of this inverse problem. This article presents a conductivity interface reconstruction technique, which has an inherent regularization property. Instead of calculating the conductivity distribution in the whole region of interest, the interface between two different conductivities is reconstructed. A narrowband level-set method has been implemented to describe the interfaces. An iterative optimization scheme has been used to modify the interface estimation in each iteration step, so that the predicated forward solution is closed to the measured data. The results are presented using experimental data representative of an application of MIT in molten metal flow visualization.

A Narrow-Band Level Set Method Applied to EIT in Brain for Cryosurgery Monitoring

In this paper, we investigate the feasibility of applying a novel level set reconstruction technique to electrical imaging of the human brain. We focus particularly on the potential application of electrical impedance tomography (EIT) to cryosurgery monitoring. In this application, cancerous tissue is treated by a local freezing technique using a small needle-like cryosurgery probe. The interface between frozen and nonfrozen tissue can be expected to have a relatively high contrast in conductivity and we treat the inverse problem of locating and monitoring this interface during the treatment. A level set method is used as a powerful and flexible tool for tracking the propagating interfaces during the monitoring process. For calculating sensitivities and the Jacobian when deforming the interfaces we employ an adjoint formula rather than a direct differentiation technique. In particular, we are using a narrow-band technique for this procedure. This combination of an adjoint technique and a narrow-band technique for calculating Jacobians results in a computationally efficient and extremely fast method for solving the inverse problem. Moreover, due to the reduced number of unknowns in each step of the narrow-band approach compared to a pixel- or voxel-based technique, our reconstruction scheme tends to be much more stable. We demonstrate that our new method also outperforms its pixel-/voxel-based counterparts in terms of image quality in this application.

Fast data extrapolating

Data-extrapolating (extension) technique has important applications in image processing on implicit surfaces and in level set methods. The existing data-extrapolating techniques are inefficient because they are designed without concerning the specialities of the extrapolating equations. Besides, there exists little work on locating the narrow band after data extrapolating—a very important problem in narrow band level set methods. In this paper, we put forward the general Huygens’ principle, and based on the principle we present two efficient data-extrapolating algorithms. The algorithms can easily locate the narrow band in data extrapolating. Furthermore, we propose a prediction–correction version for the data-extrapolating algorithms and the corresponding band locating method for a special case where the direct band locating method is hard to apply. Experiments demonstrate the efficiency of our algorithms and the convenience of the band locating method.

Electrical impedance tomography imaging using a priori ultrasound data

BackgroundDifferent imaging systems (e.g. electrical, magnetic, and ultrasound) rely on a wide variety of physical properties, and the datasets obtained from such systems provide only partial information about the unknown true state. One approach is to choose complementary imaging systems, and to combine the information to achieve a better representation.MethodsThis paper discusses the combination of ultrasound and electrical impedance tomography (EIT) information. Ultrasound reflection signals are good at locating sharp acoustic density changes associated with the boundaries of objects. Some boundaries, however, may be indeterminable due to masking from intermediate boundaries or because they are outside the ultrasound beam. Conversely, the EIT data contains relatively low-quality information, but it includes the whole region enclosed by the electrodes.ResultsResults are shown from a narrowband level-set method applied to 2D and 3D EIT incorporating limited angle ultrasound time of flight data.ConclusionThe EIT reconstruction is shown to be faster and more accurate using the additional edge information from both one and four transducer ultrasound systems.

A coupled level set-boundary integral method for moving boundary simulations

A numerical method for moving boundary problems based upon level set and boundary integral formulations is presented. The interface velocity is obtained from the boundary integral solution using a Galerkin technique for post-processing function gradients on the interface. We introduce a new level set technique for propagating free boundary values in time, and couple this to a narrow band level set method. Together, they allow us to both update the function values and the location of the interface. The methods are discussed in the context of the well-studied two-dimensional nonlinear potential flow model of breaking waves over a sloping beach. The numerical results show wave breaking and rollup, and the algorithm is verified by means of convergence studies and comparisons with previous techniques. 1. Introduction and overview

Structural Boundary Design via Level Set and Immersed Interface Methods

We develop and test an algorithmic approach to the boundary design of elastic structures. The goal of our approach is two-fold: first, to develop a method which allows one to rapidly solve the two-dimensional Lamé equations in arbitrary domains and compute, for example, the stresses, and second, to develop a systematic way of modifying the design to optimize chosen properties. At the core, our approach relies on two distinct steps. Given a design, we first apply an explicit jump immersed interface method to compute the stresses for a given design shape. We then use a narrow band level set method to perturb this shape and progress towards an improved design. The equations of 2D linear elastostatics in the displacement formulation on arbitrary domains are solved quickly by domain embedding and the use of fast elastostatic solvers. This effectively reduces the dimensionality of the problem by one. Once the stresses are found, the level set method, which represents the design structure through an embedded implicit function, is used in the second step to alter the shape, with velocities depending on the stresses in the current design. Criteria are provided for advancing the shape in an appropriate direction and for correcting the evolving shape when given constraints are violated.

An overview of level set methods for etching, deposition, and lithography development

The range of surface evolution problems in etching, deposition, and lithography development offers significant challenge for numerical methods in front tracking. Level set methods for evolving interfaces are specifically designed for profiles which can develop sharp corners, change topology, and undergo orders of magnitude changes in speed. They are based on solving a Hamilton-Jacobi type equation for a level set function, using techniques borrowed from hyperbolic conservation laws. Over the past few years, a body of level set methods have been developed with application to microfabrication problems. In this paper, we give an overview of these techniques, describe the implementation in etching, deposition, and lithography simulations, and present a collection of fast level set methods, each aimed at a particular application. In the case of photoresist development and isotropic etching/deposition, the fast marching level set method, introduced by Sethian (1996), can track the three-dimensional photoresist process through a 200/spl times/200/spl times/200 rate function grid in under 55 s on a Sparc10. In the case of more complex etching and deposition, the narrow band level set method, introduced in Adalsteinsson and Sethian (1995), can be used to handle problems in which the speed of the interface delicately depends on the orientation of the interface versus an incoming beam, the effects of visibility, surface tension, reflection and re-emission, and complex three-dimensional effects. Our applications include photoresist development, etching/deposition problems under the effects of masking, visibility, complex flux integrations over sources, nonconvex sputter deposition problems, and simultaneous deposition and etch phenomena.