Narrow Band Level Set Research Articles

Prediction–correction projection immersed interface method for interfacial stress-induced flows and applications to electrohydrodynamics

We propose a robust, high-resolution prediction–correction projection immersed interface method (IIM) for solving the unsteady incompressible Navier–Stokes equations with traction boundary conditions, which arise from free surface flows driven by capillary, electric, and elastic forces. This method combines the advantages of traditional body-fitted moving mesh methods and immersed boundary methods (IBM), allowing for the accurate imposition of boundary conditions on free surfaces using Cartesian grids and providing detailed interface information that is typically smoothed out in traditional IBM. The irregular liquid-phase domain is embedded within a square region and discretized using a dynamically adaptive Cartesian mesh. The free surface is captured using a narrow-band level set with hybrid reinitialization. A prediction–correction projection scheme is constructed, incorporating additional pressure predictions and corrections to enhance robustness. The resulting Helmholtz/Poisson equations are solved using the augmented IIM for boundary value problems. Grid refinement analysis demonstrates second-order convergence of the L∞ error, even in challenging cases such as the oscillating drop test with low viscosity. We further apply this method to electrohydrodynamic (EHD) problems, constructing an implicit augmented IIM to solve the equations governing the electric field and charge conservation. Numerical experiments demonstrate that this method accurately addresses highly intense EHD phenomena, such as the formation of Taylor cones, highlighting its robustness.

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.

Multi-level voxel representations for digital twin models of tunnel geological environment

• An efficient linear segmentation-based multi-level voxel representation method is proposed, aiming to represent the geological environment of the long and deep tunnel. Based on the results of the comparative experiment, the spatial efficiency was augmented by 30% approximately by using this technique. • VDB data structure is used to meet the dynamic update requirement of the digital twin applications. It has the consistent time complexity of random access and uses a narrow-band level set to reduce space complexity. • Multi-source data is integrated to represent the multi-feature geological environment. Four typical data with different modalities (parametric BIM model, B-rep solid model, triangle mesh model, 3D regular grid model) are successfully integrated into the digital twin model. Intelligent tunnel engineering requires accurate and comprehensive digital twin models to represent complex geological environments. The digital twin model of tunnel geological environment has multi-level and diversified in-depth applications such as problem diagnosis, risk assessment, trend prediction, emergency response, etc. Since tunnel construction is a long-term continuous dynamic spatial–temporal progress, the tunnel face constantly advances during excavations. Thus, the geological conditions of the construction surface and surrounding areas are continuously revealed and updated, which causes the digital twin model to have a very high update frequency of the geological information in tunnel engineering. The existing methods fail to represent and update the geological environment comprehensively and in real-time, especially for those long deep tunnels with the complicated topology of geological structures and the heterogeneous distribution of internal properties. Due to the digital twin application having a high-level requirement of completeness, accuracy, and timeliness, 3D modeling of tunnel geological environments has remained challenging within digital twin application contexts. This study aims to deliver a solution that efficiently represents and updates the geological structures and internal non-uniform properties of tunnel engineering. Since dense voxels can represent inner intricate heterogeneous property information, sparse voxels can efficiently represent complex structural information. Meanwhile, voxels using Volumetric Dynamic B + trees (VDB) data structure are easy to integrate and update. However, according to the characteristics of long strip distribution of tunnel geological environments, directly using the VDB will still cause an efficiency problem. Therefore, this study proposes an efficient linear segmentation-based multi-level voxel representation method for the prolonged deep tunnel geological environment using the VDB data structure to support dynamic updates. The typical Mountain Tunnel of China is employed for experimental analysis to validate the proposed method, and four representative data with different modalities are integrated into the digital twin model. The results demonstrate that spatial efficiency augments 28.49% after segmentation, and data access with O(1) time complexity supports efficiently dynamic updates.

Hierarchical median narrow band for level set segmentation of cervical cell nuclei

This paper presents a novel hierarchical nuclei segmentation algorithm for isolated and overlapping cervical cells based on a narrow band level set implementation. Our method applies a new multiscale analysis algorithm to estimate the number of clusters in each image region containing cells, which turns into the input to a narrow band level set algorithm. We assess the nuclei segmentation results on three public cervical cell image databases. Overall, our segmentation method outperformed six state-of-the-art methods concerning the number of correctly segmented nuclei and the Dice coefficient reached values equal to or higher than 0.90. We also carried out classification experiments using features extracted from our segmentation results and the proposed pipeline achieved the highest average accuracy values equal to 0.89 and 0.77 for two-class and three-class problems, respectively. These results demonstrated the suitability of the proposed segmentation algorithm to integrate decision support systems for cervical cell screening.

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.

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.

Power diagrams and sparse paged grids for high resolution adaptive liquids

We present an efficient and scalable octree-inspired fluid simulation framework with the flexibility to leverage adaptivity in any part of the computational domain, even when resolution transitions reach the free surface. Our methodology ensures symmetry, definiteness and second order accuracy of the discrete Poisson operator, and eliminates numerical and visual artifacts of prior octree schemes. This is achieved by adapting the operators acting on the octree's simulation variables to reflect the structure and connectivity of a power diagram , which recovers primal-dual mesh orthogonality and eliminates problematic T-junction configurations. We show how such operators can be efficiently implemented using a pyramid of sparsely populated uniform grids, enhancing the regularity of operations and facilitating parallelization. A novel scheme is proposed for encoding the topology of the power diagram in the neighborhood of each octree cell, allowing us to locally reconstruct it on the fly via a lookup table, rather than resorting to costly explicit meshing. The pressure Poisson equation is solved via a highly efficient, matrix-free multigrid preconditioner for Conjugate Gradient, adapted to the power diagram discretization. We use another sparsely populated uniform grid for high resolution interface tracking with a narrow band level set representation. Using the recently introduced SPGrid data structure, sparse uniform grids in both the power diagram discretization and our narrow band level set can be compactly stored and efficiently updated via streaming operations. Additionally, we present enhancements to adaptive level set advection, velocity extrapolation, and the fast marching method for redistancing. Our overall framework gracefully accommodates the task of dynamically adapting the octree topology during simulation. We demonstrate end-to-end simulations of complex adaptive flows in irregularly shaped domains, with tens of millions of degrees of freedom.

Coastline Detection in SAR Images Using a Hierarchical Level Set Segmentation

This paper proposes a new coastline detection method for both single-polarization and quad-polarization synthetic aperture radar (SAR) images. Unlike other coarse-to-fine methods using a combination of two boundary extraction techniques in two layers, the proposed method extracts coastlines by a hierarchical structure from coarse one to fine one using level set and narrow-band level set techniques. The number of layers in the hierarchical structure is adaptive and controlled by an offset analysis of the coarse result. In the method, coarse coastline is first extracted by the level set algorithm with filtered data because the scattering of land and ocean are varied. A multilayer level set segmentation, performed in a narrow band, is then applied to gradually locate more accurate coastlines to decrease the offset in the coarse result caused by the smoothing processing. Finally, the determination of the structure parameters of the proposed method is analyzed through the calculated offset. A number of real polarimetric SAR images are used for validation. Experimental results show that the proposed method is more accurate and is less sensitive to the initial parameters than the other typical method based on level set with filtered or unfiltered data. In addition, the experimental results also show that the proposed method is robust and accurate for data of different microwave bands and different coastal environments.

Multiphase permittivity imaging using absolute value electrical capacitance tomography data and a level set algorithm.

Multiphase flow imaging is a very challenging and critical topic in industrial process tomography. In this article, simulation and experimental results of reconstructing the permittivity profile of multiphase material from data collected in electrical capacitance tomography (ECT) are presented. A multiphase narrowband level set algorithm is developed to reconstruct the interfaces between three- or four-phase permittivity values. The level set algorithm is capable of imaging multiphase permittivity by using one set of ECT measurement data, so-called absolute value ECT reconstruction, and this is tested with high-contrast and low-contrast multiphase data. Simulation and experimental results showed the superiority of this algorithm over classical pixel-based image reconstruction methods. The multiphase level set algorithm and absolute ECT reconstruction are presented for the first time, to the best of our knowledge, in this paper and critically evaluated. This article is part of the themed issue 'Supersensing through industrial process tomography'.

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.

Treatment of contact separation in Eulerian high-speed multimaterial dynamic simulations

SUMMARY A frictionless contact separation treatment in a sharp-interface Eulerian framework is presented to handle the general situation of high-speed impact and separation of materials. The algorithm has been developed for an established Eulerian-based Cartesian grid multimaterial flow code in which the interfaces are tracked in a sharp manner using a standard narrow-band level set approach. Boundary conditions have been applied using a modified ghost fluid method for elasto-plastic materials. The sharp-interface treatment maintains the distinct interacting interfaces without smearing the contact zone while also removing the difficulties associated with Lagrangian moving mesh entities in contact-separation situations. The algorithm has been tested and verified against experimental and numerical results for three different problems in the high strain rate regime, which involve contact, separation and sliding of materials. Copyright © 2014 John Wiley & Sons, Ltd.

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.

Detection and Extraction of Moving Object in Intelligent Surveillance System

To solve the low automatic degree and low accurate alarm rate in the traditional intelligent surveillance system, a motion object segmentation algorithm based on level set method is proposed and implemented. The algorithm gains the primal contour curve by luminance difference between the video frames, and sets the curve as the primal zero level set. Then the narrow band level set algorithm is used to evolve the curve until achieving the segmentation result. Experimental results show that this method can greatly save the level set segmentation time and increase the detecting efficiency.

Detecting end-effectors on 2.5D data using geometric deformable models: Application to human pose estimation

End-effectors are usually related to the location of limbs, and their reliable detection enables robust body tracking as well as accurate pose estimation. Recent innovation in depth cameras has re-stated the pose estimation problem. We focus on the information provided by these sensors, for which we borrow the name 2.5D data from the Graphics community. In this paper we propose a human pose estimation algorithm based on topological propagation. Geometric Deformable Models are used to carry out such propagation, implemented according to the Narrow Band Level Set approach. A variant of the latter method is proposed, including a density restriction which helps preserving the topological properties of the object under analysis. Principal end-effectors are extracted from a directed graph weighted with geodesic distances, also providing a skeletal-like structure describing human pose. An evaluation against reference methods is performed with promising results. The proposed solution allows a frame-wise end-effector detection, with no temporal tracking involved, which may be generalized to the tracking of other objects beyond human body.

Tensor-SIFT Based Earth Mover’s Distance for Contour Tracking

Contour tracking in complex environments is a difficult problem due to the cluttered backgrounds, illumination changes, occlusion and camera viewpoint variations etc. This paper presents a region functional based on the Earth Mover's Distance (EMD), computation of which is mathematically modeled as the transportation problem (TP), for robust contour tracking in the challenging conditions. Formulation of EMD-based functional can be described as variational EMD (VEMD) since the contour curve function is involved for optimization. Minimizing the EMD-based functional is nontrivial and we develop a two-phase method for its optimization. In the first phase, letting the candidate contour be fixed, we seek the best solution to the TP by the Simplex algorithm. Then through the shape derivative theory, we make a perturbation analysis of the contour around the best solution to the TP. As a result we obtain a partial differential equation (PDE) that is solved by the level-set algorithm. The two-phase procedure iterates until the appropriate stopping criterions are satisfied. Alongside the EMD-based functional formulation, we introduce a dimensionality reduction method by tensor decomposition, achieving a low-dimensional Tensor-SIFT features for object representation. Applicable to both the color and gray-level images, Tensor-SIFT features are distinctive, insensitive to illumination and viewpoint changes. Finally, we develop an integrated algorithm that combines various techniques, e.g. the Simplex algorithm, narrow-band level set and fast marching algorithms. Particularly, we provide a method for the level-set initialization between two successive frames and the criterions for stopping the iterative functional optimization. Experiments in challenging image sequences show that the proposed work has promising performance.

Parallel, sharp interface Eulerian approach to high-speed multi-material flows

This paper describes the challenges in developing a parallel implementation of a sharp interface high-speed multi-material dynamics solver. To facilitate large scale computations the algorithm is designed to retain strict data localization on processors. A high-order conservative ENO scheme is used for calculating the numerical fluxes and level sets are used to define the objects immersed in the flow field. A modified ghost fluid method is used for interface treatment of embedded objects. The issues involved in parallelization of the moving boundary flow solver are presented with emphasis on strong shocks interacting with embedded interfaces (solid–fluid and solid–solid) in a three-dimensional compressible flow framework. The handling of moving boundaries tracked using a narrow-band level set technique leads to issues peculiar to the multi-processor environment. The solution to object passage between sub-domains and treatment of ghost regions for inter-processor communication are addressed in the current work. Example calculations for three-dimensional impact-penetration problems and shocked particulate flows are presented.

A hybrid level set-volume constraint method for incompressible two-phase flow

A second-order hybrid level set-volume constraint method (HLSVC) for numerically simulating deforming boundaries is presented. We combine the HLSVC interface advection algorithm with a two phase flow solver in order to numerically capture deforming bubbles and drops whose actual volume (s) fluctuate about fixed “target” volume (s). Three novel developments are described: (1) a new method for enforcing a volume constraint in which the number of bubbles and drops can change due to merging or splitting, (2) a new, second order, semi-lagrangian narrow band level set reinitialization algorithm, and (3) validation of a two-phase flow numerical method by comparison with linear stability analysis results for a co-flowing liquid jet in gas. The new interface capturing method is tested on benchmark problems in which the velocity is prescribed (passive advection of interfaces) and in which the velocity is determined by the incompressible Navier–Stokes equations for two-phase flow. The error in interface position when using the hybrid level set-volume constraint method is reported for many benchmark problems in polar coordinates, cylindrical coordinates, and on an adaptive grid in which one criteria of adaptivity is the magnitude of the interface curvature.