Level Set Framework Research Articles

On the impact of the mesostructure on the creep response of cellular NiAl-Mo eutectics

Directionally solidified eutectics of NiAl matrix and fibrous refractory metals, like Mo, can form cellular mesostructures with significant fiber misalignment and changing fiber volume fraction, for example, when being solidified at high growth rates or when increased solidification intervals are present in the alloys. In order to reveal the deteriorating impact of the mesostructure, i.e., the volume fraction and aspect ratio of the well-aligned cells, on the creep response of such cellular eutectics, we rely on scale-bridging numerical simulations, using the level-set framework by Sonon et al. [1] for microstructure generation and FFT-based solvers for computing the creep response. Our results indicate, firstly, that the fraction of properly aligned regions in cellular NiAl composites is lower than estimated in earlier experimental studies, due to the existence of degenerated regions surrounding the well-aligned cell interiors. Secondly, studying the influence of the cell aspect ratio shows that the apparent stress exponent of the composite is very sensitive with respect to this parameter, providing a possible explanation for the large scatter of experimentally determined stress exponents in previous studies. A comparison of the numerical simulations to a linear rule of mixtures and the frequently applied analytical Kelly-Street model illustrates that both fail to accurately describe the magnitude of minimum creep rates in the investigated ranges of volume fractions and aspect ratios. The heterogeneity of the strain-rate field on the mesoscale is identified as the primary error source, demonstrating that either numerical simulations or more sophisticated analytical models are required for reliably predicting for the creep response of cellular materials.

AVLSM: Adaptive Variational Level Set Model for Image Segmentation in the Presence of Severe Intensity Inhomogeneity and High Noise.

Intensity inhomogeneity and noise are two common issues in images but inevitably lead to significant challenges for image segmentation and is particularly pronounced when the two issues simultaneously appear in one image. As a result, most existing level set models yield poor performance when applied to this images. To this end, this paper proposes a novel hybrid level set model, named adaptive variational level set model (AVLSM) by integrating an adaptive scale bias field correction term and a denoising term into one level set framework, which can simultaneously correct the severe inhomogeneous intensity and denoise in segmentation. Specifically, an adaptive scale bias field correction term is first defined to correct the severe inhomogeneous intensity by adaptively adjusting the scale according to the degree of intensity inhomogeneity while segmentation. More importantly, the proposed adaptive scale truncation function in the term is model-agnostic, which can be applied to most off-the-shelf models and improves their performance for image segmentation with severe intensity inhomogeneity. Then, a denoising energy term is constructed based on the variational model, which can remove not only common additive noise but also multiplicative noise often occurred in medical image during segmentation. Finally, by integrating the two proposed energy terms into a variational level set framework, the AVLSM is proposed. The experimental results on synthetic and real images demonstrate the superiority of AVLSM over most state-of-the-art level set models in terms of accuracy, robustness and running time.

A hybrid moment of fluid–level set framework for simulating primary atomization

This paper presents a hybrid moment of fluid–level set (HyMOFLS) method of liquid/gas interface reconstruction for the application to simulate primary atomization of liquid fuel. This method combines the moment of fluid (MOF) method and the level set framework in the coupled level set volume of fluid (CLSVOF) method. In this hybrid method, the MOF and CLSVOF methods are used to reconstruct the interface in the under-resolved and the resolved regions of the flow, respectively. An interface surface resolution metric called interface resolution quality (IRQ) is introduced to identify and classify these two flow regions in the computational domain. Such a strategy classifies/tags each computational cell with MOF or CLSVOF method based on a threshold value for the IRQ. The MOF method uses liquid volume fraction as well as centroids of liquid and gas phases for the interface reconstruction. The CLSVOF method uses the level set for describing the interface and liquid volume fraction for conserving the mass. The phase centroids in the HyMOFLS method are computed and transported on-the-fly during the cell tagging process. The transport of the liquid volume fraction, level set, and the phase centroids are performed using a directionally split algorithm. This algorithm is coupled with the Navier-Stokes equations solver that uses ghost fluid method as well as consistent mass and momentum flux computation for the momentum equation. Various numerical tests that exhaustively assess the capabilities, accuracy, and computational time consumption of the HyMOFLS method under multiple flow conditions and configurations are presented. The results from these tests suggest that this hybrid framework is capable of well capturing the liquid/gas interface belonging to thin and under-resolved structures that are often encountered in simulations of turbulent atomization of liquids. Following these tests, a detailed parametric study on the threshold value of IRQ is presented to test its effect on the accuracy of interface reconstruction. Finally, this hybrid framework is employed to simulate turbulent jet injection and pre-filming planar Airblast atomization cases of engineering applications. The proposed HyMOFLS method is found to achieve a good balance between the accuracy and the computational cost of reconstructing the liquid/gas interface for complex and turbulent atomization configurations.

Full sensitivity-driven gap/overlap free design of carbon fiber-reinforced composites for 3D printing

This paper presents a mathematically stringent method for gap/overlap free design of carbon fiber-reinforced composites for 3D printing. The proposed method employs signed distance level set function to represent the fiber paths by extracting the equidistant iso-level set profiles, through which neighboring fiber paths keep a constant distance, eliminating the gap and overlap defects of existing methods that generate fiber paths from discretely defined fiber angle variables. Then, a compliance minimization fiber path optimization problem is formulated under the level set framework for optimal fiber-reinforcement design. A major contribution lies in the solution of the optimization problem. The adjoint sensitivity analysis is performed to derive the gradient information for fiber path design update. More importantly, the domain integral term inside the sensitivity result is transformed into a boundary integral expression facilitated by extraction of the structural skeletons and rays. Hence, the full sensitivity result is derived instead of eliminating the non-executable domain integral terms in existing studies, which results in even faster and more stable convergence. A few numerical examples are studied to demonstrate the effectiveness of the proposed fiber path optimization method. 3D printing and mechanical testing results validate the optimized fiber-reinforcement effect, as well as the manufacturability improvement by avoiding gap and overlap defects.

Anatomical knowledge based level set segmentation of cardiac ventricles from MRI

This paper represents a novel level set framework for segmentation of cardiac left ventricle (LV) and right ventricle (RV) from magnetic resonance images based on anatomical structures of the heart. We first propose a level set approach to recover the endocardium and epicardium of LV by using a bi-layer level set (BILLS) formulation, in which the endocardium and epicardium are represented by the 0-level set and k-level set of a level set function. Furthermore, the recovery of LV endocardium and epicardium is achieved by a level set evolution process, called convexity preserving bi-layer level set (CP-BILLS). During the CP-BILLS evolution, the 0-level set and k-level set simultaneously evolve and move toward the true endocardium and epicardium under the guidance of image information and the impact of the convexity preserving mechanism as well. To eliminate the manual selection of the k-level, we develop an algorithm for automatic selection of an optimal k-level. As a result, the obtained endocardial and epicardial contours are convex and consistent with the anatomy of cardiac ventricles. For segmentation of the whole ventricle, we extend this method to the segmentation of RV and myocardium of both left and right ventricles by using a convex shape decomposition (CSD) structure of cardiac ventricles based on anatomical knowledge. Experimental results demonstrate promising performance of our method. Compared with some traditional methods, our method exhibits superior performance in terms of segmentation accuracy and algorithm stability. Our method is comparable with the state-of-the-art deep learning-based method in terms of segmentation accuracy and algorithm stability, but our method has no need for training and the manual segmentation of the training data.

A parallel cell-centered adaptive level set framework for efficient simulation of two-phase flows with subcycling and non-subcycling

We develop a unified adaptive level set (LS) framework using the multi-level collocated grid for incompressible two-phase flows. This framework allows us to advance all variables level by level using either the subcycling or the non-subcycling method such that the data advancement on each level is fully decoupled. A series of synchronization operations are designed to keep the momentum and mass conserved across all levels. A multi-level re-initialization method for the LS function is also proposed, which greatly improves the mass conservation of the two-phase flows. The collocated grid allows the use of a single set of differential schemes and interpolation operations for all variables, which greatly simplifies the numerical implementation. The capability and robustness of the computational framework are validated by a variety of canonical problems, including the inviscid shear layer, gravity wave, rising bubble, and Rayleigh-Taylor instability. It is shown that the present multi-level scheme can accurately resolve the interfaces of the two-phase flows with gravitational and surface tension effects while having good momentum and energy conservation. At last, a three-dimensional dam breaking problem is simulated to show the efficiency and significant speedup of the proposed framework.

Geometrical level set reinitialization using closest point method and kink detection for thin filaments, topology changes and two-phase flows

We introduce a robust and high order strategy to perform the reinitialization in a level set framework. The reinitialization by closest points (RCP) method is based on geometric considerations. It relies on a gradient descent to find the closest points at the interface in order to solve the Eikonal equation and thus reinitializing the level set field. Furthermore, a new algorithm, also based on a similar geometric approach, is introduced to detect precisely all the ill-defined points of the level set. These points, also referred to as kinks, can mislead the gradient descent and more widely impact the accuracy of level set methods. This algorithm, coupled with the precise computation of the closest points of the interface, permits the novel method to be robust and accurate when performing the reinitialization every time step after solving the advection equation. Furthermore, they both require very few given parameters with the advantage of being based on a geometrical approach and independent of the application. The proposed method was tested on various benchmarks, and demonstrated equivalent or even better results compared to solving the Hamilton-Jacobi equation.

Numerical simulation of droplet evaporation using interface tracking methods: phase change modelling

The present work gives a description and comparison of recent methods for the direct numerical simulation of droplet vaporization using a two-scalar approach for energy and species equations. Those methods require a choice of modelling for the phase change process. The comparison relies on the work of Palmore at al. in the context of Volume of fluid and on the phase change procedure of Rueda Villegas et al. [2] in the Level set framework. Both approaches have been implemented and coupled to the same two-phase low Mach solver. A quantitative analysis is given on the canonical Stefan flow problem where analytical solutions are available. First the 1D planar Stefan problem is performed to avoid any errors associated to topology. Then, the 3D spherical Stefan problem is tested to evaluate both methodologies on a multidimensional case where the choice of interface representation is prevalent. Finally, a 2D droplet convected in a quiescent ambient gas is presented. This last test case aims to demon- strate robustness of the solver on a more demanding test case implying convection, interface deformation and non homogeneous vaporization.

A weighted region-based level set method for image segmentation with intensity inhomogeneity.

Image segmentation is a fundamental task in image processing and is still a challenging problem when processing images with high noise, low resolution and intensity inhomogeneity. In this paper, a weighted region-based level set method, which is based on the techniques of local statistical theory, level set theory and curve evolution, is proposed. Specifically, a new weighted pressure force function (WPF) is first presented to flexibly drive the closed contour to shrink or expand outside and inside of the object. Second, a faster and smoother regularization term is added to ensure the stability of the curve evolution and that there is no need for initialization in curve evolution. Third, the WPF is integrated into the region-based level set framework to accelerate the speed of the curve evolution and improve the accuracy of image segmentation. Experimental results on medical and natural images demonstrate that the proposed segmentation model is more efficient and robust to noise than other state-of-the-art models.

A neighbor level set framework minimized with the split Bregman method for medical image segmentation

Medical image segmentation has a huge challenge due to intensity inhomogeneity and the similarity of the background and the object. To meet this challenge, we propose an improved active contour model, in which we combine the level set method and the split Bregman method, and provide the two-phase formulation, the multi-phase formulation and 3D formulation. In this paper, the proposed model is presented in a level set framework by including the neighbor region information for segmenting medical images in which the energy functional contains the data fitting term and the length term. The neighbor region and the local intensity variances in the data fitting term are designed to optimize the minimization process. To minimize the energy functional then we apply the split Bregman method which contributes to get faster convergence. Besides, we extend our model to the multi-phase segmentation model and the 3D segmentation model for cardiac MR images, which have all achieved good results. Experimental results show that the new model not only has strong robustness to other cardiac tissue effects and image intensity inhomogeneity, but it also can much better conduce to the extraction of effective tissues. As we expected, our model has higher segmentation accuracy and efficiency for medical image segmentation.

An inverse technique to identify participant-specific bone adaptation from serial CT measurements.

Simulated bone adaptation is framed as an interface evolution problem. The interface is extracted from a high-resolution computed tomography (CT) image of trabecular bone microarchitecture and modified by the level set equation. A model and its parameters determine the bone adaptation rate and thus the bone structure at any future time. This study develops an inverse problem and solver to identify model parameters from multiple high-resolution CT images of bone within the level set framework. We demonstrate the technique on a model of advection and mean curvature flow, termed curvature-driven adaptation. The inverse solver uses two CT scans to estimate model parameters, which map the bone surface from one image to the next. The solver was tested with synthetic images of bone changing according to the curvature-driven model with known model parameters. The algorithm recovered known model parameters excellently (R2 > .99, p < .001). A grid search indicated that the estimated model parameters were insensitive to hyper-parameter selection for learning rate 1e-5 5e-5 and gradient scaling factor 5e-5 5e-4 . Finally, we tested the algorithm's sensitivity to salt-and-pepper noise of probability , where .0 .9. Model parameter accuracy did not change for < .7, corresponding to Dice coefficients greater than .7. The inverse problem estimates bone adaptation parameters from multiple CT images of changing bone microarchitecture. In the future, this technique could be used to determine participant-specific bone adaptation parameters in vivo, validate bone adaptation models, and predict bone health.

A finite-volume method for simulating contact lines on unstructured meshes in a conservative level-set framework

Accurate numerical simulation of moving contact lines on complex boundaries with surface wettability effect remains a challenging problem. In this paper, we introduce a robust and accurate method to perform 3D contact line simulations on unstructured meshes with an imposed contact angle. The contact angle is imposed through a sub-grid scale curvature term and the contact line motion is enabled thanks to partial slip on the wall. Moreover, an original strategy has been designed to improve normal and curvature computation at contact line from the level-set field. The whole method is validated on 2D and 3D test cases and shows good mass conservation properties. The drop detachment from a horizontal fiber due to gravity or surface tension is then investigated. For this purpose, dynamic mesh adaptation is used to keep high resolution around the interface with moderate number of cells. These realistic cases demonstrate the ability of the numerical method to handle surface wettability effects on resolved complex geometries.

A level-set framework for the wind turbine wake analysis: from high-fidelity unsteady simulations to 1D momentum theory

In the context of yawed wind turbine wakes, the validity of the so-called 1D momentum theory is arguable. The 1D momentum theory emerges from an inviscid, steady and irrotational analysis of the streamtube surrounding a wind turbine while the wake aerodynamics under yaw is modified. In this work, the mean flow streamtube around a single DTU 10MW wind turbine, under yaw misalignement and turbulent inflow is investigated with Large-Eddy Simulation combined to the Actuator Line method. The simulations are performed on a highly resolved grid counting billions of elements. The streamtube construction from the mean flow is based on the transport of accurate conservative level set functions. Integration of local flow quantities within the streamtube presents similarities when the streamtube expansion occurs past the turbine until the velocity deficit starts to recover. Mean kinetic energy and momentum budget are then presented to explain the yawed wake recovery and deflection process. Background turbulence plays a key role in the recovery process while the deflection of the wake is impacted by pressure forces on the streamtube. From these budgets, four wake regions showing similar flow dynamics are defined and correlated to local flow structures.

A variational level set model with closed-form solution for bimodal image segmentation

In this work, we present a variational level set model with closed–form solution via combining with the fuzzy clustering method for robust and efficient image segmentation. For the designed energy functional, the two region parameters are first quickly pre–computed by means of the fuzzy c–means method and then embedded into a variational binary level set framework. Unlike the traditional variational level set models and optimization algorithms, our proposed model could directly obtain an exact closed–form solution of the level set function without using any iterative calculations and it is thus the globally optimal solution. Furthermore, we investigate the closed–form formula and achieve a significant property of the solution. As a byproduct, the manual initialization of the level set function and the sophisticated setting of time step in the process of numerical implementation are completely eliminated and thus leads to more robust segmentation results. Numerical experiments on both synthetic and real images verify the theoretical analysis of the proposed model and confirm the segmentation performance of the proposed method in terms of efficiency, accuracy and insensitiveness to parameters tuning.

Robust segmentation method for noisy images based on an unsupervised denosing filter

Level-set-based image segmentation has been widely used in unsupervised segmentation tasks. Researchers have recently alleviated the influence of image noise on segmentation results by introducing global or local statistics into existing models. Most existing methods are based on the assumption that the distribution of image noise is known or observable. However, real-time images do not meet this assumption. To bridge this gap, we propose a novel level-set-based segmentation method with an unsupervised denoising mechanism. First, a denoising filter is acquired under the unsupervised learning paradigm. Second, the denoising filter is integrated into the level-set framework to separate noise from the noisy image input. Finally, the level-set energy function is minimized to acquire segmentation contours. Extensive experiments demonstrate the robustness and effectiveness of the proposed method when applied to noisy images.

Level set framework with transcendental constraint for robust and fast image segmentation

Though image segmentation models are plentiful and have many applications nowadays, it can be difficult to segment images with complex boundaries and serious intensity inhomogeneity. To some extent, the region-scalable fitting energy model can segment images suffering from intensity inhomogeneity since it considers image intensity as a function, but it relies on initial conditions dramatically. Nowadays, prior knowledge has been widely applied in image segmentation models, which can integrate automatic method and experts experience in one robust and fast segmentation model. In this paper we present a new model that can segment various images accurately by taking the advantages of the region-scalable fitting energy model and the advanced transcendental constraint from artificial experience. The proposed energy functional consists of a smooth length term, a target image data term and a transcendental constraint term. The transcendental constraint term plays a key role in the proposed model, which not only gives the accurate segmentation results but also provides us the chance to carry out the parallel computation. In the proposed-parallel model, the efficiency is improved a lot and the results become more precise compared with other methods. The split Bregman method is applied to minimize the energy functional. Furthermore, we present the convergence analysis and the time complexity analysis of our algorithm. Multiple experimental results and comparisons including parameters sensitivity discussion are shown to demonstrate the superiority of the proposed model such as high accuracy, robustness and efficiency.

Generation and homogenization of foamed polymer RVEs: microstructure-mechanical properties relationship

The main purpose of this study is to better understand the relationship between the microstructure of foamed polymer and mechanical properties. X-Ray tomography was performed on polypropylene foam specimens machined from injected plates. These plates were obtained for different thicknesses and exhibit different microstructure morphologies. The tomography scans were first digitalized and meshed. Then, numerical simulations were performed on representative volume elements (RVEs) to get homogeneous mechanical property of the material using a parallel C++ library Cimlib developed at CEMEF. Numerical methods described in this study focused on immerged or body-fitted strategy (FE context - level set framework - meshing adaptation) for exact and statistical RVEs generation. The numerical results were compared to experimental testing performed under tension and compression at different strain rates using image correlation. Good agreement was observed between simulations performed at the mesoscale and experimental tests carried out at the macroscale for both real and statistical RVEs. This methodology opens a way for the development of digital materials designed for specific mechanical properties.

Adaptive segmentation model for liver CT images based on neural network and level set method

Accurate segmentation is difficult for liver computed tomography (CT) images, since the liver CT images do not always have obvious and smooth boundaries. The location of the tumor is not specified and the image intensity is similar to that of the liver. Although manual and automatic segmentation methods, traditional and deep learning models currently exist, none can be specifically and effectively applied to segment liver CT images. In this paper, we propose a new model based on a level set framework for liver CT images in which the energy functional contains three terms including the data fitting term, the length term and the bound term. Then we apply the split Bregman method to minimize the energy functional that leads the energy functional to converge faster. The proposed model is robust to initial contours and can segment liver CT images with intensity inhomogeneity and unclear boundaries. In the bound term, we use the U-Net to get constraint information which has a considerable influence on effective and accurate segmentation. We improve a multi-phase level set of our model to get contours of tumor and liver at the same time. Finally, a parallel algorithm is proposed to improve segmentation efficiency. Results and comparisons of experiments are shown to demonstrate the merits of the proposed model including robustness, accuracy, efficiency and intelligence.

Numerical modelling of solitary wave and structure interactions using level-set and immersed boundary methods by adopting adequate inlet boundary conditions

ABSTRACT Solitary waves are often used to replicate tsunami waves and, therefore, the study of their propagation and interactions with structures could help to understand the impacts of tsunami waves on infrastructures. This paper presents a numerical model that uses the level-set framework for simulating the propagation of solitary waves and their interactions with structures using the immersed boundary method. The model imposes a set of appropriate boundary conditions to prescribe the incoming solitary waves within the sharp-interface immersed boundary method. Turbulence is modelled using the large-eddy simulation. Experimental tests are conducted to measure the free-surface elevation and velocity field evolution of solitary waves, as they propagate downwave interacting with two different wall-mounted structures. Analysis of the computed and experimental results revealed interesting dynamics of primary vortex-tubes forming near the sharp edges of structures. It is shown that the primary vortices eventually split to form pairs of asymmetrical doublets.

On the role of solute drag in reconciling laboratory and natural constraints on olivine grain growth kinetics

SUMMARY We investigate the effect of solute drag on the grain growth (GG) kinetics in olivine-rich rocks through full field and mean field modelling. Considering a drag force exerted by impurities on grain boundary migration allows reconciling laboratory and natural constraints on olivine GG kinetics. Solute drag is implemented in a full field level-set framework and in a mean field model that explicitly accounts for a grain size distribution. After calibration of the mean field model on full field results, both models are able to both reproduce laboratory GG kinetics and predict grain sizes consistent with observations in peridotite xenoliths from different geological contexts.