Level Set Technique Research Articles

The use of a simple model in the inverse characterization of cardiac ischemic regions

Abstract In this paper, we analyze the use of simple models for solving the inverse problem in electrocardiography (IPE), which aims at recovering the heart condition from a set of remote voltages measurements. Specifically, we consider here the problem of estimating the shape, size and location of cardiac ischemic regions. The forward problem to generate the data (voltage measurements) is formulated by using the Luo–Rudy model, which provides a detailed description of the electrical behavior of cardiac cells. As for the inversion process, we use the two-current phenomenological model. The inversion procedure also incorporates a semi-automatic stage to characterize the conduction properties of the cardiac tissue. The ischemic regions are modeled by using standard level set techniques. Numerical results show that the algorithm is capable of estimating the position, size and shape of cardiac ischemic regions from noisy voltage measurements, for both 2D and 3D geometries. Our inverse procedure is benchmarked against zero-order Tikhonov regularization. This work is a proof of principle demonstrating the possibility of using simple models in the IPE towards realistic situations.

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.

A level-set based IGA formulation for topology optimization of flexoelectric materials

This paper presents a design methodology based on a combination of isogeometric analysis (IGA), level set and point wise density mapping techniques for topology optimization of piezoelectric/flexoelectric materials. The fourth order partial differential equations (PDEs) of flexoelectricity, which require at least C1 continuous approximations, are discretized using Non-Uniform Rational B-spline (NURBS). The point wise density mapping technique with consistent derivatives is directly used in the weak form of the governing equations. The boundary of the design domain is implicitly represented by a level set function. The accuracy of the IGA model is confirmed through numerical examples including a cantilever beam under a point load and a truncated pyramid under compression with different electrical boundary conditions. Finally, we provide numerical examples demonstrating the significant enhancement in electromechanical coupling coefficient that can be obtained using topology optimization.

Abdomen and spinal cord segmentation with augmented active shape models.

Active shape models (ASMs) have been widely used for extracting human anatomies in medical images given their capability for shape regularization of topology preservation. However, sensitivity to model initialization and local correspondence search often undermines their performances, especially around highly variable contexts in computed-tomography (CT) and magnetic resonance (MR) images. In this study, we propose an augmented ASM (AASM) by integrating the multiatlas label fusion (MALF) and level set (LS) techniques into the traditional ASM framework. Using AASM, landmark updates are optimized globally via a region-based LS evolution applied on the probability map generated from MALF. This augmentation effectively extends the searching range of correspondent landmarks while reducing sensitivity to the image contexts and improves the segmentation robustness. We propose the AASM framework as a two-dimensional segmentation technique targeting structures with one axis of regularity. We apply AASM approach to abdomen CT and spinal cord (SC) MR segmentation challenges. On 20 CT scans, the AASM segmentation of the whole abdominal wall enables the subcutaneous/visceral fat measurement, with high correlation to the measurement derived from manual segmentation. On 28 3T MR scans, AASM yields better performances than other state-of-the-art approaches in segmenting white/gray matter in SC.

Analysis of a chemotaxis system modeling ant foraging

In this paper, we analyze a system of PDEs recently introduced in [P. Amorim, Modeling ant foraging: A chemotaxis approach with pheromones and trail formation, J. Theor. Biol. 385 (2015) 160–173], in order to describe the dynamics of ant foraging. The system is made of convection–diffusion–reaction equations, and the coupling is driven by chemotaxis mechanisms. We establish the well-posedness for the model, and investigate the regularity issue for a large class of integrable data. Our focus is on the (physically relevant) two-dimensional case with boundary conditions, where we prove that the solutions remain bounded for all times. Further, we prove a hypercontractivity result (instantaneous formation of all [Formula: see text]-norms, [Formula: see text]). The proofs involve a series of fine a priori estimates in Lebesgue spaces and a De Giorgi level set technique.

Steady and unsteady simulations for annular internal condensing flows, part I: Algorithm and its accuracy

ABSTRACTThis paper presents an algorithm for accurately solving the full two-dimensional governing equations, along with the interface conditions that govern laminar/laminar annular/stratified internal condensing flows. The simulation approach - which can be generalized to adiabatic and evaporating flows, a 3-D level-set technique, and so on - uses a sharp-interface model, separate liquid and vapor domain computational solutions with interface conditions embedded as boundary conditions, and a moving grid technique to locate the dynamic wavy interface (in amplitude and phase) by a method of characteristics solution of the interface tracking equation. The moving grid is spatially fixed for a defined number of instants, but changes when the current marker instant advances in time.

Integration over curves and surfaces defined by the closest point mapping

We propose a new formulation for integrating over smooth curves and surfaces that are described by their closest point mappings. Our method is designed for curves and surfaces that are not defined by any explicit parameterization and is intended to be used in combination with level set techniques. However, contrary to the common practice with level set methods, the volume integrals derived from our formulation coincide exactly with the surface or line integrals that one wishes to compute. We study various aspects of this formulation and provide a geometric interpretation of this formulation in terms of the singular values of the Jacobian matrix of the closest point mapping. Additionally, we extend the formulation—initially derived to integrate over manifolds of codimension one—to include integration along curves in three dimensions. Some numerical examples using very simple discretizations are presented to demonstrate the efficacy of the formulation.

A new approach to calculate the nodule density of ductile cast iron graphite using a Level Set

This paper proposes a new approach with digital image processing techniques to determine the number of graphite nodules on samples of nodular cast iron by following the NBR 6913 standard. Counting errors and excessive inspection time are common problems if the procedure is performed without the assistance of computational systems. To overcome these drawbacks, we propose here an algorithm for graphite nodule segmentation based on the Level Set technique. The proposed approach and two other computational methods, Watershed and Region Growing, are compared with the results given by experts using optical microscopy (OM). The results of the proposed method were closer to those of the experts using OM than the other two computational methods. The proposed method presented greater accuracy and faster execution time than the traditional method by visual inspection.

Demons versus Level-Set motion registration for coronary 18F-sodium fluoride PET.

Ruptured coronary atherosclerotic plaques commonly cause acute myocardial infarction. It has been recently shown that active microcalcification in the coronary arteries, one of the features that characterizes vulnerable plaques at risk of rupture, can be imaged using cardiac gated 18F-sodium fluoride (18F-NaF) PET. We have shown in previous work that a motion correction technique applied to cardiac-gated 18F-NaF PET images can enhance image quality and improve uptake estimates. In this study, we further investigated the applicability of different algorithms for registration of the coronary artery PET images. In particular, we aimed to compare demons vs. level-set nonlinear registration techniques applied for the correction of cardiac motion in coronary 18F-NaF PET. To this end, fifteen patients underwent 18F-NaF PET and prospective coronary CT angiography (CCTA). PET data were reconstructed in 10 ECG gated bins; subsequently these gated bins were registered using demons and level-set methods guided by the extracted coronary arteries from CCTA, to eliminate the effect of cardiac motion on PET images. Noise levels, target-to-background ratios (TBR) and global motion were compared to assess image quality. Compared to the reference standard of using only diastolic PET image (25% of the counts from PET acquisition), cardiac motion registration using either level-set or demons techniques almost halved image noise due to the use of counts from the full PET acquisition and increased TBR difference between 18F-NaF positive and negative lesions. The demons method produces smoother deformation fields, exhibiting no singularities (which reflects how physically plausible the registration deformation is), as compared to the level-set method, which presents between 4 and 8% of singularities, depending on the coronary artery considered. In conclusion, the demons method produces smoother motion fields as compared to the level-set method, with a motion that is physiologically plausible. Therefore, level-set technique will likely require additional post-processing steps. On the other hand, the observed TBR increases were the highest for the level-set technique. Further investigations of the optimal registration technique of this novel coronary PET imaging technique are warranted.

Whole Abdominal Wall Segmentation using Augmented Active Shape Models (AASM) with Multi-Atlas Label Fusion and Level Set.

The abdominal wall is an important structure differentiating subcutaneous and visceral compartments and intimately involved with maintaining abdominal structure. Segmentation of the whole abdominal wall on routinely acquired computed tomography (CT) scans remains challenging due to variations and complexities of the wall and surrounding tissues. In this study, we propose a slice-wise augmented active shape model (AASM) approach to robustly segment both the outer and inner surfaces of the abdominal wall. Multi-atlas label fusion (MALF) and level set (LS) techniques are integrated into the traditional ASM framework. The AASM approach globally optimizes the landmark updates in the presence of complicated underlying local anatomical contexts. The proposed approach was validated on 184 axial slices of 20 CT scans. The Hausdorff distance against the manual segmentation was significantly reduced using proposed approach compared to that using ASM, MALF, and LS individually. Our segmentation of the whole abdominal wall enables the subcutaneous and visceral fat measurement, with high correlation to the measurement derived from manual segmentation. This study presents the first generic algorithm that combines ASM, MALF, and LS, and demonstrates practical application for automatically capturing visceral and subcutaneous fat volumes.

Multi-scale texture-based level-set segmentation of breast B-mode images

Automatic segmentation of ultrasonographic breast lesions is very challenging, due to the lesions′ spiculated nature and the variance in shape and texture of the B-mode ultrasound images. Many studies have tried to answer this challenge by applying a variety of computational methods including: Markov random field, artificial neural networks, and active contours and level-set techniques. These studies focused on creating an automatic contour, with maximal resemblance to a manual contour, delineated by a trained radiologist. In this study, we have developed an algorithm, designed to capture the spiculated boundary of the lesion by using the properties from the corresponding ultrasonic image. This is primarily achieved through a unique multi-scale texture identifier (inspired by visual system models) integrated in a level-set framework. The algorithm׳s performance has been evaluated quantitatively via contour-based and region-based error metrics. We compared the algorithm–generated contour to a manual contour delineated by an expert radiologist. In addition, we suggest here a new method for performance evaluation where corrections made by the radiologist replace the algorithm-generated (original) result in the correction zones. The resulting corrected contour is then compared to the original version. The evaluation showed: (1) Mean absolute error of 0.5 pixels between the original and the corrected contour; (2) Overlapping area of 99.2% between the lesion regions, obtained by the algorithm and the corrected contour. These results are significantly better than those previously reported. In addition, we have examined the potential of our segmentation results to contribute to the discrimination between malignant and benign lesions.

Numerical study of the migration of a silicone plug inside a capillary tube subjected to an unsteady wall temperature gradient

In this study, the movement of a silicone plug is actuated by the application of heat flux to one end of a capillary tube. The transient motion of the plug is investigated in a numerical simulation. The finite element method with the two-phase level set technique, developed by Comsol Multiphysics, is used to solve the incompressible Navier–Stokes equations coupled with the energy equation. The results show that the flow motion is affected by the thermocapillary effect generated by the temperature gradient along the gas–liquid interface near the receding side and the capillary force caused by the temperature difference between the ends of the liquid plug. For a longer migration time, the flow mainly moves horizontally from the hot side to the cold side near the tube wall and then returns to the hot side near the center of the tube due to the capillary force effect. There is a smaller clockwise circulation near the receding contact angle caused by the thermocapillary convection. The flow motion causes significant distortion of the isotherms inside the silicone plug. The temperature gradient along the tube is enhanced by the flow motion inside the capillary tube. The liquid plug accelerates rapidly in the initial stage and then decelerates after it reaches the maximum speed. During the migration process, the receding contact angle is always greater than the advancing one. An increase in the input heat flux leads to a higher migration velocity due to the higher temperature gradient along the tube wall. When the initial contact angle is smaller, the migration velocity moves faster due to the higher capillary force. A liquid plug with a lower viscosity moves faster owing to the lower viscous force. The numerical simulation results are in good agreement with the results from previous experiments.

Efficient formulation of scale separation for multi-scale modeling of interfacial flows

We propose an efficient formulation of the scale-separation approach which has been developed by Han et al. 10 for multi-scale sharp interface modeling of multi-phase flows based on the level-set technique. Instead of shifting the entire level-set field twice as in the original method, the improved method identifies the non-resolved interface structures from two auxiliary level-sets close to the interface. Non-resolved structures are separated from the interface by a localized re-distancing method, which increases the computational efficiency considerably compared to the original global reinitialization procedure. Several tests for two-phase flow problems, involving simple and complex interface structures, are carried out to show that the present method maintains sharper interface structures than the original method, and achieves effective scale-separation.

Classification of benign and malignant breast tumors based on hybrid level set segmentation

Computer-aided Diagnosis (CADx) technology can substantially aid in early detection and diagnosis of breast cancers. However, the overall performance of a CADx system is tied, to a large extent, to the accuracy with which the tumors can be segmented in a mammogram. This implies that the segmentation of mammograms is a critical step in the diagnosis of benign and malignant tumors. In this paper, we develop an enhanced mammography CADx system with an emphasis on the segmentation step. In particular, we present two hybrid algorithms based upon region-based, contour-based and clustering segmentation techniques to recognize benign and malignant breast tumors. In the first algorithm, in order to obtain the most accurate final segmented tumor, the initial segmented image, that is required for the level set, is provided by one of spatial fuzzy clustering (SFC), improved region growing (RG), or cellular neural network (CNN). In the second algorithm, all of the parameters which control the level set are obtained from a dynamic training procedure by the combination of both genetic algorithms (GA) and artificial neural network (ANN) or memetic algorithm (MA) and ANN. After segmenting tumors using one of the hybrid proposed methods, intensity, shape and texture features are extracted from tumors, and the appropriate features are then selected by another GA algorithm. Finally, to classify tumors as benign or malignant, different classifiers such as ANN, random forest, naïve Bayes, support vector machine (SVM), and K-nearest neighbor (KNN) are used. Experimental results confirm the efficiency of the proposed methods in terms of sensitivity, specificity, accuracy and area under ROC curve (AUC) for the classification of breast tumors. It was concluded that RG and GA in adaptive RG-LS method produce more accurate primary boundary of tumors and appropriate parameters for the level set technique in segmentation and subsequently in classification.

Enablers for high‐order level set methods in fluid mechanics

SummaryIn the context of numerical simulations of multiphysics flows, accurate tracking of an interface and consistent computation of its geometric properties are crucial. In this paper, we investigate a level set technique that satisfies these requirements and ensures local third‐order accuracy on the level set function (near the interface) and first‐order accuracy on the curvature, even for long‐time computations. The method is developed in a finite differences framework on Cartesian grids. As in usual level set strategies, reinitialization steps are involved. Several reinitialization algorithms are reviewed and mixed to design an accurate and fast reinitialization procedure. When coupled with a time evolution of the interface, the reinitialization procedure is performed only when there are too large deformations of the isocontours. This strategy limits the number of reinitialization steps and shows a good balance between accuracy and computational cost. Numerical results compare well with usual level set strategies and confirm the necessity of the reinitialization procedure, together with a limited number of reinitialization steps. Copyright © 2015 John Wiley & Sons, Ltd.

Structural optimization of multibody system components described using level set techniques

The structural optimization of the components in multibody systems is performed using a fully coupled optimization method. The design's predicted response is obtained from a flexible multibody system simulation under various service conditions. In this way, the resulting optimization process enhances most existing studies which are limited to weakly coupled (quasi-) static or frequency domain loading conditions. A level set description of the component geometry is used to formulate a generalized shape optimization problem which is solved via efficient gradient-based optimization methods. Gradients of cost and constraint functions are obtained from a sensitivity analysis which is revisited in order to facilitate its implementation and retain its computational efficiency. The optimizations of a slider-crank mechanism and a 2-dof robot are provided to exemplify the procedure.

Evaluating printability of buried native extreme ultraviolet mask phase defects through a modeling and simulation approach

Since completely defect-free masks will be hard to achieve, it is essential to have a good understanding of the printability of the native extreme ultraviolet (EUV) mask defects. In this work, we performed a systematic study of native mask defects to understand the defect printability they cause. The multilayer growth over native substrate mask blank defects was correlated to the multilayer growth over regular-shaped defects having similar profiles in terms of their width and height. To model the multilayer growth over the defects, a multilayer growth model based on a level-set technique was used that took into account the tool deposition conditions of the Veeco Nexus ion beam deposition tool. Further, the printability of the characterized native defects was studied at the SEMATECH-Berkeley Actinic Inspection Tool (AIT), an EUV mask-imaging microscope at Lawrence Berkeley National Laboratory. Printability of the modeled regular-shaped defects, which were propagated up the multilayer stack using level-set growth model, was studied using defect printability simulations implementing the waveguide algorithm. Good comparison was observed between AIT and the simulation results, thus demonstrating that multilayer growth over a defect is primarily a function of a defect’s width and height, irrespective of its shape.

Alleviation of Electric Field Intensity in High-Voltage System by Topology and Shape Optimization of Dielectric Material Using Continuum Design Sensitivity and Level Set Method

A new design method for topology and shape optimization to preserve high-voltage systems is proposed. The level set technique for the topology optimization is employed with the finite-element method. For the velocity field in the level set equation, the continuum sensitivity formula is used for accurate information of the electric field effect on the topology and shape variation. This technique is applied to three practical examples and the optimum designs of insulating dielectric for the systems are obtained. The optimum designs could suppress troubles, such as thermal deterioration or electrical breakdown, in the systems.

Level-set multilayer growth model for predicting printability of buried native extreme ultraviolet mask defects

The availability of defect-free masks is considered to be a critical issue for enabling extreme ultraviolet lithography (EUVL) as the next generation technology. Since completely defect-free masks will be hard to achieve, it is essential to have a good understanding of the printability of EUV mask defects. In this work, two native mask blank defects were characterized using atomic force microscopy (AFM) and cross-section transmission electron microscopy (TEM), and the defect printability of the characterized native mask defects was evaluated using simulations implementing the finite-difference time-domain and the waveguide algorithms. The simulation results were compared with through-focus aerial images obtained at the SEMATECH Berkeley Actinic Inspection Tool (AIT), an EUV mask-imaging microscope at Lawrence Berkeley National Laboratory. The authors found agreement between the through-focus simulation results and the AIT results. To model the Mo/Si multilayer growth over the native defects, which served as the input for the defect printability simulations, a level-set technique was used to predict the evolution of the multilayer disruption over the defect. Unlike other models that assume a constant flux of atoms (of materials to be deposited) coming from a single direction, this model took into account the direction and incident fluxes of the materials to be deposited, as well as the rotation of the mask substrate, to accurately simulate the actual deposition conditions existing inside the ion beam deposition tool. The modeled multilayer growth was compared to the cross-section TEM images through the defects, as well as to the AFM scans for the given defects, and a good agreement was observed between them.

The LS-STAG immersed boundary method for non-Newtonian flows in irregular geometries: flow of shear-thinning liquids between eccentric rotating cylinders

This paper presents the extension of a well-established immersed boundary/cut-cell method, the LS-STAG method (Cheny and Botella in J Comput Phys 229:1043–1076, 2010), to non-Newtonian flow computations in 2D irregular geometries. One of the distinguished features of our IB method is to use level-set techniques in the cut-cells near the irregular boundary, where accurate discretization is of paramount importance for stability and accuracy of the computations. For this purpose, we present here an accurate discretization of the velocity gradients and shear rate in the cut-cells that fits elegantly in the framework of the velocity–pressure–stress staggered arrangement and the special quadratures developed previously for viscoelastic flows. After assessing the accuracy of the discretization on a benchmark solution for power-law fluids, the LS-STAG code is applied to the flow of various shear-thinning xanthan solutions in a wide-gap, non-coaxial, Taylor–Couette reactor for which rheological characterization, experimental flow measurements (PIV) and FLUENT simulations have recently been performed in our group. Our numerical investigation will give new insight on the flow patterns (onset, size and position of the recirculation zone) and will firmly correlate them to global flow properties such as shear-thinning index, generalized Reynolds number and torque ratio at the cylinders.