Multiphase Level Set Research Articles

A Parametric Level set Method for Imaging Multiphase Conductivity Using Electrical Impedance Tomography

Electrical impedance tomography (EIT) is an imaging modality that provides cross-sectional images of objects that carry contrasts in electrical conductivity. EIT is suitable for example for monitoring industrial processes involving multiple phases with different conductivities. This paper presents a parametric level set (PLS) based reconstruction scheme for an EIT-imaging of conductivity distributions within multiphase systems. The proposed scheme involves applying a multiphase level set model to solve the inverse problem of finding interfaces between the regions having different conductivity values and estimating the conductivities of phases. The unknown conductivity to be reconstructed is assumed to be piecewise constant while the interface between the regions are represented by the two PLS functions employing Gaussian radial basis functions (GRBF). The level set-based scheme handles topological merging and breaking naturally during the evolution process. It also offers several advantages compared to the traditional pixel-based approaches. For example, the representation of the PLS function by using GRBF provides flexibility in describing a large class of shapes with fewer unknowns. Numerical simulations and phantom experiments are performed to validate the proposed method.

Image segmentation based on multi-region multi-scale local binary fitting and Kullback–Leibler divergence

The inhomogeneity of intensity and the noise of image are the two major obstacles to accurate image segmentation by region-based level set models. To provide a more general solution to these challenges and address the difficulty of image segmentation methods to handle an arbitrary number of regions, we propose a region-based multi-phase level set method, which is based on the multi-scale local binary fitting (MLBF) and the Kullback–Leibler (KL) divergence, called KL–MMLBF. We first apply the multi-scale theory and multi-phase level set framework to the local binary fitting model to build the multi-region multi-scale local binary fitting (MMLBF). Then the energy term measured by KL divergence between regions to be segmented is incorporated into the energy function of MMLBF. KL–MMLBF utilizes the between-cluster distance and the adaptive kernel function selection strategy to formulate the energy function. Being more robust to the initial location of the contour than the classical segmentation models, KL–MMLBF can deal with blurry boundaries and noise problems. The results of experiments on synthetic and medical images have shown that KL–MMLBF can improve the effectiveness of segmentation while ensuring the accuracy by accelerating this minimization of this energy function and the model has achieved better segmentation results in terms of both accuracy and efficiency to analyze the multi-region image.

A multi-material level set-based topology optimization of flexoelectric composites

We present a computational design methodology for topology optimization of multi-material-based flexoelectric composites. The methodology extends our recently proposed design methodology for a single flexoelectric material. We adopt the multi-phase vector level set (LS) model which easily copes with various numbers of phases, efficiently satisfies multiple constraints and intrinsically avoids overlap or vacuum among different phases. We extend the point wise density mapping technique for multi-material design and use the B-spline elements to discretize the partial differential equations (PDEs) of flexoelectricity. The dependence of the objective function on the design variables is incorporated using the adjoint technique. The obtained design sensitivities are used in the Hamilton–Jacobi (H–J) equation to update the LS function. We provide numerical examples for two, three and four phase flexoelectric composites to demonstrate the flexibility of the model as well as the significant enhancement in electromechanical coupling coefficient that can be obtained using multi-material topology optimization for flexoelectric composites.

Remotely Sensed Image Segmentation using Multiphase Level-Set ACM

In remote sensing image analysis, segmentation of an image is an important aspect. It classifies similar pixels within the image. Image Segmentation is helpful in analyzing the patterns, objects, and edges within an image. There are many ways for performing image segmentation. In this paper, we are segmenting a satellite image using Multiphase Chan-Vese model. Chan-Vese models are based on ‘Active Contours without edges’. Active contour model is also known as Snake and Energy-Based Model, which is finding local minima in the equivalent energy function. Chan-Vese model gives effective results of segmented image. The multiphase level set construction is mechanized to avoid the drawback of overlap and vacuum; it can also signify edges with convoluted topologies. Researchers conclude in this paper with the findings that the multiphase CV method can give a sensible segmented image of satellite imagery with 2D-DWT, when they manipulate Heaviside function.

A MULTIPHASE LEVEL SET FRAMEWORK FOR IMAGE SEGMENTATION USING GLOBAL AND LOCAL IMAGE FITTING ENERGY

Segmenting the image into multiple regions is at the core of image processing. Many segmentation formulations of an images with multiple regions have been suggested over the years. We consider segmentation algorithm based on the multi-phase level set method in this work. Proposed method gives the best result upon other methods found in the references. Moreover it can segment images with intensity inhomogeneity and have multiple junction. We extend our method (GLIF) in [T. Dultuya, and M. Kang, Segmentation with shape prior using global and local image fitting energy, J.KSIAM Vol.18, No.3, 225–244, 2014.] using a multiphase level set formulation to segment images with multiple regions and junction. We test our method on different images and compare the method to other existing methods.

A level set method for multiple sclerosis lesion segmentation

In this paper, we present a level set method for multiple sclerosis (MS) lesion segmentation from FLAIR images in the presence of intensity inhomogeneities. We use a three-phase level set formulation of segmentation and bias field estimation to segment MS lesions and normal tissue region (including GM and WM) and CSF and the background from FLAIR images. To save computational load, we derive a two-phase formulation from the original multi-phase level set formulation to segment the MS lesions and normal tissue regions. The derived method inherits the desirable ability to precisely locate object boundaries of the original level set method, which simultaneously performs segmentation and estimation of the bias field to deal with intensity inhomogeneity. Experimental results demonstrate the advantages of our method over other state-of-the-art methods in terms of segmentation accuracy.

Mechanisms for trapping and mobilization of residual fluids during capillary‐dominated three‐phase flow in porous rock

AbstractWe use a multiphase level set approach to simulate capillary‐controlled motions of isolated fluid ganglia surrounded by two other continuous fluids (i.e., double displacements) during three‐phase flow on 3‐D porous rock geometries. Double displacements and three‐phase snap‐off mechanisms are closely related. Water snap‐off on gas/oil interfaces can initiate double displacements that mobilize isolated oil ganglia in water‐wet rock, but it can also terminate ongoing double displacements and trap oil in water. The multiphase level set approach allows for calculating the evolution of disconnected‐phase pressure during the motion. In the events of pore filling by double displacement of oil ganglia, and water snap‐off on gas/oil interfaces, we find that the local gas/oil capillary pressure drops, while local oil/water capillary pressure increases, by a similar magnitude as observed for the capillary pressure drops during single‐pore filling events in dynamic pore‐scale experiments of two‐phase drainage. We also find that oil ganglia decrease their surface area, and achieve a more compact shape, when the gas/oil interfacial area decreases at the expense of increased oil/water interfacial area during double displacement. By comparison with similar two‐phase gas/water simulations, we find that the level of the gas/water capillary pressure curves, including hysteresis loops, are smaller when a mobile, disconnected oil is present, which suggests double displacement of oil is more favorable than direct gas/water displacement. We also present cases in which phase trapping occurred in the three‐phase simulations, but not in the corresponding two‐phase simulations, supporting the view that more trapping is possible in three‐phase flow.

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'.

Topological design for mechanical metamaterials using a multiphase level set method

Metamaterials usually refer to artificially engineered composites with unusual properties that cannot be easily found in nature. This paper will develop a topological shape optimization method for design of mechanical metamaterials of thermoelastic micro-structured composites, which integrates numerical homogenization method with a multi-phase level set method (MPLSM). The homogenization method is applied to evaluate the effective macroscopic properties of a periodic microstructure, while the MPLSM will be utilized to implement shape and topology evolutions of the microstructure. A multi-phase level set representation model is established to describe the boundaries of the multi-material microstructure using a combination of all level set functions, without overlaps and empties. The Hamilton-Jacobi partial differential equation-based topological shape optimization problem will be transformed to a generalized size optimization problem. Typical numerical examples are used to demonstrate the effectiveness of the proposed method for designing metamaterials with expected and extreme thermal expansion coefficients.

Multiphase vs. single-phase variational level set approach for video data association

Multiphase vs. single-phase variational level set approach for video data association

Level-set-based partitioning and packing optimization of a printable model

As the 3D printing technology starts to revolutionize our daily life and the manufacturing industries, a critical problem is about to e-merge: how can we find an automatic way to divide a 3D model into multiple printable pieces, so as to save the space, to reduce the printing time, or to make a large model printable by small printers. In this paper, we present a systematic study on the partitioning and packing of 3D models under the multi-phase level set framework. We first construct analysis tools to evaluate the qualities of a partitioning using six metrics: stress load, surface details, interface area, packed size, printability, and assembling. Based on this analysis, we then formulate level set methods to improve the qualities of the partitioning according to the metrics. These methods are integrated into an automatic system, which repetitively and locally optimizes the partitioning. Given the optimized partitioning result, we further provide a container structure modeling algorithm to facilitate the packing process of the printed pieces. Our experiment shows that the system can generate quality partitioning of various 3D models for space saving and fast production purposes.

Pixel-based meshfree modelling of skeletal muscles

This paper introduces the meshfree reproducing kernel particle method for 3D image-based modelling of skeletal muscles. This approach allows for construction of simulation model based on pixel data obtained from medical images. The material properties and muscle fibre direction obtained from diffusion tensor imaging (DTI) are input at each pixel point. The reproducing kernel approximation allows a representation of material heterogeneity with smooth transition. A multiphase multichannel level set based segmentation framework is adopted for individual muscle segmentation using magnetic resonance images and DTI. The application of the proposed methods for modelling the human lower leg is demonstrated.

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.

Optimal Rotor Design of IPM Motor for Improving Torque Performance Considering Thermal Demagnetization of Magnet

This paper proposes a new design technique for improving torque performance of interior permanent magnet (IPM) motors with consideration of the thermal characteristic of magnet. To verify the driving performance of IPM motor at operating temperature, a magnetic-thermal coupled analysis was performed with a heat source, such as iron loss and copper loss, and the thermal characteristics of permanent magnet (PM) is considered to define the magnetic property. The optimization problem is formulated to minimize the harmonics of magnetic flux, which cause iron loss, as well as to maximize the output torque for satisfying the design target. To obtain an optimal rotor shape of the IPM motor, which is composed of both PM and ferromagnetic material, a multi-phase level set model is employed for representing the precise boundaries of the magnetic materials. A design example of a motor with Nd-Fe-B magnet, which has a tendency to be demagnetized at high temperature, is provided to verify the effectiveness of the proposed method.

Active contours driven by local likelihood image fitting energy for image segmentation

Accurate image segmentation is an essential step in image analysis and understanding, where active contour models play an important part. Due to the noise, low contrast and intensity inhomogeneity in images, many segmentation algorithms suffer from limited accuracy. This paper presents a novel region-based active contour model for image segmentation by using the variational level set formulation. In this model, we construct the local likelihood image fitting (LLIF) energy functional by describing the neighboring intensities with local Gaussian distributions. The means and variances of local intensities in the LLIF energy functional are spatially varying functions, which can be iteratively estimated during an energy minimization process to guide the contour evolving toward object boundaries. To address diverse image segmentation needs, we also expand this model to the multiphase level set, multi-scale Gaussian kernels and narrowband formulations. The proposed model has been compared with several state-of-the-art active contour models on images with different modalities. Our results indicate that the proposed LLIF model achieves superior performance in image segmentation.

Coupled segmentation of nuclear and membrane-bound macromolecules through voting and multiphase level set

Membrane-bound macromolecules play an important role in tissue architecture and cell–cell communication, and is regulated by almost one-third of the genome. At the optical scale, one group of membrane proteins expresses themselves as linear structures along the cell surface boundaries, while others are sequestered; and this paper targets the former group. Segmentation of these membrane proteins on a cell-by-cell basis enables the quantitative assessment of localization for comparative analysis. However, such membrane proteins typically lack continuity, and their intensity distributions are often very heterogeneous; moreover, nuclei can form large clump, which further impedes the quantification of membrane signals on a cell-by-cell basis. To tackle these problems, we introduce a three-step process to (i) regularize the membrane signal through iterative tangential voting, (ii) constrain the location of surface proteins by nuclear features, where clumps of nuclei are segmented through a delaunay triangulation approach, and (iii) assign membrane-bound macromolecules to individual cells through an application of multi-phase geodesic level-set. We have validated our method using both synthetic data and a dataset of 200 images, and are able to demonstrate the efficacy of our approach with superior performance.Supplementary Information: One online video example can be found with: http://vision.lbl.gov/People/hang/evolving_fronts.gif

Segmentation and analysis of sub-cortical regions of autistic MR brain images using Gaussian distribution model based reaction diffusion multi-phase level sets and geometric feature

Segmentation and analysis of sub-cortical regions of autistic MR brain images using Gaussian distribution model based reaction diffusion multi-phase level sets and geometric feature

Segmentation and analysis of brain subcortical regions using regularized multiphase level set in autistic MR images

ABSTRACTIn this work, subcortical regions of autistic magnetic resonance brain images are analyzed using multiphase level set method. The images considered in this work are obtained from autism brain image data exchange database. The subcortical regions such as corpus callosum, cerebellum, and brain stem are segmented from the cortical region using Fuzzy c‐means (FCM)‐based multiphase level set method. FCM with three cluster center is used as the intensity discriminator and the evolution of the level set curve is regularized by a distance function. The results show that the multiphase level set method is able to segment the desired subcortical regions. The results are validated with the ground truth images. The average similarity values are found to be 0.85. The segmented subcortical regions of autistic have reduced tissue area and are distinct from the controls (p < 0.0001). Further, it is observed that the subcortical area gives comparable results with clinical intelligent quotient values and is able to discriminate the controls and autistic subjects. As the feature area extracted from brain subcortical regions are significant, this study seems to be clinically helpful in mass screening of autistic subjects. © 2014 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 24, 256–262, 2014

A Novel Level Set Method for Remote Sensing Image

Due to the characteristic of remote sensing image, we propose a novel method based on K-means algorithm also with the improved multi-phrase level set model. Comparing with the classical multi-phase C-V model, the improved model considers the region area information, gradient information and edge detection .Proper use of gradient information can overcome the inaccurate edge localization defects in image segmentation. The edge detection is used for keeping the boundary information better in the evolution process .For the reason of picking up the contour’s convergent speed and enable the avoidance of trap .Four stages are constructed. Firstly, a median filtering is applied to smooth the original image and reduce parts of noise. Secondly, the usage of K-means algorithm gains more obvious differences of characteristics. Next, the reconstruction of gradient is obtained by using Sobel operator. Finally, segmentation result is achieved by using an improved method of multi-phase level set image segmentation. Experimental results show that the proposed approach has advantages in rapid and efficient application of remote sensing image segmentation.

A New Medical Image Segmentation Method Based on Chan-Vese Model

The traditional segmentation method for medical image segmentation is difficult to achieve the accuracy requirement, and when the edges of the image are blurred, it will occurs incomplete segmentation problem, in order to solve this problem, we propose a medical image segmentation method which based on Chan-Vese model and mathematical morphology. The method integrates Chan-Vese model, mathematical morphology, composite multiphase level sets segmentation algorithm, first, through iterative etching operation to extract the outline of the medical image, and then the medical image is segmented by the Chan-Vese model based on the complex multiphase level sets, finally the medical image image is dilated iteratively by using morphological dilation to restore the image. The experimental results and analysis show that, this method improves the multi-region segmentation accuracy during the segmentation of medical image and solves the problem of incomplete segmentation.