Level Set Scheme Research Articles

Integrated Segmentation and Interpolation of Sparse Data

We address the two inherently related problems of segmentation and interpolation of 3D and 4D sparse data and propose a new method to integrate these stages in a level set framework. The interpolation process uses segmentation information rather than pixel intensities for increased robustness and accuracy. The method supports any spatial configurations of sets of 2D slices having arbitrary positions and orientations. We achieve this by introducing a new level set scheme based on the interpolation of the level set function by radial basis functions. The proposed method is validated quantitatively and/or subjectively on artificial data and MRI and CT scans and is compared against the traditional sequential approach, which interpolates the images first, using a state-of-the-art image interpolation method, and then segments the interpolated volume in 3D or 4D. In our experiments, the proposed framework yielded similar segmentation results to the sequential approach but provided a more robust and accurate interpolation. In particular, the interpolation was more satisfactory in cases of large gaps, due to the method taking into account the global shape of the object, and it recovered better topologies at the extremities of the shapes where the objects disappear from the image slices. As a result, the complete integrated framework provided more satisfactory shape reconstructions than the sequential approach.

Engineering feature design for level set based structural optimization

Engineering features are regular and simple shape units containing specific engineering significance. It is useful to combine feature design with structural optimization. This paper presents a generic method to design engineering features for level set based structural optimization. A Constructive Solid Geometry based Level Sets (CSGLS) description is proposed to represent a structure based on two types of basic entities: a level set model containing either a feature shape or a freeform boundary. By treating both entities implicitly and homogeneously, the optimal design of engineering features and freeform boundary are unified under the level set framework. For feature models, constrained affine transformations coupled with an accurate particle level set updating scheme are utilized to preserve feature characteristics, where the design velocity approximates continuous shape variation via a least squares fitting. Meanwhile, freeform models undergo a standard shape and topology optimization using a semi-Lagrangian level set scheme. With this method, various feature requirements can be translated into a CSGLS model, and the constrained motion provides flexible mechanisms to design features at different stages of the model tree. As a result, a truly optimal structure with engineering features can be created in a convenient way. Several numerical examples are provided to demonstrate the applicability and potential of this method.

A discontinuous Galerkin conservative level set scheme for interface capturing in multiphase flows

The accurate conservative level set (ACLS) method of Desjardins et al. [O. Desjardins, V. Moureau, H. Pitsch, An accurate conservative level set/ghost fluid method for simulating turbulent atomization, J. Comput. Phys. 227 (18) (2008) 8395–8416] is extended by using a discontinuous Galerkin (DG) discretization. DG allows for the scheme to have an arbitrarily high order of accuracy with the smallest possible computational stencil resulting in an accurate method with good parallel scaling. This work includes a DG implementation of the level set transport equation, which moves the level set with the flow field velocity, and a DG implementation of the reinitialization equation, which is used to maintain the shape of the level set profile to promote good mass conservation. A near second order converging interface curvature is obtained by following a height function methodology (common amongst volume of fluid schemes) in the context of the conservative level set. Various numerical experiments are conducted to test the properties of the method and show excellent results, even on coarse meshes. The tests include Zalesak’s disk, two-dimensional deformation of a circle, time evolution of a standing wave, and a study of the Kelvin–Helmholtz instability. Finally, this novel methodology is employed to simulate the break-up of a turbulent liquid jet.

Face Recognition Using a Coarse-to-Fine Level Set Scheme

This study inscribes a new approach for determining face-recognition system’s accuracy using a novel coarse-to-fine level set scheme. Recognizing a face in a facial database by using segmentation is a trivial challenge for many researchers. To distinguish facial photographic images from a background, the discrete wavelet transform is utilized to extract facial images. Novel energy function model is used for solving a contour extraction problem. In order to segment images, coarse-to-fine level set scheme is implemented. Finally face recognition process is done by face detection through the segmented images and matches the face with their same photograph, which is avail in the database. Extensive experiments have been carried out on capturing a facial photograph dynamically to validate the proposed method.

A New Image Segmentation Method Based on Improved Fast Implicit Level Set Scheme in X/γ-Ray Inspection System

Digital X/γ-ray imaging technology has been widely used to help people deliver effective and reliable security in airports, train stations, and public buildings. Nowadays, luggage inspection system with digital radiographic/computed tomography (DR/CT) represents a most advanced nondestructive inspection technology in aviation system, which is capable of automatically discerning interesting regions in the luggage objects with CT subsystem. In this paper, we propose a new model for active contours to detect luggage objects in the system, in order to facilitate people to identify the things in luggage. The proposed method is based on techniques of piecewise constant and piecewise smooths Chan-Vese Model, semi-implicit additive operator splitting (AOS) scheme for image segmentation. Different from traditional models, the fast implicit level set scheme (FILS) is ordinary differential equation (ODE). Characterized by no need of any pre-information of topology of images and efficient segmentation of images with complex topology, the FILS scheme is fast more than traditional level set scheme 30 times. At the same time, it performs well in image segmentation of DR images in our experiments.

Proposal of Fast Implicit Level Set Scheme for Medical Image Segmentation Using the Chan and Vese Model

People living in the information age, are more and more attention to their lives. It is also said, social life is more important in present and future. The social life contains three fields. In this paper, we propose a new model for active contours to detect objects in a given medical image, in order to facilitate people to have medical treatment. The proposed method is based on techniques of piecewise constant and piecewise smooths Chan-Vese Model, semi-implicit additive operator splitting (AOS) scheme for image segmentation. Different from traditional models, our model uses the level set which are corresponding to ordinary differential equation (ODE). Our model has more improved characteristics than traditional models, such as: less sensibility of noise; unnecessary of re-initialization and high speed by the simplified ordinary differential function. Finally, we validate the proposed model by numerical synthetic and real images. The experimental results demonstrate that our model is at least two times more efficient than the widely used methods.

Deflated preconditioned conjugate gradient solvers for the pressure‐Poisson equation: Extensions and improvements

AbstractExtensions and improvements to a deflated preconditioned conjugate gradient technique for the solution of the pressure‐Poisson equation within an incompressible flow solver are described. In particular, the use of the technique for embedded grids, for cases where volume of fluid or level set schemes are required and its implementation on parallel machines are considered. Several examples are included that demonstrate a considerable reduction in the number of iterations and a remarkable insensitivity to the number of groups/ regions chosen and/or to the way the groups are formed. Copyright © 2010 John Wiley & Sons, Ltd.

Conflation of Vector Buildings With Imagery

This letter presents a system to solve the vector-to-imagery building conflation problem. To drive the system, structure outlines in high-resolution images are extracted via a shape-driven level set scheme. Shape and relative position features are then computed for the image-extracted buildings and for vector graphics buildings from a geospatial information system (GIS). These two features are used by a graph-matching procedure that finds correspondences between the image-extracted buildings and those from a GIS. Extensions of our system to vector-to-vector building conflation, generic polygonal object conflation, and image-to-image registration are also possible.

Radial basis function based level set interpolation and evolution for deformable modelling

We present a study in level set representation and evolution using radial basis functions (RBFs) for active contour and active surface models. It builds on recent works by others who introduced RBFs into level sets for structural topology optimisation. Here, we introduce the concept into deformable models and present a new level set formulation able to handle more complex topological changes, in particular perturbation away from the evolving front. In the conventional level set technique, the initial active contour/surface is implicitly represented by a signed distance function and periodically re-initialised to maintain numerical stability. We interpolate the initial distance function using RBFs on a much coarser grid, which provides great potential in modelling in high dimensional space. Its deformation is considered as an updating of the RBF interpolants, an ordinary differential equation (ODE) problem, instead of a partial differential equation (PDE) problem, and hence it becomes much easier to solve. Re-initialisation is found no longer necessary, in contrast to conventional finite difference method (FDM) based level set approaches. The proposed level set updating scheme is efficient and does not suffer from self-flattening while evolving, hence it avoids large numerical errors. Further, more complex topological changes are readily achievable and the initial contour or surface can be placed arbitrarily in the image. These properties are extensively demonstrated on both synthetic and real 2D and 3D data. We also present a novel active contour model, implemented with this level set scheme, based on multiscale learning and fusion of image primitives from vector-valued data, e.g. colour images, without channel separation or decomposition.

Explicit and implicit modeling of nanobubbles in hydrophobic confinement

Water at normal conditions is a fluid thermodynamically close to the liquid-vapor phase coexistence and features a large surface tension. This combination can lead to interesting capillary phenomena on microscopic scales. Explicit water molecular dynamics (MD) computer simulations of hydrophobic solutes, for instance, give evidence of capillary evaporation on nanometer scales, i.e., the formation of nanometer-sized vapor bubbles (nanobubbles) between confining hydrophobic surfaces. This phenomenon has been exemplified for solutes with varying complexity, e.g., paraffin plates, coarse-grained homopolymers, biological and solid-state channels, and atomistically resolved proteins. It has been argued that nanobubbles strongly impact interactions in nanofluidic devices, translocation processes, and even in protein stability, function, and folding. As large-scale MD simulations are computationally expensive, the efficient multiscale modeling of nanobubbles and the prediction of their stability poses a formidable task to the'nanophysical' community. Recently, we have presented a conceptually novel and versatile implicit solvent model, namely, the variational implicit solvent model (VISM), which is based on a geometric energy functional. As reviewed here, first solvation studies of simple hydrophobic solutes using VISM coupled with the numerical level-set scheme show promising results, and, in particular, capture nanobubble formation and its subtle competition to local energetic potentials in hydrophobic confinement.

FAST TRACKING OF OBJECT CONTOUR BASED ON COLOR AND TEXTURE

This paper presents an efficient algorithm to track the object contour in image sequences. Firstly, the probability distributions of color feature and texture feature are approximated by different schemes. Secondly, the object and the background pixels are distinguished by calculating their posterior probability in light of Bayesian formula based on the two models. Finally, an energy functional is proposed and solved by gradient descent flow to evolve the initial contour which is estimated by motion feature, so that minimum energy contour corresponds to the object contour. In order to save the computational resource, a new texture descriptor is applied to analyze pixels merely in the neighborhood of a contour rather than the whole image. Furthermore, the algorithm's implementation based on the narrow band level set scheme can help to reduce the processing time further. In some experiments, the contours of various objects such as human, car and body organ are successfully tracked by our algorithm and the processing time is short enough for practical application.

Dynamic Texture Detection Based on Motion Analysis

Motion estimation is usually based on the brightness constancy assumption. This assumption holds well for rigid objects with a Lambertian surface, but it is less appropriate for fluid and gaseous materials. For these materials an alternative assumption is required. This work examines three possible alternatives: gradient constancy, color constancy and brightness conservation (under this assumption the brightness of an object can diffuse to its neighborhood). Brightness conservation and color constancy are found to be adequate models. We propose a method for detecting regions of dynamic texture in image sequences. Accurate segmentation into regions of static and dynamic texture is achieved using a level set scheme. The level set function separates each image into regions that obey brightness constancy and regions that obey the alternative assumption. We show that the method can be simplified to obtain a less robust but fast algorithm, capable of real-time performance. Experimental results demonstrate accurate segmentation by the full level set scheme, as well as by the simplified method. The experiments included challenging image sequences, in which color or geometry cues by themselves would be insufficient.

Development of a dispersively accurate conservative level set scheme for capturing interface in two-phase flows

A two-step interface capturing scheme, implemented within the framework of conservative level set method, is developed in this study to simulate the gas/water two-phase fluid flow. In addition to solving the pure advection equation, which is used to advect the level set function for tracking interface, both nonlinear and stabilized features are taken into account for the level set function so that a sharply varying interface can be stably predicted. To preserve the conservative property, the mapping given by ξ ̲ = x ̲ - u ̲ t is performed between two coordinates x ̲ and ξ ̲ for the advection–diffusion equation in a flow field with velocity u . To capture the interface, the flux term capable of compressing the level set contours is also adopted in the construction of linear inviscid Burgers’ equation, which is indispensable in the level set method. To resolve the physically sharp interface without incurring contact discontinuity oscillations, a damping term which is nonlinear in terms of the level set function and can render an adequate artificial diffusion to stabilize the contact surface is added into the reinitialization step in the modified level set method. For accurately predicting the level set function, the advection scheme for solving the linear inviscid Burgers’ equation in the advection step of the modified level set method is developed to accommodate the true dispersion relation. The solution computed from the resulting two-dimensional dispersion-relation-preserving advection scheme can minimize the phase error. Less artificial damping is needed to damp the oscillations in the vicinity of contact surface and the interface can be less numerically smeared. For the sake of programming simplicity, the incompressible two-phase flow will be discretized in non-staggered grids without incurring checkerboard oscillations by the developed explicit compact scheme for the approximation of pressure gradient terms. For the verification of the proposed two-dimensional dispersion-relation-preserving scheme and the non-staggered incompressible flow solver, three benchmark problems have been chosen in this study. The proposed conservative level set method for capturing the interface in incompressible fluid flows is also verified by solving the dam-break, bubble rising in water, droplet falling in water and Rayleigh–Taylor instability problems. Good agreements with the referenced solutions are demonstrated for all the four investigated problems.

Shape Reconstruction Using the Level Set Method for Microwave Applications

A shape reconstruction algorithm based on contour deformation using the full-band level set method is presented. Transverse magnetic plane waves are used for excitation. The results of full-band level set scheme are compared with those of narrowband scheme. A proposed measurement configuration is shown to produce more accurate results.

The Flexible, Extensible and Efficient Toolbox of Level Set Methods

Level set methods are a popular and powerful class of numerical algorithms for dynamic implicit surfaces and solution of Hamilton-Jacobi PDEs. While the advanced level set schemes combine both efficiency and accuracy, their implementation complexity makes it difficult for the community to reproduce new results and make quantitative comparisons between methods. This paper describes the Toolbox of Level Set Methods, a collection of Matlab routines implementing the basic level set algorithms on fixed Cartesian grids for rectangular domains in arbitrary dimension. The Toolbox’s code and interface are designed to permit flexible combinations of different schemes and PDE forms, allow easy extension through the addition of new algorithms, and achieve efficient execution despite the fact that the code is entirely written as m-files. The current contents of the Toolbox and some coding patterns important to achieving its flexibility, extensibility and efficiency are briefly explained, as is the process of adding two new algorithms. Code for both the Toolbox and the new algorithms is available from the Web.

Dynamic Tubular Grid: An Efficient Data Structure and Algorithms for High Resolution Level Sets

Level set methods [Osher and Sethian. Fronts propagating with curvature-dependent speed: algorithms based on Hamilton---Jacobi formulations. J. Comput. Phys. 79 (1988) 12] have proved very successful for interface tracking in many different areas of computational science. However, current level set methods are limited by a poor balance between computational efficiency and storage requirements. Tree-based methods have relatively slow access times, whereas narrow band schemes lead to very large memory footprints for high resolution interfaces. In this paper we present a level set scheme for which both computational complexity and storage requirements scale with the size of the interface. Our novel level set data structure and algorithms are fast, cache efficient and allow for a very low memory footprint when representing high resolution level sets. We use a time-dependent and interface adapting grid dubbed the Dynamic Tubular Grid or DT-Grid. Additionally, it has been optimized for advanced finite difference schemes currently employed in accurate level set computations. As a key feature of the DT-Grid, the associated interface propagations are not limited to any computational box and can expand freely. We present several numerical evaluations, including a level set simulation on a grid with an effective resolution of 10243

Level-set algorithm for the reconstruction of functional activation in near-infrared spectroscopic imaging

We introduce a new algorithm for the reconstruction of functional brain activations from near-infrared spectroscopic imaging (NIRSI) data. While NIRSI offers remarkable biochemical specificity, the attainable spatial resolution with this technique is rather limited, mainly due to the highly scattering nature of brain tissue and the low number of measurement channels. Our approach exploits the support-limited (spatially concentrated) nature of the activations to make the reconstruction problem well-posed. The new algorithm considers both the support and the function values of the activations as unknowns and estimates them from the data. The support of the activations is represented using a level-set scheme. We use a two-step alternating iterative scheme to solve for the activations. Since our approach uses the inherent nature of functional activations to make the problem well-posed, it provides reconstructions with better spatial resolution, fewer artifacts, and is more robust to noise than existing techniques. Numerical simulations and experimental data indicate a significant improvement in the quality (resolution and robustness to noise) over standard techniques such as truncated conjugate gradients (TCG) and simultaneous iterative reconstruction technique (SIRT) algorithms. Furthermore, results on experimental data obtained from simultaneous functional magnetic resonance imaging (fMRI) and optical measurements show much closer agreement of the optical reconstruction using the new approach with fMRI images than TCG and SIRT.

Study of the growth and motion of graphitic foam bubbles

In this paper, a numerical study is carried out to comprehend growth and movement of spherical bubble during foam processing. The numerical model is based on a level set technique for capturing the phase interface. The influences of surface tension, viscosity, pressure and diffusion through the system are monitored and related through simultaneous transfer of energy and mass between the liquid and vapor regions. Incorporating a level set scheme, the present model compares well with previous work. Through the contribution of non-dimensional parameters, a comparative study is performed to investigate and predict the effect of varying initial bubble radius and pressure as well as liquid viscosity. The predicted results shed light on the carbon foam formation, which will assist the achievement of tailoring carbon foams.

An Efficient, Interface-Preserving Level Set Redistancing Algorithm and Its Application to Interfacial Incompressible Fluid Flow

In Sussman, Smereka, and Osher [ J. Comp. Phys., 94 (1994), pp. 146--159], a numerical was presented for computing incompressible air--water flows using the level set method. Crucial to the above method was a new iteration method for maintaining the level set function as the signed from the zero level set. In this paper we implement a along with higher order difference schemes in order to make the iteration method more accurate and efficient. Accuracy is measured in terms of the new computed signed function and the original level set function having the same zero level set. We apply our redistancing to incompressible flows with noticeably better resolved results at reduced cost. We validate our results with experiment and theory. We show that our distance level set scheme with the added constraint competes well with available interface tracking schemes for basic advection of an interface. We perform basic accuracy checks and more stringent tests involving complicated interfacial structures. As with all level set schemes, our method is easy to implement.

An Adaptive Level Set Approach for Incompressible Two-Phase Flows

We present a numerical method using the level set approach for solving incompressible two-phase flow with surface tension. In the level set approach, the free surface is represented as the zero level set of a smooth function; this has the effect of replacing the advection of density, which has steep gradients at the free surface, with the advection of the level set function, which is smooth. In addition, the free surface can merge or break up with no special treatment. We maintain the level set function as the signed distance from the free surface in order to accurately compute flows with high density ratios and stiff surface tension effects. In this work, we couple the level set scheme to an adaptive projection method for the incompressible Navier–Stokes equations, in order to achieve higher resolution of the free surface with a minimum of additional expense. We present two-dimensional axisymmetric and fully three-dimensional results of air bubble and water drop computations.