Traditional Level Set Methods Research Articles

Improving level set method for fast auroral oval segmentation.

Auroral oval segmentation from ultraviolet imager images is of significance in the field of spatial physics. Compared with various existing image segmentation methods, level set is a promising auroral oval segmentation method with satisfactory precision. However, the traditional level set methods are time consuming, which is not suitable for the processing of large aurora image database. For this purpose, an improving level set method is proposed for fast auroral oval segmentation. The proposed algorithm combines four strategies to solve the four problems leading to the high-time complexity. The first two strategies, including our shape knowledge-based initial evolving curve and neighbor embedded level set formulation, can not only accelerate the segmentation process but also improve the segmentation accuracy. And then, the latter two strategies, including the universal lattice Boltzmann method and sparse field method, can further reduce the time cost with an unlimited time step and narrow band computation. Experimental results illustrate that the proposed algorithm achieves satisfactory performance for auroral oval segmentation within a very short processing time.

A Fast Level Set Algorithm for Building Roof Recognition From High Spatial Resolution Panchromatic Images

Traditional level set methods usually require repeated tuning of parameters, which is quite laborious and thus limits their applications. In order to simplify the parameter setting, this letter presents a fast level set algorithm that is a further extension of the original Chan-Vese model. For computational efficiency, we start by initializing the level set function in our algorithm as a binary step function rather than the often used signed distance function. Then, we eliminate the curvature-based regularizing term that is commonly used in traditional models. Thus, we can use a relatively larger time step in the numerical scheme to expedite our model. Furthermore, to keep the evolving level curves smooth, we introduce a Gaussian kernel into our algorithm to convolve the updated level set function directly. Finally, compared with other existing popular algorithms in an experiment of recognizing building roofs from high spatial resolution panchromatic images, the proposed model is much more computationally efficient while object recognition performance is comparable to other popular models.

A modification of level set re-initialized method for the shock waves through the air bubble

For the re-initialization problem of the level set method, a new re-initialization formula of smoothing parameter based on the traditional implicit method is proposed. The improved method is applied to describe the process of the shock through the air bubble by means of numerical simulation. Numerical results show that the method is superior to the traditional level set method.

Active contours driven by normalized local image fitting energy

SUMMARYIn this paper, a new local region‐based active contour model that is driven by normalized local image fitting energy is proposed. By considering the local image fitting energy to extract the local image information, our model can effectively and efficiently segment images with intensity inhomogeneities. In addition, to keep the smoothness of the level set function, the time‐consuming reinitialization step widely adopted in traditional level set methods can be avoided by introducing a Gaussian filtering process. Experimental results on synthetic and real images demonstrate that the proposed model has much less CPU time and sensitivity to the initial contour than the well‐known local binary fitting model. Copyright © 2013 John Wiley & Sons, Ltd.

Interactive geospatial object extraction in high resolution remote sensing images using shape-based global minimization active contour model

In this work, we propose a novel algorithm to extract geospatial objects with regular shape in remote sensing images, using shape-based global minimization active contour model (SGACM). Specially, we define a new energy function combining both image appearance information and object shape prior, and minimize it with an iterative global minimization method. In the proposed energy, not only image edge and color information are utilized, but also a new shadow region term is introduced to obtain more accurate extraction result; moreover, a new shape energy term in which we use kernel principle component analysis (KPCA) to model shapes is defined in our method, which provides good constraint on the extraction process and makes results more robust with respect to disturbances. In the energy numerical minimization process, Split Bregman method is used to get a global solution which overcomes the drawback of running into local minimum for the traditional level set method. Experiment results demonstrate more robustness and accuracy of our proposed method compared with others without shape constraint.

An Edge-and Region-Based Level Set Method with Shape Priors for Image Segmentation

Traditional level set methods could not deal with the segmentation of overlapped objects and the ones having the similar gray value with background,since these methods just take image data into consideration.Aiming for this problem,we propose a new edge-and region-based level set method for image segmentation.Our method firstly fuses the regional information into the edge-based level set method,and then incorporates shape priors to design a new level set method with shape priors.The comparison results show that the proposed method can segment the overlapped objects better and also achieve better performance on the objects with the similar gray value as background since it integrates multiple kinds of information together.

A novel segmentation method for breast ultrasound images based on neutrosophic l‐means clustering

Fully automatic and accurate breast lesion segmentation is an essential and challenging task. In this paper, the authors develop a novel, effective, and fully automatic method for breast ultrasound (BUS) image segmentation. The segmentation method utilizes a novel phase feature to improve the image quality, and a novel neutrosophic clustering approach to detect the accurate lesion boundary. First, a region of interest is generated to cut off complex background. After speckle reduction, an enhancement algorithm based on phase in max-energy orientation (PMO) is developed to further improve the image quality. The PMO is a newly proposed 2D phase feature obtained by filtering the image in the frequency domain and calculating the phase accumulation in the orientation with maximum energy. Finally, the authors propose a novel clustering approach called neutrosophic l-means (NLM) to detect the lesion boundary. NLM is a generalized clustering method that can be used to solve other clustering problems as well. In this paper, NLM is used to segment images with vague boundaries, and to deal with uncertainty better. To evaluate the performance of the proposed method, the authors compare it with the traditional fuzzy c-means clustering, active contour, level set, and watershed-based segmentation methods, using a common database. Radiologist's manual delineations are used as the golden standards. Five assessment metrics are utilized to evaluate the performance from different aspects. Both accuracy and efficiency are analyzed. Sensitivity analysis is also conducted to test the robustness of the proposed method. Compared with the other methods, the proposed method generates the most similar boundaries to the radiologist's manual delineations (TP rate is 92.4%, FP rate is 7.2%, and similarity rate is 86.3%; Hausdorff distance is 22.5 pixels and mean absolute distance is 4.8 pixels), with efficient processing speed (averagely 9.8 s per image). Sensitivity analysis shows the robustness of the proposed method as well. The proposed method is a fully automatic segmentation method for BUS images that can generate accurate lesion boundaries even for complicated cases. The fast processing speed, robustness, and accuracy of the proposed method suggest its potential applications in clinics.

Fast and Regularization less Active Contour

The application of the level set method in image segmentation has been very popular due to its capability of automatically handling changes in topology. However, a re-initialization procedure, which leads to expensive computation, is required in the traditional level set method to keep the level set function as a signed distance function to its interface. A method based on Gaussian filtering and binary level set is proposed for the level set function of region based active contour model (ACM). The proposed level set method is integrated with the global region based Chan-Vese (C-V) ACM for image segmentation. The proposed method can, not only ensure the smoothness of the level set function by Gaussian filtering, but also eliminate the requirement of re-initialization, which is very computationally expensive task. The level set function can also be easily initialized as a binary function, which is more efficient to construct practically than the widely used signed distance function (SDF). Moreover, as the proposed scheme allows using larger time step than what can be used with the standard C-V model, it is tremendously faster than standard C-V model. Finally, the proposed algorithm can be efficiently implemented by the simple finite difference scheme. Experimental results on synthetic and real images shows that the proposed method is more efficient in terms of computational time and accuracy than global region based C-V active contour model.

Automatic left ventricle segmentation in volumetric SPECT data set by variational level set

Left ventricle (LV) quantification in nuclear medicine images is a challenging task for myocardial perfusion scintigraphy. A hybrid method for left ventricle myocardial border extraction in SPECT datasets was developed and tested to automate LV ventriculography. Automatic segmentation of the LV in volumetric SPECT data was implemented using a variational level set algorithm. The method consists of two steps: (1) initialization and (2) segmentation. Initially, we estimate the initial closed curves in SPECT images using adaptive thresholding and morphological operations. Next, we employ the initial closed curves to estimate the final contour by variational level set. The performance of the proposed approach was evaluated by comparing manually obtained boundaries with automated segmentation contours in 10 SPECT data sets obtained from adult patients. Segmented images by proposed methods were visually compared with manually outlined contours and the performance was evaluated using ROC analysis. The proposed method and a traditional level set method were compared by computing the sensitivity and specificity of ventricular outlines as well as ROC analysis. The results show that the proposed method can effectively segment LV regions with a sensitivity and specificity of 88.9 and 96.8%, respectively. Experimental results demonstrate the effectiveness and reasonable robustness of the automatic method. A new variational level set technique was able to automatically trace the LV contour in cardiac SPECT data sets, based on the characteristics of the overall region of LV images. Smooth and accurate LV contours were extracted using this new method, reducing the influence of nearby interfering structures including a hypertrophied right ventricle, hepatic or intestinal activity, and pulmonary or intramammary activity.

Dynamical systems over the space of upper semicontinuous fuzzy sets

Given a locally compact separable metric space E, a perfect transformation defined on E induces a Zadeh extension, which is a transformation from the space of all upper semicontinuous fuzzy sets defined on E to itself. Here, the latter space is equipped with the hit-or-miss topology. In this setting, each upper semicontinuous fuzzy set is identified with its hypograph, a closed subset in the product space of E and [0,1]. This approach does not require the relevant fuzzy sets to hold a compact support, and it also overcomes the drawback of the traditional level-set method. Further, it is proved that the Zadeh extension with this setting is continuous in the hit-or-miss topology; and dynamical properties of Zadeh extension regarding iteration have been explored.

Parametric level set reconstruction methods for hyperspectral diffuse optical tomography

A parametric level set method (PaLS) is implemented for image reconstruction for hyperspectral diffuse optical tomography (DOT). Chromophore concentrations and diffusion amplitude are recovered using a linearized Born approximation model and employing data from over 100 wavelengths. The images to be recovered are taken to be piecewise constant and a newly introduced, shape-based model is used as the foundation for reconstruction. The PaLS method significantly reduces the number of unknowns relative to more traditional level-set reconstruction methods and has been show to be particularly well suited for ill-posed inverse problems such as the one of interest here. We report on reconstructions for multiple chromophores from simulated and experimental data where the PaLS method provides a more accurate estimation of chromophore concentrations compared to a pixel-based method.

Topology Optimization of Compliant Mechanisms Using Level Set Method without Re-Initialization

In this paper, a new level set method for topology optimization of compliant mechanisms is presented. A new formulation is developed and built in the traditional level set method to force the level set function to be close to a signed distance function during the optimal process. The validity of the method is illustrated by topology optimization of a widely studied compliant mechanism.

Active contours with selective local or global segmentation property for multiobject image

In this paper, a novel region-based active contour model is proposed. Unlike the Chan-Vese model, the energy function of our model only uses information outside the evolving curve. A restriction matrix is introduced for restricting the curve to evolve in the desired region. By minimizing the proposed energy function, the corresponding level set function is obtained. The proposed method has four advantages over the traditional region-based level set methods. First, the level set function is no longer required to be initialized as a sign distance function. Second, due to the simplified level set formulation and its fast curve evolution speed, the level set function does not need to be re-initialized and the computational cost is low. Third, our model is applicable to multiobject images since it can segment objects by separating background from an image. Finally, the proposed model has the property of selective local or global segmentation; it can segment not only the desired object but also the other objects in an image. The advantages of our model are demonstrated using synthetic and real images. C 2011 Society of Photo-Optical

On a Novel Dual-Grid Level-Set Method for Two-Phase Flow Simulation

In this work, a hypothesis is proposed for two-phase flow simulation: The number of grid points required for the grid-independent solution of the flow field is lesser than that required to capture the grid-independent interface. Based on this, a dual-grid level-set(LS) method (DGLSM) is proposed, where the LS and energy equations are solved on a uniform grid which is twice finer than the continuity and momentum equations. This novel grid arrangement is aimed at improving interface resolution with only a slight increase in computational time. Qualitative and quantitative results of the DGLSM are compared against analytical, experimental, and numerical results on three stringent test problems: dam break, Rayleigh-Taylor instability, and film boiling. The results show that the DGLSM is accurate and robust, even for surface tension-dominant flows. Moreover, the hypothesis is corroborated by showing that the DGLSM is nearly as accurate as the completely refined traditional LS method at substantially less computational expense.

Evolutionary level set method for structural topology optimization

This paper proposes an evolutionary accelerated computational level set algorithm for structure topology optimization. It integrates the merits of evolutionary structure optimization (ESO) and level set method (LSM). Traditional LSM algorithm is largely dependent on the initial guess topology. The proposed method combines the merits of ESO techniques with those of LSM algorithm, while allowing new holes to be automatically generated in low strain energy within the nodal neighboring region during optimization. The validity and robustness of the new algorithm are supported by some widely used benchmark examples in topology optimization. Numerical computations show that optimization convergence is accelerated effectively.

Parametric Level Set Methods for Inverse Problems

In this paper, a parametric level set method for reconstruction of obstacles in general inverse problems is considered. General evolution equations for the reconstruction of unknown obstacles are derived in terms of the underlying level set parameters. We show that using the appropriate form of parameterizing the level set function results a significantly lower dimensional problem, which bypasses many difficulties with traditional level set methods, such as regularization, re-initialization and use of signed distance function. Moreover, we show that from a computational point of view, low order representation of the problem paves the path for easier use of Newton and quasi-Newton methods. Specifically for the purposes of this paper, we parameterize the level set function in terms of adaptive compactly supported radial basis functions, which used in the proposed manner provides flexibility in presenting a larger class of shapes with fewer terms. Also they provide a "narrow-banding" advantage which can further reduce the number of active unknowns at each step of the evolution. The performance of the proposed approach is examined in three examples of inverse problems, i.e., electrical resistance tomography, X-ray computed tomography and diffuse optical tomography.

Nodal Evolutionary Computation Enhanced Level Set Algorithm for Structural Topology Optimization

This paper proposes an improved computational algorithm for structure topology optimization. It integrates the merits of Evolutionary Structure Optimization and Level Set Method (LSM) for structure topology optimization. Traditional LSM algorithm has some drawbacks, for instance, its optimal topology configuration is largely dependent on the structural topology initialization. Additionally, new holes cannot be evolved within the updated topology during the optimization iteration. The method proposed in this paper combines the merits of ESO techniques with the LSM scheme, allowing new holes to be automatically inserted in regions with low deformation energy at prescribed iterations of the optimization. The nodal neighboring region is a good selection. For complex structures in which holes cannot be properly inserted in advance, the proposed method considerably improves the ability of LSM to search the optimal topology. In addition to achieving more accurate results, the proposed method also yields higher efficiency during optimization. Benchmark problems are presented to show the effectiveness and robustness of the new proposed algorithm.

Adaptive Distance Preserving Level Set Evolution for Image Segmentation

The distance preserving level set method proposed by Li et al. has many advantages over the traditional variational level set methods. However, it has the disadvantage of requiring the initial curve to surround (let in or keep out) the objects to be detected. In this paper, an adaptive distance preserving level set method is proposed, in which the initial curve is no longer required to surround (let in or keep out) the objects to be detected, i.e., the initial curve can be anywhere in the image. The proposed method can detect certain object boundaries, for which the original method is not applicable. E.g. it can automatically detect interior and exterior contours of an object and edges of multi-objects, starting with only one initial curve whose position is anywhere in the image. Moreover, active contours can move into boundary concavities and perform better in the presence of weak boundaries. The proposed method has been applied to synthetic and real images of different object boundaries with promising results.

An efficient local Chan–Vese model for image segmentation

In this paper, a new local Chan–Vese (LCV) model is proposed for image segmentation, which is built based on the techniques of curve evolution, local statistical function and level set method. The energy functional for the proposed model consists of three terms, i.e., global term, local term and regularization term. By incorporating the local image information into the proposed model, the images with intensity inhomogeneity can be efficiently segmented. In addition, the time-consuming re-initialization step widely adopted in traditional level set methods can be avoided by introducing a new penalizing energy. To avoid the long iteration process for level set evolution, an efficient termination criterion is presented which is based on the length change of evolving curve. Particularly, we proposed constructing an extended structure tensor (EST) by adding the intensity information into the classical structure tensor for texture image segmentation. It can be found that by combining the EST with our LCV model, the texture image can be efficiently segmented no matter whether it presents intensity inhomogeneity or not. Finally, experiments on some synthetic and real images have demonstrated the efficiency and robustness of our model. Moreover, comparisons with the well-known Chan–Vese (CV) model and recent popular local binary fitting (LBF) model also show that our LCV model can segment images with few iteration times and be less sensitive to the location of initial contour and the selection of governing parameters.

The Piecewise Smooth Mumford–Shah Functional on an Arbitrary Graph

The Mumford-Shah functional has had a major impact on a variety of image analysis problems, including image segmentation and filtering, and, despite being introduced over two decades ago, it is still in widespread use. Present day optimization of the Mumford-Shah functional is predominated by active contour methods. Until recently, these formulations necessitated optimization of the contour by evolving via gradient descent, which is known for its overdependence on initialization and the tendency to produce undesirable local minima. In order to reduce these problems, we reformulate the corresponding Mumford-Shah functional on an arbitrary graph and apply the techniques of combinatorial optimization to produce a fast, low-energy solution. In contrast to traditional optimization methods, use of these combinatorial techniques necessitates consideration of the reconstructed image outside of its usual boundary, requiring additionally the inclusion of regularization for generating these values. The energy of the solution provided by this graph formulation is compared with the energy of the solution computed via traditional gradient descent-based narrow-band level set methods. This comparison demonstrates that our graph formulation and optimization produces lower energy solutions than the traditional gradient descent based contour evolution methods in significantly less time. Finally, we demonstrate the usefulness of the graph formulation to apply the Mumford-Shah functional to new applications such as point clustering and filtering of nonuniformly sampled images.