Traditional Level Set Methods Research Articles

Tumor Segmentation in Intraoperative Fluorescence Images Based on Transfer Learning and Convolutional Neural Networks.

To propose a transfer learning based method of tumor segmentation in intraoperative fluorescence images, which will assist surgeons to efficiently and accurately identify the boundary of tumors of interest. We employed transfer learning and deep convolutional neural networks (DCNNs) for tumor segmentation. Specifically, we first pre-trained four networks on the ImageNet dataset to extract low-level features. Subsequently, we fine-tuned these networks on two fluorescence image datasets (ABFM and DTHP) separately to enhance the segmentation performance of fluorescence images. Finally, we tested the trained models on the DTHL dataset. The performance of this approach was compared and evaluated against DCNNs trained end-to-end and the traditional level-set method. The transfer learning-based UNet++ model achieved high segmentation accuracies of 82.17% on the ABFM dataset, 95.61% on the DTHP dataset, and 85.49% on the DTHL test set. For the DTHP dataset, the pre-trained Deeplab v3 + network performed exceptionally well, with a segmentation accuracy of 96.48%. Furthermore, all models achieved segmentation accuracies of over 90% when dealing with the DTHP dataset. To the best of our knowledge, this study explores tumor segmentation on intraoperative fluorescent images for the first time. The results show that compared to traditional methods, deep learning has significant advantages in improving segmentation performance. Transfer learning enables deep learning models to perform better on small-sample fluorescence image data compared to end-to-end training. This discovery provides strong support for surgeons to obtain more reliable and accurate image segmentation results during surgery.

A new efficient parametric level set method based on radial basis function-finite difference for structural topology optimization

To overcome a significant challenge in traditional parameterized level set methods based on globally supported radial basis functions, we propose employing a local differentiation construction of radial basis functions using finite difference, a technique previously applied to solving partial differential equations but novel in the context of topology optimization. We present a novel parameterized level set method for structural topology optimization of compliance minimization and compliant mechanism, with the main aim of reducing computational costs associated with fully dense matrices when approximating systems with a large number of collocation points. The new scheme implemented with rectangular mesh elements and polygonal mesh generation accommodates both rectangular and complex design domains. Numerical results are provided to demonstrate the algorithm's effectiveness.

A generalized variational level set method without frequent reinitialization for simulations of gas-liquid flows

A generalized variational level set method without frequent reinitialization process is proposed to address the issue of the traditional level set method for detailed numerical simulations of gas-liquid flows. The gas-liquid interface is captured by the level set method and the discontinuity across the interface is discretized by the ghost fluid method. A penalty term is added in the classical level set advection equation to reduce the frequent reinitialization process. The effect of the frequency of the reinitialization step on the performance of the level set method is evaluated and the effect of the penalty factor on the interface evolution is investigated in the present work. Three typical benchmark cases, including rigid body rotation, two-dimensional shear motion, and three-dimensional shear motion, are used to validate the accuracy of the present variational level set method. It is found that the reinitialization process is not necessary for every time step with the penalty term. A spatially averaged parameter near the interface is proposed to quantitatively evaluate the necessity of reinitialization. The present method is also shown to have second-order accuracy. This work provides an accurate and efficient way to simulate the gas-liquid flows.

Enhancing level set brain tumor segmentation using fuzzy shape prior information and deep learning

AbstractMagnetic resonance imaging (MRI) brain tumor segmentation is a crucial task for clinical treatment. However, it is challenging owing to variations in type, size, and location of tumors. In addition, anatomical variation in individuals, intensity non‐uniformity, and noises adversely affect brain tumor segmentation. To address these challenges, an automatic region‐based brain tumor segmentation approach is presented in this paper which combines fuzzy shape prior term and deep learning. We define a new energy function in which an Adaptively Regularized Kernel‐Based Fuzzy C‐Means (ARKFCM) Clustering algorithm is utilized for inferring the shape of the tumor to be embedded into the level set method. In this way, some shortcomings of traditional level set methods such as contour leakage and shrinkage have been eliminated. Moreover, a fully automated method is achieved by using U‐Net to obtain the initial contour, reducing sensitivity to initial contour selection. The proposed method is validated on the BraTS 2017 benchmark dataset for brain tumor segmentation. Average values of Dice, Jaccard, Sensitivity and specificity are 0.93 ± 0.03, 0.86 ± 0.06, 0.95 ± 0.04, and 0.99 ± 0.003, respectively. Experimental results indicate that the proposed method outperforms the other state‐of‐the‐art methods in brain tumor segmentation.

An adaptive parametric level-set method for lung health monitoring with smartphone-based electrical impedance tomography

In this paper, an adaptive parametric level-set method is presented for lung health monitoring with smartphone-based electrical impedance tomography (EIT). Firstly, assuming that the conductivity distribution to be reconstructed is piecewise constant, the shape of lung-like targets is represented by a PLS function using a Gaussian radial basis function. Secondly, the unknown parameters (e.g. centers, widths, and weights) are computed adaptively without a prior information about targets. Thirdly, rectified Adam is proposed to adaptively adjust the learning rate during the iterative process. The proposed method is evaluated quantitatively by simulated lung imaging, water tank tests, and human breathing data. In addition, the robustness of the proposed method is performed by considering different gradient descent methods and different number of RBF centers. The reconstruction results show that the proposed method not only overcomes some problems associated with the traditional level-set method (e.g. reinitialization and use of signed distance function), but also avoids empirical parameter selections in the PLS method, resulting in faster imaging speed and better imaging quality with an average image correlation coefficient greater than 0.90. It is found that the one-second rate of the proposed method is closer to the true value with an average error of no more than 2% when the forced vital capacity tests are repeatedly performed on five volunteers with healthy lungs. The proposed method is promising in providing the reliable assessment of lung health monitoring with smartphone-based EIT.

Learning high-order geometric flow based on the level set method

Recently, the development of deep learning has accomplished unbelievable success in many fields, especially in scientific computational fields. And almost all computational problems and physical phenomena can be described by partial differential equations. In this work, we proposed two potential high-order geometric flows. Motivation by the physical-information neural networks and the traditional level set method (LSM), we have integrated deep neural networks and LSM to make the proposed method more robust and efficient. Also, to test the sensitivity of the system to different input data, we set up three sets of initial conditions to test the model. Furthermore, numerical experiments on different input data are implemented to demonstrate the effectiveness and superiority of the proposed models compared to the state-of-the-art approach.

An Automatically Initialized Level Set Method for Ochotona Curzoniae Image Segmentation

In order to effectively solve this problem that that the traditional level set method needs to mark the initial contour manually, a novel method that automatic initialization by utilizing deep learning is proposed in this paper. Firstly, a target detection network based on Faster-RCNN is used for target detection of ochotona curzoniae. Secondly, the detected target boxes are regarded as the initial contour of level set models, and ochotona curzoniae images are segmented by level set models, by which the problem of manually plotting the initial contour required by traditional level set models is solved. The experimental results of ochotona curzoniae image segmentation show that there is little difference between the level set segmentation method in which the initial contour of the target is automatically generated by deep learning(LSECA) is used to automatically target initial contour and the level set segmentation method where initial contour needs to be manually plotted. Therefore, the experimental results prove that it is feasible to automatically obtain the target initial contour through deep learning.

Topology Optimization of Nonlinear Material Structures Based on Parameterized Level Set and Substructure Methods

In order to overcome the problems of complicated calculation process and lower computational efficiency of the traditional level set method (LSM), for nonlinear structure topology optimization, a parameterized level set method (PLSM) was introduced. Through interpolation of the initial level set function with the globally supported radial basis function (GSRBF), a nonlinear material structure topology optimization model was established with the interpolation coefficient as the design variable, the minimum strain energy of the structure as the objective function, and the material amount as the constraint condition. The equilibrium equation for the nonlinear material structure was established by finite element analysis, and solved with the iterative method. In addition, the substructure method (i.e. the domain decomposition method) was used to divide the design area into several sub-areas, and the solution to the full degree of freedom equilibrium equation was decomposed into a set of solutions of reduced equilibrium equations and solutions of multiple substructures’ internal displacements, which could reduce the computation cost. Examples show that, this method can ensure the numerical stability, improve the computational efficiency, and obtain the topology optimization configuration with clear boundaries and reasonable structures.

Enhancement and Segmentation of Medical Images Using AGCWD and ORACM

Images that are obtained in the real world in low contrast are inappropriate for human eyes to read the medical images. Enhancement and segmentation have an important role to play in digital image processing, pattern recognition, and the computer vision. Here, this paper presents an effective way of changing histograms and improving contrast in digital images. Segmentation is done on AGCWD enhanced images. Histogram equalization is an important technique for contrast enhancement. Nevertheless, modern Histogram Equalization commonly results in unnecessary contrast enhancement, which in turn offers an un-natural presence to the processed image and produces visual artifacts. We present an automated transformation technique that helps boost dimmed image brightness by gamma correction and weighted distribution, commonly known as Adaptive Gamma Correction Weighted Distribution (AGCWD). The contrast enhancement level can be modified using this technique; noise robustness, white or black stretching, and the protection of medium brightness can be easily integrated into the optimization process. Finally, a contrast enhancement algorithm with low complexity is introduced. All the process of enhancement will be done during the process of pre-processing the image. Later, in post-processing, we introduce a specific level set method known as ORACM for better segmentation of an enhanced AGCWD image, and it is compared with the traditional level set method.

A mass-preserving interface-correction level set/ghost fluid method for modeling of three-dimensional boiling flows

We present an efficient method for the direct numerical simulation of three-dimensional (3D) boiling flows. The liquid-vapor interface dynamics is captured using an interface-correction level set method, modified to account for the interface heat and mass transfer due to phase change. State-of-the-art computational techniques, such as the fast pressure-correction and ghost-fluid methods, are implemented to accurately solve the coupled thermo-fluid problem involving large density contrasts and jump conditions. The solver is thoroughly validated against four benchmark cases with increasing complexity, which show better mass conservation properties than traditional level set methods, thus allowing for coarser grid resolutions and lower computational costs. We further demonstrate our method by simulating two realistic 3D boiling flows in greater details. In the first case, a saturated film boiling of water vapor at near critical conditions over a horizontal hot flat plate is considered. The results are analyzed by comparing the transient evolution of the interface morphology, temperature distribution, space and time averaged Nusselt numbers obtained from numerical simulations with the semi-empirical correlation of Berenson and existing numerical literature. In the second case, we simulate the condensation and buoyancy-driven motion of a single spherical water vapor bubble at different subcooled liquid temperatures and saturation pressures. We find opposite trends of the condensation rate and the bubble rising velocity when the degree of subcooling is increased, and an increase of the condensation rate at lower saturation pressures, due to variation of the thermophysical properties.

Image Segmentation Using Level Set Driven by Generalized Divergence

Image segmentation is an important analysis tool in the field of computer vision. In this paper, on the basis of the traditional level set method, a novel segmentation model using generalized divergences is proposed. The main advantage of generalized divergences is their smooth connection performance among various kinds of well-known and frequently used fundamental divergences with one formula. Therefore, the discrepancy between two probability distributions of segmented image parts can be measured by generalized divergences. We also found a solution to determine the optimal divergence automatically for different images. Experimental results on a variety of synthetic and natural images are presented, which demonstrate the potential of the proposed method. Compared with the previous active contour models formulated to solve the same nonparametric statistical segmentation problem, our method performs better both qualitatively and quantitatively.

An integrated two-stage approach for image segmentation via active contours

A novel integrated two-stage approach is proposed for image segmentation, where the edge, global and local region information of images are in turn incorporated to define the intensity fitting energy. In the first stage, the Chan-Vese model flexibly assimilates the edge indicator function in the beginning, and then the Laplace operator is introduced to regularize the level set function when minimizing the energy functional. As an edge-based and global region-based active contour, it can be inclined to rapidly produce a coarse segmentation result. In the second stage, we further segment the image by absorbing the local region fitting energy, where its initialization is acquired by the final active contour of the first stage. In addition, we present a generalized level set regularization term, which efficiently eliminates the periodically re-initialization procedure of traditional level set methods and maintains the corresponding signed distance property. Compared with the first stage, the local object details are accurately segmented in the second stage, which can acquire an accurate segmentation result. Qualitative and quantitative experimental results demonstrate the accuracy, robustness and efficiency of our approach with applications to some synthetical and real-world images.

Detailed Voxel-Based Implicit Modeling With Local Boolean Composition of Discrete Level Sets

Compared with the functionally-based implicit models, the level set models are usually defined by discretely sampling the implicit function values over the volume grid to represent the shapes, which are suitable for scientific computing and engineering. However, the voxel-based level set methods usually lose some features and details to represent the solids due to the finite grid resolutions. In this paper, we propose a more accurate voxel-based implicit modeling method based on discrete level sets. Compared with the traditional level set methods, more than one level set function can be defined in an implicit model with our approach by classifying the cells of the volume grid. The local Boolean compositions conducted over the compound cells are used to depict the interactions of different implicit surfaces represented by corresponding level set functions, and the sharp and thin details caused by Boolean operations are preserved owing to the definition of the compound cells. We show in our experiments that our method is robust to provide the more detailed implicit description of the shapes with less loss of the features than the conventional voxel-based level set methods.

Level set based shape prior and deep learning for image segmentation

Deep convolutional neural network can effectively extract hidden patterns in images and learn realistic image priors from the training set. And fully convolutional networks (FCNs) have achieved state-of-the-art performance in the image segmentation. However, these methods have the disadvantages of noise, boundary roughness and no prior shape. Therefore, this study proposes a level set with the deep prior method for the image segmentation based on the priors learned by FCNs. The FCNs can learn high-level semantic patterns from the training set. Also, the output of the FCNs represents the high-level semantic information as a probability map and the global affine transformation can obtain the optimal affine transformation of the intrinsic prior shape. Moreover, the improved level set method integrates the information of the original image, the probability map and the corrected prior shape to achieve the image segmentation. Compared with the traditional level set method of simple scenes, the proposed method solves the disadvantage of FCNs by using the high-level semantic information to segment images of complex scenes. Finally, Portrait data set are used to verify the effectiveness of the proposed method. The experimental results show that the proposed method can obtain more accurate segmentation results than the traditional FCNs.

Contextual Level-Set Method for Breast Tumor Segmentation

Breast ultrasound image segmentation is the foundation of the diagnosis and treatment of breast cancer. The level set method is widely used for medical image segmentation. However, it remained a challenge for traditional level set methods because they cannot fully understand the tumor regions with complex characteristics by only low-level features. Considering that contextual features can provide complementary discriminative information to low-level features, this paper proposed a contextual level set method for breast tumor segmentation. Firstly, an encoder-decoder architecture network such as UNet is developed to learn high-level contextual features with semantic information. After that, the contextual level set method has been proposed to incorporate the novel contextual energy term. The proposed term has the ability to embed the high-level contextual knowledge into the level set framework. The learned contextual features with semantic information can provide more discriminative information, which has been directly associated with category labels, instead of the original intensity. Therefore, it is robust to serious intensity inhomogeneity, which is helpful to improve segmentation performance. The experiments had taken place with the help of three databases, which indicates that the proposed method outperformed traditional methods.

A variational level set methodology without reinitialization for the prediction of equilibrium interfaces over arbitrary solid surfaces

A robust numerical methodology to predict equilibrium interfaces over arbitrary solid surfaces is developed. The kernel of the proposed method is the distance regularized level set equations (DRLSE) with techniques to incorporate the no-penetration and volume-conservation constraints. In this framework, we avoid reinitialization that is typically used in traditional level set methods. This allows for a more efficient algorithm since only one advection equation is solved, and avoids numerical error associated with the re-distancing step. A novel surface tension distribution, based on harmonic mean, is prescribed such that the zero level set has the correct liquid-solid surface tension value. This leads to a more accurate prediction of the triple contact point location. The method uses second-order central difference schemes which facilitates easy parallel implementation, and is validated by comparing to traditional level set methods for canonical problems. The application of the method in the context of Gibbs free energy minimization, to obtain liquid-air interfaces is validated against existing analytical solutions. The capability of the methodology to predict equilibrium shapes over both structured and realistic rough surfaces is demonstrated.

Carotid artery segmentation using level set method with double adaptive threshold (DATLS) on TOF-MRA images

PurposeThis study aimed to propose a method to semi-automatically segment lumen of carotid artery on TOF-MRA images with well performance on images with weak boundary. MethodsThe proposed method modified traditional level set method with double adaptive threshold (DATLS). Two thresholds were calculated from probability density function of initial region of interest. Threshold Th1 was used to generate initial contour and threshold Th2 was used to control evolution by modifying energy function of the level set. The performance of the proposed method was tested on TOF-MRA images from CARE II study via using manual delineation as reference. Sixty cases were randomly selected to compare the performance of traditional level set with DATLS, all 283 cases were used to test the robustness of DATLS and 20 cases were used to compare the intra- and inter-operator reproducibility of manual delineation with DATLS. The Dice Similarity Coefficient, Mean Contour Distance and Hausdorff Distance between the proposed method and the manual segmentation were reported. ResultsTraditional level set failed to segment carotid artery on 13 cases because of over convergence. Compared to traditional level set, DATLS showed a higher DSC (0.88 ± 0.07 vs. 0.75 ± 0.15), lower MCD (0.48 ± 0.37 mm vs. 1.89 ± 2.24 mm) and HD (1.41 ± 1.11 mm vs. 4.59 ± 4.59 mm) in the remaining 47 cases. The average DSC, MCD and HD of DATLS on 283 cases were 0.87 ± 0.09, 0.64 ± 0.87 mm and 1.76 ± 2.23 mm, respectively. Compared to manual delineation, DATLS had better reproducibility on DSC (intra-operator: 0.97 ± 0.09 and inter-operator: 0.97 ± 0.09 vs. intra-operator: 0.91 ± 0.04 and inter-operator: 0.91 ± 0.04), as well as MCD (intra-operator: 0.08 ± 0.18 mm and inter-operator: 0.13 ± 0.52 mm vs. intra-operator: 0.35 ± 0.20 mm and inter-operator: 0.37 ± 0.19 mm) and HD (intra-operator: 0.30 ± 0.66 mm and inter-operator: 0.48 ± 1.38 mm vs. intra-operator: 0.99 ± 0.79 mm and inter-operator: 0.90 ± 0.85 mm). ConclusionCompared to traditional level set, DATLS out-performed on computing time, robustness and accuracy of segmentation on TOF-MRA. The proposed method using modified level set with double adaptive threshold might be a promising tool for lumen segmentation of carotid artery on TOF-MRA.

An Adrenal Segmentation Model Based on Shape Associating Level Set in Sequence of CT Images

The segmentation challenge of adrenal and surrounding tissues lie in the similar CT values and adhesion in a medical image. An adrenal segmentation model (SALS) based on shape associating level set is proposed to segment the adrenal accurately. The objective function of adrenal boundary is expressed by a level set model. The prior shape curve of the adrenal to be segmented is calculated by the gradual change relationship between the adrenal glands in adjacent CT images, and is converted into shape constraint term of the level set models. A 3D Laplace method is used to improve adrenal grey scale information. The improved result of CT image is converted into grey scale constraint term of the level set models. Under the two constraints, the objective function of adrenal boundary converges to the best boundary. The level set methods in the literature obtain a prior shape by training a large number of sample images, and use the shape modes to segment CT images. The SALS model does not depend on the sample images. The adrenal boundaries in sequence of CT images can be directly segmented by SALS model, and the segmented boundaries are more accurate than the traditional level set methods. The SALS model has stronger adaptability to adherent adrenal boundary.

Coronary Arteries Segmentation Based on 3D FCN With Attention Gate and Level Set Function

Coronary heart disease is one of the most serious health problems in the world nowadays. By segmenting and examining the coronary arteries in medical images, we can find artery stenosis and plaque, which are the main causes of this certain disease. Segmenting coronary arteries manually is time-consuming and subjective, and the traditional segmentation method requires a good initial point, which is also difficult to apply for the 3D coronary computed tomography angiography (CTA) data. In this paper, we propose a joint framework for coronary CTA segmentation based on deep learning and traditional level set method. A 3D fully convolutional network (FCN) is used to learn the 3D semantic features of coronary arteries, which provides an excellent initial point for the traditional level set. Moreover, an attention gate is added to the entire network, aiming to enhance the vessels and suppress irrelevant regions. The output of 3D FCN with attention gate is optimized by the level set to smooth the boundary to better fit the ground truth segmentation. The proposed algorithm is evaluated by the Jaccard index (JI) and the Dice similarity coefficient (DSC) scores. The experimental results show that the proposed framework provides significant better segmentation results than the vanilla 3D FCN intuitively and quantitively.

Underwater image segmentation based on fast level set method

Image segmentation is a fundamental process in image processing that has found application in many fields, such as neural image analysis, and underwater image analysis. In this paper, we propose a novel fast level set method (FLSM)-based underwater image segmentation method to improve the traditional level set methods by avoiding the calculation of signed distance function (SDF). The proposed method can speed up the computational complexity without re-initialisation. We also provide a fast semi-implicit additive operator splitting (AOS) algorithm to improve the computational complex. The experiments show that the proposed FLSM performs well in selecting local or global segmentation regions.