Variational Level Set Method Research Articles

A novel locally statistical active contour model for SAR image segmentation and faster algorithm

Abstract In this paper, a novel locally statistical active contour model (LACM) based on the Aubert-Aujol (AA) denoising model and variational level set method is proposed, which can be used for SAR image segmentation with intensity inhomogeneity. By simple transformation, a fast segmentation algorithm with a global optimization solver can be obtained. Experiments using some challenging synthetic images and Envisat SAR images demonstrate the superiority of our proposed models with respect to classic models. Further, we can find that the structure of the proposed algorithm is the same as that of the Transformer or RNN. We will study the nature of the above two types of algorithms to propose a more effective segmentation algorithm based on the energy model.

Model-based hybrid variational level set method applied to lung cancer detection

<p>The precise segmentation of lung lesions in computed tomography (CT) scans holds paramount importance for lung cancer research, offering invaluable information for clinical diagnosis and treatment. Nevertheless, achieving efficient detection and segmentation with acceptable accuracy proves to be challenging due to the heterogeneity of lung nodules. This paper presents a novel model-based hybrid variational level set method (VLSM) tailored for lung cancer detection. Initially, the VLSM introduces a scale-adaptive fast level-set image segmentation algorithm to address the inefficiency of low gray scale image segmentation. This algorithm simplifies the (Local Intensity Clustering) LIC model and devises a new energy functional based on the region-based pressure function. The improved multi-scale mean filter approximates the image’s offset field, effectively reducing gray-scale inhomogeneity and eliminating the influence of scale parameter selection on segmentation. Experimental results demonstrate that the proposed VLSM algorithm accurately segments images with both gray-scale inhomogeneity and noise, showcasing robustness against various noise types. This enhanced algorithm proves advantageous for addressing real-world image segmentation problems and nodules detection challenges.</p>

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.

Skull Surface Reconstruction with Euler’s Elastica Model from Point Cloud Data

In order to reconstruct accurate smooth implicit surfaces from skull point cloud data with complex topological relations, a variational level set method based on Euler’s Elastica model is proposed. Firstly, Euler’s Elastica is introduced into the variational energy functional as a regularization constraint, and the variational energy functional minimization problem is transformed into a series of subproblems by the augmented Lagrange method. Secondly, each subproblem is solved by generalized soft threshold formula, analytical formula and fast Fourier transform respectively. Finally, the projection algorithm is used during the computation to avoid the re-initialization of the level set function effectively. The experimental results show that the proposed variational level set method based on Euler’s Elastica has better convergence and effectiveness than the existing methods, which can improve the reconstruction accuracy and avoid missing surface edges.

RVLSM: Robust variational level set method for image segmentation with intensity inhomogeneity and high noise

Intensity inhomogeneity and high noise are two common but challenging issues in image segmentation and is particularly pronounced when the two issues simultaneously appear in one image. As a result, most existing level set methods yield poor performance when applied to these images. To address this issue, this paper proposes a robust variational level set method (RVLSM) based on adaptive diffusion mechanism and local cluster criterion, which can not only correct the severe inhomogeneous intensity but also denoise in segmentation. Specifically, we first define an adaptive-scale representation term using the proposed adaptive diffusion mechanism to transform the image data towards diffusion-induced space, which successfully restrains different types/levels of noise while enhancing image details. Then, a new bias field correction term is constructed via estimating the bias in transformed domain to better correct the severe inhomogeneous intensity while segmentation. Finally, an enhanced fourth-order piecewise polynomial penalty term is designed to eradicate numerical calculation instability and tedious re-initialization during the evolution of the level set. The experimental results on synthetic and real images with severe intensity inhomogeneity and high noise demonstrate the superiority of the proposed method over most existing methods in both accuracy and robustness.

Noisy image segmentation model combining PDE and improved variational level set method

During image shooting, transmission and acquisition, noise is easily introduced into the image. For pixels in an image, the introduction of noise often changes the intensity values of some pixels, resulting in a large difference in intensity between those pixels and their neighbors. Aiming at the image segmentation problem of weak edge and different types of noise, this paper proposes a new variational horizontal set noise image segmentation model, which is mainly used for the segmentation of target images of different noises. Experimental results show that the traditional PDE segmentation model method does not have obvious segmentation effect on noisy images, while the segmentation method proposed in this paper that combines PDE and improved variational level set has a better segmentation effect on different types of noisy images.

Automatic three‐dimensional detection and volume estimation of low‐grade gliomas

AbstractBrain tumor segmentation is routinely needed in diagnostic radiology. Automatic volume estimation has been used for diagnosis improvement and treatment process. This article presents a new approach for tumor volume estimation, using a variational level set method. The new adapted representation of intensity allows the method to be efficient in the region of interest identification, regardless the shape, size, and location of the tumor. For the estimation of an optimal bounding box, a fuzzy preference optimization model is used. The proposed approach is suitable for the zero level set initialization as well as for the reduction of the processing area, which ultimately speeds up the curve evolution. Moreover, tumor contours are determined using the hybrid level set technique, which combines the gradient and local phase information as an edge indicator term. Such an approach is robust to attenuation and intensity inhomogeneity. The proposed method is evaluated using a set of real and synthetic images. Our method achieved a performance of 96% accuracy, with an average execution time of 4.75 seconds. The proposed method is fast, accurate, and does not require training data or prior knowledge. With such experimental results, our approach outperforms 18 state‐of‐the‐art methods.

Non-destructive 3D geometric modeling of maize root-stubble in-situ via x-ray computed tomography.

No-tillage seeding has become an important approach to improve crop productivity, which needs colters of high performance to cut the root-stubble-soil composite. However, the difficulty of maize root-stubbles three-dimensional (3D) modeling hinders finite element (FE) simulation to improve development efficiency of such colters because of maize root system complexity and opaque nature of the soil. Fortunately, the non-destructive 3D geometric model of the maize root-stubble in-situ can be established via X-ray computed tomography (CT) following by a systematic procedure. The whole procedure includes CT scanning of the maize root-stubble-soil composite sample, image reconstruction via filtered back-projection (FBP) with the Hanning filter, segmentation of root-stubble via a variational level set method, and post-processing via morphological operations. The 3D reconstruction model of the maize root-stubble in-situ presents a complete, complex and in-situ geometrical morphology, which cannot be realized via other methods, including the destructive modelling after washing via CT. This study is the first to build a 3D geometric model of a maize root-stubble in-situ via CT, which opens up new possibilities for simulation of root-stubble-soil cutting using FEM, and much other research related to plant root-stubbles. Keywords: maize root-stubble, non-destructive modeling, X-ray computed tomography, variational level set method DOI: 10.25165/j.ijabe.20201303.5268 Citation: Zhao X, Xing L Y, Shen S F, Liu J M, Zhang D X. Non-destructive 3D geometric modeling of maize root-stubble in-situ via X-ray computed tomography. Int J Agric & Biol Eng, 2020; 13(3): 174–179.

A medical image segmentation method based on hybrid active contour model with global and local features

SummaryIn this article, we proposed an improved region‐based active contour model based on curve evolution theory and variational level set method. Our method can be used to segment image with intensity inhomogeneity, such as medical computed tomography images. Our model contains a local intensity fitting term that makes the evolution curve stop at boundaries of the object and a global expansion term that makes the evolution curve have the chance to get to every location in the image. Therefore, our model has a good performance to solve the problem of flexible initialization, which exposed in region‐scalable fitting energy model. For the curvature term that occurs during the calculation, we calculated it with a more efficiency and accuracy method. Compared with other models, our model shows good segmentation result and less computation expense. Finally, we will present some experimental results, especially the result of contrast experiment.

Non-destructive 3D geometric modeling of maize root-stubble in-situ via X-ray computed tomography

No-tillage seeding has become an important approach to improve crop productivity, which needs colters of high performance to cut the root-stubble-soil composite. However, the difficulty of maize root-stubbles three-dimensional (3D) modeling hinders finite element (FE) simulation to improve development efficiency of such colters because of maize root system complexity and opaque nature of the soil. Fortunately, the non-destructive 3D geometric model of the maize root-stubble in-situ can be established via X-ray computed tomography (CT) following by a systematic procedure. The whole procedure includes CT scanning of the maize root-stubble-soil composite sample, image reconstruction via filtered back-projection (FBP) with the Hanning filter, segmentation of root-stubble via a variational level set method, and post-processing via morphological operations. The 3D reconstruction model of the maize root-stubble in-situ presents a complete, complex and in-situ geometrical morphology, which cannot be realized via other methods, including the destructive modelling after washing via CT. This study is the first to build a 3D geometric model of a maize root-stubble in-situ via CT, which opens up new possibilities for simulation of root-stubble-soil cutting using FEM, and much other research related to plant root-stubbles. Keywords: maize root-stubble, non-destructive modeling, X-ray computed tomography, variational level set method DOI: 10.25165/j.ijabe.20201303.5268 Citation: Zhao X, Xing L Y, Shen S F, Liu J M, Zhang D X. Non-destructive 3D geometric modeling of maize root-stubble in-situ via X-ray computed tomography. Int J Agric & Biol Eng, 2020; 13(3): 174–179.

Variational Level Set Evolution for Non-Rigid 3D Reconstruction From a Single Depth Camera.

We present a framework for real-time 3D reconstruction of non-rigidly moving surfaces captured with a single RGB-D camera. Based on the variational level set method, it warps a given truncated signed distance field (TSDF) to a target TSDF via gradient flow without explicit correspondence search. We optimize an energy that contains a data term which steers towards voxel-wise alignment. To ensure geometrically consistent reconstructions, we develop and compare different strategies, namely an approximately Killing vector field regularizer, gradient flow in Sobolev space and newly devised accelerated optimization. The underlying TSDF evolution makes our approach capable of capturing rapid motions, topological changes and interacting agents, but entails loss of data association. To recover correspondences, we propose to utilize the lowest-frequency Laplacian eigenfunctions of the TSDFs, which encode inherent deformation patterns. For moderate motions we are able to obtain implicit associations via a term that imposes voxel-wise eigenfunction alignment. This is not sufficient for larger motions, so we explicitly estimate voxel correspondences via signature matching of lower-dimensional eigenfunction embeddings. We carry out qualitative and quantitative evaluation of our geometric reconstruction fidelity and voxel correspondence accuracy, demonstrating advantages over related techniques in handling topological changes and fast motions.

Variational level set method for image segmentation with simplex constraint of landmarks

Landmarks are prior image features for a variety of computer vision tasks. In the image processing domain, research on image segmentation methods has always been a significant topic. Due to the image characteristics of heterogeneous nature, lack of clear boundaries, noise and so on, accurate segmentation of the image is still a challenge. In this paper, utilizing a level set framework and the simplex constraint, preferred image point landmarks are combined into a variational segmentation model to enforce the contour evolve with prior points. Then the alternating minimization algorithm of the proposed model is designed, meanwhile the landmarks constraints are doubled ensured with simplex projection. Finally, experiments on many synthetic and real-world images were implemented. Comparing with other state-of-the-art segmentation variational models, the most striking result to emerge from the data is that the proposed method has higher segmentation performance. Benefiting from appropriate point landmarks, the proposed segmentation method can tackle noisy, weak edges and corrupted area images effectively and robustly.

A new approach to automatic fetal brain extraction from MRI using a variational level set method.

Appropriate images extracted from the MRI of mothers' wombs can be of great help in the medical diagnosis of fetal abnormalities. As maternal tissue may appear in such images, affecting visualization of myelination of the fetal brain, it is not possible to use methods routinely used for extraction of adult brains for fetal brains. The aim of the present study was to use a variational level set approach to extract fetal brain from T2-weighted MR images of the womb. Coronal T2-weighted images were acquired using fast MRI protocols (to avoid artifacts). The database includes 105 MR images from eight subjects. After correcting the inhomogeneity of the images, the fetal eyes were located, and from that information, the location of the fetus brain was automatically determined. Then, the variational level set was used for fetus brain extraction. The results were analyzed by a clinical specialist (radiologist) and the similarity (Dice and Jaccard coefficients), sensitivity and specificity were calculated. The means of the statistical analysis for the Dice and Jaccard coefficients, sensitivity and specificity, were 99.56%, 96.89%, 95.71%, and 97.96%, respectively. Thus, extraction of fetal brain from MR images was confirmed, both statistically and visually through cross-validation.

Level set evolution with intensity prior knowledge for multiple sclerosis lesion segmentation

Background and Objectives: Multiple sclerosis (MS) lesion segmentation is important in estimating the progress of the disease and measuring the impact of new clinical treatments. Manual lesion delineation for the segmentation of lesions is time-consuming and suffers from observer variability. Therefore, a fully automated MS lesion segmentation method is considerable important in clinical practice. Subjects and Methods: In this study, we present a multilabel fusion embedded level set method for white matter lesion segmentation from MS patient images. Specifically, we focus on the validation of the variational level set method. Lesion segmentation is achieved by extending the level set contour which consists of an intensity-constrained term, an image data term, and a regularization term. Results: To compare the performance of our method with other state-of-the-art methods, we evaluated the methods with 25 magnetic resonance imaging datasets of MS patients. The dice score reaches an average of 0.55 for the proposed method. The sensitivity value and specificity value reach an average of 0.89 and 0.14, respectively. Conclusions: Experimental results demonstrate that our method is robust to parameter setting and outperforms other methods. The intensity-constrained term plays a key role in improving the segmentation accuracy. The experimental results show that our approach is effective and robust for lesion segmentation, which might simplify the quantification of lesions in basic research and even clinical trials.

A level set method based on local direction gradient for image segmentation with intensity inhomogeneity

Many medical and real images are suffered from intensity inhomogeneity and weak edges. For higher image segmentation quality, lots of level set-based methods have been proposed. Some of them however cannot take advantage of image gradient information. And severe intensity inhomogeneity and weak edges are not disposed properly. To address these problems, a new level set method integrated with local direction gradient information is presented in this paper. Firstly, according to the two assumptions on image intensity inhomogeneity adopted by many existing methods, a new pixel classification model based on image gradient is introduced. Secondly, we employ variational level set method combined with image spatial information, which improves the anti-noise capability of the proposed method. Finally, considering the gray gradients in homogeneous regions are close to constants, an improved diffusion process is incorporated into the level set function to make the evolving curves stay around true image edges. To verify our method, different testing images including synthetic images, magnetic resonance imaging (MRI) and real-world images are introduced. The image segmentation results demonstrate that our method can deal with the relatively severe intensity inhomogeneity and obtain the comparatively ideal segmentation results efficiently.

An enhanced variational level set method for MRI brain image segmentation using IFCM clustering and LBM

Today's technological advances in medical imaging have given rise to efficient diagnostic procedures. Segmentation identifies and defines individual objects with various attributes such as size, shape, texture, spatial location, contrast, brightness, noise, and context. Deformable segmentation methods are Active contours, which are used to match and track images of an atomic structure by determining constraints derived from the image data. Level set method is an integral part of active contour family, considerable work towards level set methods has identified two main disadvantages i.e., initialization of controlling parameters and time complexity. In this paper, the methodology employed proposes an enhanced Variational level set methodology for Magnetic Resonance (MR) brain image segmentation with heterogeneous intensity. Core concept of IFCM is based on Intuitionistic fuzzy set. Both the values of membership and non membership values for the purpose of labelling are utilized together. As the result of experimentation reveals the efficiency of the recommended IFCM algorithm and Lattice Boltzmann Method (LBM) to overcome the drawbacks of Level Set methods by using the energy function to reduce the processing time which addresses the time complexity issue. The proposed system combines of both IFCM and LBM to form a novel approach. The system is tested on a large set of MRI brain images, extensive research and experiments were carried over on the standard dataset and the results are found to be improved in identification of tumor size detection with respect to time complexity.

The L0-regularized discrete variational level set method for image segmentation

In this paper, we present a new variant of level set methods and then propose a ternary variational level set model involving L0 gradient regularizer and L0 function regularizer in discrete framework, following the Chan-Vese model for image segmentation. Different from the existing level set methods, we use the 0.5-level set of a ternary function whose values are within {0, 0.5, 1} to implicitly represent the interfaces between subregions and use L0 counting operator to discretely measure the length of interfaces and the area of foreground subregions. The proposed model can be regarded as a discrete form of the Chan-Vese model. Based on the half-quadratic splitting method, we design an alternating minimization algorithm to solve our model efficiently. Experimental results show that the proposed method has good performance for segmentation of images with severe noise, outliers or low contrast.

A variational level set method image segmentation model with application to intensity inhomogene magnetic resonance imaging

ABSTRACT Background and Objectives: In this article, we propose an image segmentation model based on Chan-Vese (CV) for image segmentation. By taking into account the local features of the image, the new proposed model can successfully segment images with intensity nonuniformity. Materials and Methods: We quantitatively compare our method with other two state-of-the-art algorithms, namely, CV model and local binary fitting (LBF) model in segmenting synthetic MR images with the ground truth from BrainWeb; the data can be available at: https://www.mni/mcgill.ca/brainweb/. For segmenting the missing and weak boundaries, to deal with the intensity inhomogeneity, based on the LBF model, we introduced the convex total variation regularization term, for explicit smoothing of the level set function ø. The evolution equation will be solved through the level set method of calculus of variations. Results: In the experimental processing, we use some real images and magnetic resonance imaging brain images as the experimental images, to validate the stabilization of algorithm. The experimental results on comprehensive and sincerity images show the outstanding of our proposed model with reference to stabilization and availability. Conclusions: We propose a new segmentation local information of an image and introduce a new regularization functional is to keep the level set function smooth. Finally, various experimental results on real and low-contrast image, showing which is a powerful type of images, including some that would be difficult to segment with gradient-based methods. In addition, the advantages of the proposed model are better than CV model and the LBF model. Our new model can effectively segment a real image.

Mesh-free based variational level set evolution for breast region segmentation and abnormality detection using mammograms.

Automatic segmentation of abnormal region is a crucial task in computer-aided detection system using mammograms. In this work, an automatic abnormality detection algorithm using mammographic images is proposed. In the preprocessing step, partial differential equation-based variational level set method is used for breast region extraction. The evolution of the level set method is done by applying mesh-free-based radial basis function (RBF). The limitation of mesh-based approach is removed by using mesh-free-based RBF method. The evolution of variational level set function is also done by mesh-based finite difference method for comparison purpose. Unsharp masking and median filtering is used for mammogram enhancement. Suspicious abnormal regions are segmented by applying fuzzy c-means clustering. Texture features are extracted from the segmented suspicious regions by computing local binary pattern and dominated rotated local binary pattern (DRLBP). Finally, suspicious regions are classified as normal or abnormal regions by means of support vector machine with linear, multilayer perceptron, radial basis, and polynomial kernel function. The algorithm is validated on 322 sample mammograms of mammographic image analysis society (MIAS) and 500 mammograms from digital database for screening mammography (DDSM) datasets. Proficiency of the algorithm is quantified by using sensitivity, specificity, and accuracy. The highest sensitivity, specificity, and accuracy of 93.96%, 95.01%, and 94.48%, respectively, are obtained on MIAS dataset using DRLBP feature with RBF kernel function. Whereas, the highest 92.31% sensitivity, 98.45% specificity, and 96.21% accuracy are achieved on DDSM dataset using DRLBP feature with RBF kernel function.

A convex active contour model driven by local entropy energy with applications to infrared ship target segmentation

To segment ship target in infrared (IR) images, a convex active contour model based on local image entropy is proposed in this paper. Firstly, local image entropy based on kernel function is obtained; on this basis, the convex energy functional is built using the variational level set method in the convex set. Because of the introduction of entropy, the proposed method can protect the image edge and enhance the ability to deal images with heterogeneity. At the same time, the convex energy functional can get a global minimum and has robustness against initial curve placement. Compared with the state-of-the-art methods, experiment results demonstrate the performance and effectiveness of the proposed method.