Level Set Evolution Research Articles

Segmentation of Brain Tumor and Performance Evaluation Using Spatial FCM and Level Set Evolution

Background: In recent years, brain tumor is one of the major causes of death in human beings. The survival rate can be increased if the tumor is diagnosed accurately in the early stage. Hence, medical image segmentation is always a challenging task of any problem in computer guided medical procedures in hospitals. The main objective of the segmentation process is to obtain object of interest from the given image so that it can be represented in a meaningful way for further analysis. Methods: To improve the segmentation accuracy, an efficient segmentation method which combines a spatial fuzzy c-means and level sets is proposed in this paper. Results: The experiment is conducted using brain web and DICOM database. After pre-processing of an MR image, a spatial FCM algorithm is applied. The SFCM utilizes spatial data from the neighbourhood of each pixel to represent clusters. Finally, these clusters are segmented using level set active contour model for the tumor boundary. The performance of the proposed algorithm is evaluated using various performance metrics. Conclusion: In this technique, wavelets and spatial FCM are applied before segmenting the brain tumor by level sets. The qualitative results show more accurate detection of tumor boundary and better convergence rate of the contour as compared to other segmentation techniques. The proposed segmentation frame work is also compared with two automatic segmentation techniques developed recently. The quantitative results of the proposed method summarize the improvements in segmentation accuracy, sensitivity and specificity.

IVUS Image Segmentation Using Superpixel-Wise Fuzzy Clustering and Level Set Evolution

Reliable detection of the media-adventitia border (MAB) and the lumen-intima border (LIB) in intravascular ultrasound (IVUS) images remains a challenging task that is of high clinical interest. In this paper, we propose a superpixel-wise fuzzy clustering technique modified by edges, followed by level set evolution (SFCME-LSE), for automatic border extraction in 40 MHz IVUS images. The contributions are three-fold. First, the usage of superpixels suppresses the influence of speckle noise in ultrasound images on the clustering results. Second, we propose a region of interest (ROI) assignment scheme to prevent the segmentation from being distracted by pathological structures and artifacts. Finally, the contour is converged towards the target boundary through LSE with an appropriately improved edge indicator. Quantitative evaluations on two IVUS datasets by the Jaccard measure (JM), the percentage of area difference (PAD), and the Hausdorff distance (HD) demonstrate the effectiveness of the proposed SFCME-LSE method. SFCME-LSE achieves the minimal HD of 1.20 ± 0.66 mm and 1.18 ± 0.70 mm for the MAB and LIB, respectively, among several state-of-the-art methods on a publicly available dataset.

The improved level set evolution for ultrasound image segmentation in the high-intensity focused ultrasound ablation therapy

An improved level set evolution model is proposed to segment the ultrasound images accurately and efficiently in this paper. At first, the multi-scale gradient vector field is employed to reduce the image noise. We assign the standard deviation as a scale to set up several scales images, and use the gradient direction information between the adjacent scales to refine the multi-scale gradient vector field, which highlights the real boundaries and reduces the noise. Besides, the divergence operator of the multi-scale gradient vector field is used to overcome the sensitivity problem of initialization and avoid boundary leakage. The experiments results demonstrate that the performance of the proposed method is very close to the ground truths obtained from manual segmentation by specialists with higher area similarity measure (ASM) and lower mean contour distance (MCD), which demonstrated that the proposed method is reliable, accurate and robust for the tumor boundary segmentation in ultrasound images.

Kantorovich-Rubinstein misfit for inverting gravity-gradient data by the level-set method

We have developed a novel Kantorovich-Rubinstein (KR) norm-based misfit function to measure the mismatch between gravity-gradient data for the inverse gradiometry problem. Under the assumption that an anomalous mass body has an unknown compact support with a prescribed constant value of density contrast, we implicitly parameterize the unknown mass body by a level-set function. Because the geometry of an underlying anomalous mass body may experience various changes during inversion in terms of level-set evolution, the classic least-squares ([Formula: see text]-norm-based) and the [Formula: see text]-norm-based misfit functions for governing the level-set evolution may potentially induce local minima if an initial guess of the level-set function is far from that of the target model. The KR norm from the optimal transport theory computes the data misfit by comparing the modeled data and the measured data in a global manner, leading to better resolution of the differences between the inverted model and the target model. Combining the KR norm with the level-set method yields a new effective methodology that is not only able to mitigate local minima but is also robust against random noise for the inverse gradiometry problem. Numerical experiments further demonstrate that the new KR norm-based misfit function is able to recover deep dipping flanks of SEG/EAGE salt models even at extremely low signal-to-noise ratios. The new methodology can be readily applied to gravity and magnetic data as well.

Full-waveform inversion of salt models using shape optimization and simulated annealing

A good starting model is imperative in full-waveform inversion (FWI) because it solves a least-squares inversion problem using a local gradient-based optimization method. A suboptimal starting model can result in cycle skipping leading to poor convergence and incorrect estimation of subsurface properties. This problem is especially crucial for salt models because the strong velocity contrasts create substantial time shifts in the modeled seismogram. Incorrect estimation of salt bodies leads to velocity inaccuracies in the sediments because the least-squares gradient aims to reduce traveltime differences without considering the sharp velocity jump between sediments and salt. We have developed a technique to estimate velocity models containing salt bodies using a combination of global and local optimization techniques. To stabilize the global optimization algorithm and keep it computationally tractable, we reduce the number of model parameters by using sparse parameterization formulations. The sparse formulation represents sediments using a set of interfaces and velocities across them, whereas a set of ellipses represents the salt body. We use very fast simulated annealing (VFSA) to minimize the misfit between the observed and synthetic data and estimate an optimal model in the sparsely parameterized space. The VFSA inverted model is then used as a starting model in FWI in which the sediments and salt body are updated in the least-squares sense. We partition model updates into sediment and salt updates in which the sediments are updated like conventional FWI, whereas the shape of the salt is updated by taking the zero crossing of an evolving level set surface. Our algorithm is tested on two 2D synthetic salt models, namely, the Sigsbee 2A model and a modified SEG Advanced Modeling Program (SEAM) Phase I model while fixing the top of the salt. We determine the efficiency of the VFSA inversion and imaging improvements from the level set FWI approach and evaluate a few sources of uncertainty in the estimation of salt shapes.

RESLS: Region and Edge Synergetic Level Set Framework for Image Segmentation.

The active contour models with level set evolution have been visited with a vast number of methods for image segmentation. They can be mainly classified into region-based and edge-based models, and it has been validated that the hybrid variants combining both region and edge information can improve the segmentation performance. However, to the best of our knowledge, the theoretical foundation of collaboration mechanism between the region and the edge information is limited. Specifically, most existing hybrid models are just combining all the energy terms together, resulting in great challenges of choosing an appropriate weight coefficient for each term and accommodating different modalities of imaging. To overcome these difficulties, this paper proposes a region and edge synergetic level set framework named RESLS. It provides an approach to construct new hybrid level set models using a normalized intensity indicator function that allows the region information easily embedding into the edge-based model. In this case, the energy weights of region and edge terms can be constrained by the global optimization condition deduced from the framework. Some representative as well as state-of-the-art models are taken as examples to demonstrate the generality of our method. The experiments validate that under the guidance of the optimization condition, the weighting parameter of each term can be reliably chosen. Meanwhile, the segmentation accuracy, robustness, and computational efficiency of RESLS can be improved compared with its component models.

Local difference‐based active contour model for medical image segmentation and bias correction

This study proposes a local bias field and difference estimation (LBDE) model for medical image segmentation and bias field correction. Firstly, the LBDE model uses a linear combination of a given set of smooth orthogonal basis functions, which is called Chebyshev polynomial, to estimate the bias field. Then, a clustering criterion function is defined by considering the difference between the measured image and approximated image in a small region. By applying this difference in the local region, the LBDE model can obtain accurate segmentation results and estimation of the bias field. Finally, the energy functional is incorporated into a level set formulation with a regularisation term, and it is minimised via the level set evolution process. The LBDE model first appears as a two-phase model and then extends to the multi-phase one. Extensive experiments on medical images demonstrate that the LBDE model achieves more precise segmentation results in terms of Jaccard similarity and dice similarity coefficient than the comparative models. Therefore the proposed model can increase the segmentation accuracy and robustness to noise.

Shape Prior Embedded Level Set Model for Image Segmentation

This paper presents an optimized level set evolution (LSE) without reinitialization (LSEWR) model and a shape prior embedded level set model (LSM) for robust image segmentation. Firstly, by performing probability weighting and coefficient adaptive processing on the original LSEWR model, the optimized image energy term required by the proposed model is constructed. The purpose of the probability weighting is to introduce region information into the edge stop function to enhance the model’s ability to capture weak edges. The introduction of the adaptive coefficient enables the evolution process to automatically adjust its amplitude and direction according to the current image coordinate and local region information, thus completely solving the initialization sensitivity problem of the original LSEWR model. Secondly, a shape prior term driven by kernel density estimation (KDE) is additionally introduced into the optimized LSEWR model. The role of the KDE-driven shape prior term is to overcome the problem of image segmentation in the presence of geometric transformation and pattern interference. Even if there is obvious affine transformation in the shape prior and the target to be segmented, the target contour can still be reconstructed correctly. The extensive experiments on a large variety of synthetic and real images show that the proposed algorithm achieves excellent performance. In addition, several key factors affecting the performance of the proposed algorithm are analyzed in detail.

Supervised Classification of Fully PolSAR Images Using Active Contour Models

In this letter, we propose a supervised method for the classification of fully polarimetric synthetic aperture radar (PolSAR) images based on active contour models. We use an “ a priori ” estimation, obtained from training data, of the complex Wishart distributions of the different types of regions in the image (for instance, water, crops, grass, forest or urban). The information of the Wishart distributions is included in the active contour models to guide the level set evolution. We study the case of two classes and the case of three or more classes separately. We present some experimental results on the synthetic data and real PolSAR images to show the performance of the proposed model. The results are compared with other well-known supervised classification methods, and, for actual PolSAR data, our method shows an overall precision of 94.31% and a $\kappa $ coefficient of 0.937.

Active contour model based on improved fuzzy c-means algorithm and adaptive functions

Distance regularized level set evolution (DRLSE) model, which solves the re-initialization problem in early active contours, is a ground breaking edge-based model for image segmentation. However, it has the disadvantages of unsatisfactory robustness to initialization and noise, unidirectional movement, slow convergence and poor stability. In this paper, we propose an active contour model driven by improved fuzzy c-means algorithm (FCM) and adaptive functions. An adaptive sign function based on image clustering information not only increases stability, but also solves the problem of unidirectional movement. Furthermore, it gives our model the ability to selectively segment targets in image. An adaptive edge indicator function accelerates convergence with better function performance. To further increase stability, a novel double-well potential function and the corresponding evolution speed function are proposed. Due to the improved FCM, the proposed model is robust to initialization and noise. In addition, our model exhibits an edge-based and region-based characteristic. Experimental results have proved that the proposed model can not only effectively segment images with intensity inhomogeneity, but also show a good robustness to initialization. Moreover, it has shorter time spent and higher segmentation accuracy compared with other models.

Intelligent Measurement of Spinal Curvature Using Cascade Gentle AdaBoost Classifier and Region-Based DRLSE

For spinal curvature measurements, because of the anatomical complexity of the spine CT image, developing an automated method to avoid manual landmark is a challenging task. In this study, we propose an intelligent framework that integrates the cascade AdaBoost classifier and region-based distance regularized level set evolution (DRLSE) with the vertebral centroid measurement. First, the histogram-of-oriented-gradients based cascade gentle AdaBoost classifier is used to detect automatically and localize vertebral bodies from computer tomography (CT) spinal images. Considering these vertebral pathological images enables us to produce a diverse training dataset. Then, the DRLSE method introduces the local region information to converge the vertebral boundary quickly. The located bounding box is regarded as an accurate initial contour. This avoids the negative impact of manual initialization. Finally, we perform vertebral centroid extraction and spinal curve fitting. The spinal curvature angle is determined by calculating the angle between two tangents to the curve. We verified the effectiveness of the proposed method on 10 spine CT volumes. Quantitative comparison against the ground-truth centroids yielded a detection accuracy rate of 98.3% and a mean centroid location error of 1.15 mm. The comparative results with existing methods demonstrate that the proposed method can accurately detect and segment vertebral bodies. Furthermore, the spinal curvature can be automatically measured without manual landmark.

Active contours driven by adaptive functions and fuzzy c-means energy for fast image segmentation

The shortcoming of geometric active contours is that they are extremely sensitive to positions of initialization. Initial contours of the distance regularized level set evolution model must be set inside or outside target completely. In addition, the model is prone to problems of falling into false boundary, leaking from weak edge and poor anti-noise ability. In this paper, we propose a robust active contour model driven by adaptive functions (including an adaptive edge indicator function and adaptive sign function) and fuzzy c-means energy. Utilize the adaptive edge indicator function which is composed of image intensity information to substitute traditional edge indicator function in the area term. Active contours can expand or shrink from initialization automatically, which improves the disadvantages of poor robustness to initialization and unidirectional movement. Due to the adaptive sign function and fuzzy c-means energy, the problems of slow convergence and leaking from weak edge have been solved. Moreover, a novel distance regularized term (mainly a potential function and evolution speed function) is proposed to make evolution more stable. Experimental results have proved that our model can segment images with intensity inhomogeneity effectively. Compared with other classic models, the proposed model not only shortens time spent and improves segmentation accuracy, but also shows a better robustness to initialization.

Non‐local weighted fuzzy energy‐based active contour model with level set evolution starting with a constant function

In the traditional active contour models, global region-based methods fail to segment images with intensity inhomogeneity, and local region-based methods are sensitive to initial contour. In this study, a novel fuzzy energy-based active contour model is proposed to segment medical images, which are always corrupted by intensity inhomogeneity. In order to deal with intensity inhomogeneity, a local energy term is first constructed by substituting a non-local weight for Gaussian kernel widely used in traditional local region-based models. Second, the defined adaptive force can drive the level set function to adaptively increase or decrease according to image intensity information. Therefore, the initial contour can be initialised as a constant function, which eliminates the problem caused by contour initialisation. Moreover, the proposed active contour model is a convex function. Thus, the problem, resulting from optimising a non-convex functional in the traditional active contour models, can be avoided. Experimental results validate the superiorities and effectiveness of the proposed model for image segmentation with comparisons of those yielded by several state-of-the-art techniques.

Automated brain extraction from head CT and CTA images using convex optimization with shape propagation

Background and objectiveNon-Contrast Computer Tomography (NCCT) and CT angiography (CTA) are the most used and widely acceptable imaging modalities in clinical practice for the diagnosis and treatment of acute ischemic stroke (AIS) patients. Brain extraction of CT/CTA images plays an essential role in stroke imaging research. There is no robust automated brain extraction method in the literature that is well established for both NCCT and CTA images. Thus, a validated and automated brain extraction tool for CT imaging would be of great value for both research and clinical practice. MethodsThe proposed brain extraction method is based on the contour evolution technique, which extracts brain tissues from acquired NCCT and CTA images in a slice-by-slice fashion. Specifically, the proposed approach makes use of a novel propagation framework, which is initialized by a localized slice with the largest brain section in axial views, followed by a geodesic level-set evolution for automatically extracting the brain section in each slice. In particular, the segmented contour propagated from the previous slice is reused to penalize the defined object function for contour evolution to enforce the shape continuity between any two adjacent contours. We show that the defined contour evolution function can be solved iteratively by globally optimal convex optimization. ResultsThe proposed brain extraction approach is quantitatively evaluated using 40 NCCT and CTA images acquired from 20 AIS patients and drawn from 4 different vendors, compared to manual segmentations using Dice and Jaccard coefficient metrics. The quantitative results show that the proposed segmentation algorithm is consistently accurate for both NCCT and CTA images using Dice metric. The proposed method is further validated on 1736 NCCT and CTA images of 1331 AIS patients acquired from three multi-national multi-centric clinical trials. A visual check performed on these data demonstrates a low failure rate of 0.4% for 1331 NCCT images and a zero-failure rate for 405 CTA images. ConclusionsBoth quantitative and qualitative evaluation suggest that the proposed brain extraction approach for NCCT and CTA images can be used for different clinical imaging settings, thus serving to improve current image analysis in the field of neuroimaging.

IVUS images segmentation using spatial fuzzy clustering and hierarchical level set evolution

The detection of the lumen and media-adventitia (MA) borders in intravascular ultrasound (IVUS) images is crucial for quantifying plaque burdens. The challenge of the segmentation work mainly roots in various artifacts in the image. Most of the published methods involve the establishment of complex models but do not behave well on images with artifacts. In this study, aiming at automatically delineating borders in IVUS frames acquired by 20 MHz ultrasound probes, we present a fuzzy clustering-initialized hierarchical level set evolution (FC-HLSE) method. A cluster selection strategy based on the spatial fuzzy c-means (FCM) is proposed to generate the initial value and regularization term of the level set evolution (LSE). The contour convergence splits into two LSE steps between which an ingenious contour extraction (consisting of the morphological processing, the seek and linear interpolation, the gradient-based and circular fitting-based refinement) is carried out. We evaluate the proposed methodology on the publicly available 435 images by comparing auto-segmented results with the ground truth. The performance of the method is quantified using the Jaccard measure (JM), the Hausdorff distance (HD), the percentage of area difference (PAD), the linear regression and Bland-Altman analysis. Results reveal that our method can handle images with or without artifacts. The algorithm is able to extract the lumen/MA border with the JM of 0.90/0.89, the HD of 0.31/0.40 mm, the PAD of 0.07/0.08 in average, which is better in some cases compared with several state-of-the-art methods.

A study on the Development of a Korean Metabolic Syndrome Questionnaire

Segmentation of grayscale medical images is challenging because of the similarity of pixel intensities and poor gradient strength between adjacent regions. The existing image segmentation approaches based on either intensity or gradient information alone often fail to produce accurate segmentation results. Previous approaches in the literature have approached the problem by embedded or sequential integration of different information types to improve the performance of the image segmentation on specific tasks. However, an effective combination or integration of such information is difficult to implement and not sufficiently generic for closely related tasks. Integration of the two information sources in a single graph structure is a potentially more effective way to solve the problem. In this paper we introduce a novel technique for grayscale medical image segmentation called pyramid graph cut, which combines intensity and gradient sources of information in a pyramid-shaped graph structure using a single source node and multiple sink nodes. The source node, which is the top of the pyramid graph, embeds intensity information into its linked edges. The sink nodes, which are the base of the pyramid graph, embed gradient information into their linked edges. The min-cut uses intensity information and gradient information, depending on which one is more useful or has a higher influence in each cutting location of each iteration. The experimental results demonstrate the effectiveness of the proposed method over intensity-based segmentation alone (i.e. Gaussian mixture model) and gradient-based segmentation alone (i.e. distance regularized level set evolution) on grayscale medical image datasets, including the public 3DIRCADb-01 dataset. The proposed method archives excellent segmentation results on the sample CT of abdominal aortic aneurysm, MRI of liver tumor and US of liver tumor, with dice scores of 90.49±5.23%, 88.86±11.77%, 90.68±2.45%, respectively.

Integration of Spectral Histogram and Level Set for Coastline Detection in SAR Images

This study proposed a novel algorithm for coastline detection in single-polarization synthetic aperture radar (SAR) images based on the local spectral histogram (LSH) and the level set method (LSM). The proposed algorithm includes two main steps. In the processing step, a rough land/sea segmentation is done by utilizing a texture-based segmentation using LSH. In the postprocessing step, the region-based LSM is used to refine the previous segmentation and extract the coastline accurately. The level set (LS) function is initialized using the results of LSH segmentation. This prevents the development of spurious contours, becoming trapped in the local minimum, eliminates the manual support, and also speeds up the LS evolution. A hierarchical LS regularization is proposed using two Gaussian kernels, which is compatible with noisy images and able to detect very narrow regions. The proposed algorithm is able to detect a coastline at the full resolution of the input SAR image and is also robust to noise. A criterion to quantify the accuracy of the results was also proposed. The experimental results for a number of real high-resolution single-polarization SAR images demonstrate that the proposed method is robust to noise and efficient for the coastline detection in different coastal and sea environments.

Extraction of human face features from color images

Face detection has been widely studied by researchers. However, detection and extraction of human face features is very important as it plays a vital role in variety of applications involving automated face processing. This article focuses on extraction of face parts such as eyes, nose, lips, musta che, and beard on Indian people, for which we have prepared our own face dataset containing variety in faces, from both urban and rural areas. This study focuses on how a detected face part becomes useful in detecting other face parts. We implement our approaches of detecting face parts and evaluate them on our dataset. We exploit YCbCr color model, Viola Jones technique, landmark detection, and level set evolution technique in our approaches of face part detection and extraction. We found that our approaches are effective on extracting face boundary, eyes, nose, and lips and provide comparable results.

Automated Extraction of Parasite in the Microscopic Images by Distance Regularized Level Set Evolution initialized with Hough Transform

Automated Extraction of Parasite in the Microscopic Images by Distance Regularized Level Set Evolution initialized with Hough Transform

A parabolic level set reinitialisation method using a discontinuous Galerkin discretisation

Level set reinitialisation is a part of the level set methodology which allows one to generate, at any point during level set evolution, a level set function which is a signed distance function to its own zero isocontour. Whilst not in general a required condition, maintaining the level set function as a signed distance function is often desirable as it removes a known source of numerical instability. This paper presents a novel level set reinitialisation method based on the solution of a nonlinear parabolic PDE. The PDE is discretised using a symmetric interior penalty discontinuous Galerkin method in space, and an implicit Euler method in time. Also explored are explicit and semi-implicit time discretisations, however, numerical experiments demonstrate that such methods suffer from severe time step restrictions, leading to prohibitively large numbers of iterations required to achieve convergence. The proposed method is shown to be high-order accurate through a number of numerical examples. More specifically, the presented experimental orders of convergence align with the well established optimal convergence rates for the symmetric interior penalty method; that is the error in the L2 norm decreases proportionally to hp+1 and the error in the DG norm decreases proportionally to hp.