Level Set Contour Research Articles

Modelling wildland fire propagation by tracking random fronts

Abstract. Wildland fire propagation is studied in the literature by two alternative approaches, namely the reaction–diffusion equation and the level-set method. These two approaches are considered alternatives to each other because the solution of the reaction–diffusion equation is generally a continuous smooth function that has an exponential decay, and it is not zero in an infinite domain, while the level-set method, which is a front tracking technique, generates a sharp function that is not zero inside a compact domain. However, these two approaches can indeed be considered complementary and reconciled. Turbulent hot-air transport and fire spotting are phenomena with a random nature and they are extremely important in wildland fire propagation. Consequently, the fire front gets a random character, too; hence, a tracking method for random fronts is needed. In particular, the level-set contour is randomised here according to the probability density function of the interface particle displacement. Actually, when the level-set method is developed for tracking a front interface with a random motion, the resulting averaged process emerges to be governed by an evolution equation of the reaction–diffusion type. In this reconciled approach, the rate of spread of the fire keeps the same key and characterising role that is typical of the level-set approach. The resulting model emerges to be suitable for simulating effects due to turbulent convection, such as fire flank and backing fire, the faster fire spread being because of the actions by hot-air pre-heating and by ember landing, and also due to the fire overcoming a fire-break zone, which is a case not resolved by models based on the level-set method. Moreover, from the proposed formulation, a correction follows for the formula of the rate of spread which is due to the mean jump length of firebrands in the downwind direction for the leeward sector of the fireline contour. The presented study constitutes a proof of concept, and it needs to be subjected to a future validation.

English

This article presents Bayesian Classifier which controls the levels set segmentation and it detect the retinal clots at an early stage from the image captured from fundus camera. The classifier is a probabilistic and used for the control of level set contour propagation for the detection of class clot defined, extracting the retinal vessels even with minute deformation due to the clots. The algorithm is tested in MATLAB on fundus images taken at various stages of progression and results which proves the effectiveness of the proposed method.

A priori knowledge and probability density based segmentation method for medical CT image sequences.

This paper briefly introduces a novel segmentation strategy for CT images sequences. As first step of our strategy, we extract a priori intensity statistical information from object region which is manually segmented by radiologists. Then we define a search scope for object and calculate probability density for each pixel in the scope using a voting mechanism. Moreover, we generate an optimal initial level set contour based on a priori shape of object of previous slice. Finally the modified distance regularity level set method utilizes boundaries feature and probability density to conform final object. The main contributions of this paper are as follows: a priori knowledge is effectively used to guide the determination of objects and a modified distance regularization level set method can accurately extract actual contour of object in a short time. The proposed method is compared to other seven state-of-the-art medical image segmentation methods on abdominal CT image sequences datasets. The evaluated results demonstrate our method performs better and has the potential for segmentation in CT image sequences.

Novel multimodality segmentation using level sets and Jensen‐Rényi divergence

Positron emission tomography (PET) is playing an increasing role in radiotherapy treatment planning. However, despite progress, robust algorithms for PET and multimodal image segmentation are still lacking, especially if the algorithm were extended to image-guided and adaptive radiotherapy (IGART). This work presents a novel multimodality segmentation algorithm using the Jensen-Rényi divergence (JRD) to evolve the geometric level set contour. The algorithm offers improved noise tolerance which is particularly applicable to segmentation of regions found in PET and cone-beam computed tomography. A steepest gradient ascent optimization method is used in conjunction with the JRD and a level set active contour to iteratively evolve a contour to partition an image based on statistical divergence of the intensity histograms. The algorithm is evaluated using PET scans of pharyngolaryngeal squamous cell carcinoma with the corresponding histological reference. The multimodality extension of the algorithm is evaluated using 22 PET/CT scans of patients with lung carcinoma and a physical phantom scanned under varying image quality conditions. The average concordance index (CI) of the JRD segmentation of the PET images was 0.56 with an average classification error of 65%. The segmentation of the lung carcinoma images had a maximum diameter relative error of 63%, 19.5%, and 14.8% when using CT, PET, and combined PET/CT images, respectively. The estimated maximal diameters of the gross tumor volume (GTV) showed a high correlation with the macroscopically determined maximal diameters, with a R(2) value of 0.85 and 0.88 using the PET and PET/CT images, respectively. Results from the physical phantom show that the JRD is more robust to image noise compared to mutual information and region growing. The JRD has shown improved noise tolerance compared to mutual information for the purpose of PET image segmentation. Presented is a flexible framework for multimodal image segmentation that can incorporate a large number of inputs efficiently for IGART.

Correlation between hole insertion criteria in a boundary element and level set based topology optimisation method

The research work presented in this paper is based on the correlation between two hole insertion criteria in a boundary element method (BEM) and level set method (LSM) based structural topology optimisation scheme for 2D elastic problems. The hole insertion criteria used in this work are based on the von Mises stress and the topological derivative approaches. During the optimisation process holes are automatically inserted in the design domain using each of the two criteria. The LSM is used to provide an implicit description of the structural geometry, and is also capable of automatically handling topological changes, i.e. holes merging with each other or with the boundary. The evolving structural geometry (i.e. the zero level set contours) is represented by NURBS, providing a smooth geometry throughout the optimisation process and completely eliminate jagged edges. In addition the optimal NURBS geometry can be used directly in other design processes. Four different benchmark examples are considered in this study and each is tested against the two hole insertion criteria. The results obtained validate the proposed optimisation method and we demonstrate a clear correlation between the two hole insertion criteria.

Controller design for nonlinear systems using the Contoured Robust Controller Bode plot

SUMMARYIn this paper, we develop the Contoured Robust Controller Bode (CRCBode) plot and demonstrate its use in the design of robust controllers for nonlinear single‐input single‐output (SISO) systems. The CRCBode plot shows contours (level sets) of a robust performance quantity on the Bode magnitude and phase plots of the controller. An iterative frequency domain loop‐shaping design approach is employed to eliminate all intersections of the controller frequency response with certain ‘forbidden regions,’ indicating that a standard SISO robust stability and performance criterion is satisfied. Nonlinearities are accounted for by avoiding the maximum forbidden regions over a structured uncertainty set consisting of linearizations of the system dynamics about several operating points. We demonstrate this technique by designing and experimentally verifying a flow‐rate controller for a butterfly‐valve based liquid cooling system, which is robust to valve nonlinearities and flow disturbances. Finally, we compare this compensator with one generated using an automated H ∞ synthesis algorithm and discuss the advantages of the CRCBode approach. Copyright © 2013 John Wiley & Sons, Ltd.

Variational Level Set Algorithm in Image Segmentation for Foetus Ultrasound Imaging System

Segmentation on ultrasound image is difficult when the image is not clear and contains unwanted noise. Since the object to be segmented out can be changing in shape for a period of time, there is a need to apply a computerised segmentation method for future analysis without any assumptions about the object’s topology is made. In general, when performing pregnancy ultrasound scanning, seeking a snapshot with best position or angle of the foetus is often a task done by obstetrician. This snapshot is useful for the obstetrician to locate the crown and the rump of the foetus for specific measurement. In this paper, a computerized segmentation using variational level set algorithm (VLSA) is proposed here. Results showed the variational level set contour evolved well on the low contrast and noise consisting ultrasound image.

A Geodesic Active Contour Level Set Method for Image Segmentation

Image segmentation is a vital part of many applications because it makes possible for the information extraction and analysis of image contents. For image segmentation process, many approaches have been proposed earlier. The image segmentation using normal standard methods is well only for simple image contents. In existing approaches image segmentation is done through multi-resolution stochastic level set method (MSLSM), but the topology changes are undesirable and it presented nonparametric topology-constrained segmentation model. To improve the image segmentation more effective, in this work, we plan to do image segmentation using level set method with geodesic active contour to analyze medical image disease diagnosis. With level set segmentation based on geodesic active contour, active cluster objects are segregated. Cluster object formation is done with fuzzification of growing active contours with the previously known contours of diseased image portions. With segment portions new similar regions can be traced out with automatic seeded growing method. Experimentation is conducted with bench mark data sets obtained from UCI repository and proved that the proposed GAC work will be 80% efficiency for image segmentation compared to an existing MSLSM. The parametric evaluations are carried over in terms of segment size and contour growth, Contour objects in the cluster, Similarity ratio of known and unknown contours, Seed size of the detected contours.

Method: automatic segmentation of mitochondria utilizing patch classification, contour pair classification, and automatically seeded level sets

BackgroundWhile progress has been made to develop automatic segmentation techniques for mitochondria, there remains a need for more accurate and robust techniques to delineate mitochondria in serial blockface scanning electron microscopic data. Previously developed texture based methods are limited for solving this problem because texture alone is often not sufficient to identify mitochondria. This paper presents a new three-step method, the Cytoseg process, for automated segmentation of mitochondria contained in 3D electron microscopic volumes generated through serial block face scanning electron microscopic imaging. The method consists of three steps. The first is a random forest patch classification step operating directly on 2D image patches. The second step consists of contour-pair classification. At the final step, we introduce a method to automatically seed a level set operation with output from previous steps.ResultsWe report accuracy of the Cytoseg process on three types of tissue and compare it to a previous method based on Radon-Like Features. At step 1, we show that the patch classifier identifies mitochondria texture but creates many false positive pixels. At step 2, our contour processing step produces contours and then filters them with a second classification step, helping to improve overall accuracy. We show that our final level set operation, which is automatically seeded with output from previous steps, helps to smooth the results. Overall, our results show that use of contour pair classification and level set operations improve segmentation accuracy beyond patch classification alone. We show that the Cytoseg process performs well compared to another modern technique based on Radon-Like Features.ConclusionsWe demonstrated that texture based methods for mitochondria segmentation can be enhanced with multiple steps that form an image processing pipeline. While we used a random-forest based patch classifier to recognize texture, it would be possible to replace this with other texture identifiers, and we plan to explore this in future work.

Computer‐aided measurement of liver volumes in CT by means of geodesic active contour segmentation coupled with level‐set algorithms

Computerized liver extraction from hepatic CT images is challenging because the liver often abuts other organs of a similar density. The purpose of this study was to develop a computer-aided measurement of liver volumes in hepatic CT. The authors developed a computerized liver extraction scheme based on geodesic active contour segmentation coupled with level-set contour evolution. First, an anisotropic diffusion filter was applied to portal-venous-phase CT images for noise reduction while preserving the liver structure, followed by a scale-specific gradient magnitude filter to enhance the liver boundaries. Then, a nonlinear grayscale converter enhanced the contrast of the liver parenchyma. By using the liver-parenchyma-enhanced image as a speed function, a fast-marching level-set algorithm generated an initial contour that roughly estimated the liver shape. A geodesic active contour segmentation algorithm coupled with level-set contour evolution refined the initial contour to define the liver boundaries more precisely. The liver volume was then calculated using these refined boundaries. Hepatic CT scans of 15 prospective liver donors were obtained under a liver transplant protocol with a multidetector CT system. The liver volumes extracted by the computerized scheme were compared to those traced manually by a radiologist, used as "gold standard." The mean liver volume obtained with our scheme was 1504 cc, whereas the mean gold standard manual volume was 1457 cc, resulting in a mean absolute difference of 105 cc (7.2%). The computer-estimated liver volumetrics agreed excellently with the gold-standard manual volumetrics (intraclass correlation coefficient was 0.95) with no statistically significant difference (F = 0.77; p(F < or = f) = 0.32). The average accuracy, sensitivity, specificity, and percent volume error were 98.4%, 91.1%, 99.1%, and 7.2%, respectively. Computerized CT liver volumetry would require substantially less completion time (compared to an average of 39 min per case by manual segmentation). The computerized liver extraction scheme provides an efficient and accurate way of measuring liver volumes in CT.

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

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

Level set contour extraction method based on support value filter

Active contour method is a powerful approach for object contour extraction. This paper presents a new object contour extraction method, which combines the level set evolution with the support value filter. It analyzes image under the least squares support vector machine (LS-SVM) framework and uses the support values to represent salient features underlying image. The Gaussian filter, used in conventional level set method to compute the edge indicator, is replaced by the support value filter deduced from the mapped LS-SVM. The level set evolution method is implemented on the feature image obtained by convolving the support value filter with the original image. Experiments are undertaken on the synthetic and real images. The experimental results demonstrate that the support value filter can provide a good estimate for the optimal step size in a gradient descent algorithm and the proposed method has advantages over the direct level set evolution method in converging speed and contour extraction accuracy.

Quantification of Thyroid Volume Using 3-D Ultrasound Imaging

Ultrasound (US) is among the most popular diagnostic techniques today. It is non-invasive, fast, comparably cheap, and does not require ionizing radiation. US is commonly used to examine the size, and structure of the thyroid gland. In clinical routine, thyroid imaging is usually performed by means of 2-D US. Conventional approaches for measuring the volume of the thyroid gland or its nodules may therefore be inaccurate due to the lack of 3-D information. This work reports a semi-automatic segmentation approach for the classification, and analysis of the thyroid gland based on 3-D US data. The images are scanned in 3-D, pre-processed, and segmented. Several pre-processing methods, and an extension of a commonly used geodesic active contour level set formulation are discussed in detail. The results obtained by this approach are compared to manual interactive segmentations by a medical expert in five representative patients. Our work proposes a novel framework for the volumetric quantification of thyroid gland lobes, which may also be expanded to other parenchymatous organs.

Image Segmentation Project - Open source software practices class

This document describes implementation of two Level-set segmentation algorithms using Insight Toolkit ITK . The algorithms chosen for implementation are are 1) Geodesic Active contour Levelset segmentation and 2) Shape Detection Levelset segmentation. The project is oriented to expose the concepts of Open Data, Open Source and Open Access which form the pillars of open-source software ideology.

Nonparametric statistical snake based on the minimum stochastic complexity

We propose a nonparametric statistical snake technique that is based on the minimization of the stochastic complexity (minimum description length principle). The probability distributions of the gray levels in the different regions of the image are described with step functions with parameters that are estimated. The segmentation is thus obtained by minimizing a criterion that does not include any parameter to be tuned by the user. We illustrate the robustness of this technique on various types of images with level set and polygonal contour models. The efficiency of this approach is also analyzed in comparison with parametric statistical techniques.

A local cell quality metric and variational grid smoothing algorithm

A local cell quality metric is introduced and used to construct a variational functional for a grid smoothing algorithm. A maximum principle is proved and the properties of the local quality measure, which combines element shape and size control metrics, are investigated. Level set contours are displayed to indicate the effect of cell distortion. The approach is demonstrated for meshes of triangles and quadrilaterals in 2D and a test case with hexahedral cells in 3D. Issues such as the use of a penalty for folded meshes and the effect of valence change in the mesh patches are considered.

Quantitative Evaluation of Contour Segmentation of Three Dimensional Image Using Level Set Method

Quantitative evaluation of level set contour segmentation method applied to three dimensional images detecting image edge based on threshold is discussed. The integration of two popular level set methods, i.e., reinitialization method and geodesic active contour method, leads to success in development of robust, with high accuracy, level set based segmentation method. The applications of this method to both synthetic and clinical medical images are shown. Accuracy of the propose method, in the view of both averaged contour location and standard deviation of curvature in the vicinity of contour, calculated using obtained level set function is discussed.