Geodesic Active Contour Model Research Articles

CS-GAC: Compressively sensed geodesic active contours

This paper proposes an edge based compressively sensed (CS) geodesic active contour (GAC) model, termed CS-GAC, to ensure faithful edge detection and accurate object segmentation. The motivation behind this paper is that edge information driving the contour evolution can be iteratively obtained by incomplete CS measurements. In each iteration, the CS-GAC is a three-step process including edge detection, active contouring and sparse reconstruction. Instead of working on the final reconstructed images themselves, the evolution of the CS-GAC is driven by a few CS measurements and guided by updatable edge information. The edge information is generated by a complex shearlet transform (CST) based edge map. In the framework, reconstruction and edge detection work alternately. The iterative update property that takes advantages of both edge sparsity and edge detection can largely improve the evolution precision. Numerical experiments show that the CS-GAC can obtain challenging segmentation results in comparisons with the state of the art methods, and has competitive prospects.

Fiber Orientation Reconstruction from SEM Images of Fiber-Reinforced Composites

The orientation of fibers in composites reinforced with short fibers can provide insight into the microstructure of the material and considerably affect its macroscopic characteristics. However, the present standard techniques for detecting fiber orientation and length based on microscopic image processing have faults in practical applications, including high effort, low efficiency, and unreliable measurement results. In this study, a method for measuring fiber orientation based on 3D reconstructions of scanning electron microscope (SEM) images is provided. The geodesic active contour (GAC) model is applied to segment the fibers in the SEM images. Matching the fiber contours with the scale-invariant feature transformation (SIFT) algorithm successfully extracts 3D orientation information from the fiber contours. The unit vector of the fiber axis is fitted from the extracted point cloud using the ordinary least squares (OLS) method. With a maximum deviation of 3.83° and an average deviation of 1.50°, the measurement findings of this method are substantially comparable to those of the image-measuring instrument. This paper offers a quantitative approach to studying the microstructure of short fiber-reinforced composites, thereby furnishing objective evidence to support the development and research of such materials.

Adaptive Active Contour Model for Brain Tumor Segmentation

For accurately diagnosing the severity of brain tumors in MRI images, Glioma segmentation is a significant step. The Glioma segmentation is due to noise and weak edges of organs in medical images. The geodesic active contour model (GACM) is a standard method for the segmentation of complex organ structures based on edge maps. The GACM performs poorly due to this noise and weak edges. So, the authors propose a method that uses adaptive kernels instead of a constant kernel for creating strong edge maps for GACM. The kernels used in phase congruency are Log Gabor kernels, which resemble similar anisotropic properties like Gabor kernels. They have replaced these with adaptive kernels. This adaptive kernel-based phase congruency provides a robust edge map to be used in GACM. Experimentation shows that when compared with state-of-the-art edge detection techniques, adaptive kernels enhance the weak as well as strong edges and improve the overall performance. Moreover, the proposed methodology substantially requires fewer parameters compared to existing ACM methods.

Water extraction from SAR images based on improved geodesic active contour.

The rapid and accurate acquisition of water body information is of great significance to water resource investigation, flood disaster monitoring, ecological environment protection, and other fields. In this paper, the water boundary is optimized and extracted from single-polarization SAR images based on an improved geodesic active contour model (IMGAC). Firstly, the rough extraction results of the water body were obtained according to the adaptive threshold, and then a narrowband model was established, and the signed pressure force (SPF) function was introduced into the geodesic active contour (GAC) model. Finally, the optimal water boundary was obtained through continuous iteration. Compared with the active contour (AC) model without edge and the traditional GAC model, the results show that the IMGAC model proposed in this paper can reduce the calculation efficiency and improve the accuracy of water boundary detection. The F-measure index was used to evaluate the extraction accuracy of the three methods. IMGAC method had the highest extraction accuracy, which was 96.43%. The kappa coefficient reached 0.929. The F-measure index was 96.20%. Our study can provide a reference for water extraction and water boundary optimization.

Construction of Biologic Microscopic Image Segmentation Model Based on Smoothing of Fourth-Order Partial Differential Equation.

In order to solve the problem of microscopic image noise, a biological microscopic image segmentation model based on the smoothing of the fourth-order partial differential equation was proposed. Based on the functional description of image smoothness by directional curvature mode value, a fourth-order PDE image denoising model is derived, which can effectively reduce noise while preserving edges. The result of this method is piecewise linear image, and the gradient at the edge of the target has a step. Using the feature of noise reduction, a new geodesic active contour model is proposed. The experiment result shows that when the variance of Gaussian white noise is 15, the enhancement and denoising effects of the proposed method are 80.35% and 69.84 higher than those of the original vibration filtering method and L. Alvarez method. In terms of time, the proposed method is 1.3075 seconds slower than the original vibration filtering method and 17.5754 seconds faster than the L. Alvarez method. When the variance of Gaussian white noise is 25, the enhancement and denoising effects of the proposed method are 97.79% and 81.16 higher than those of the original vibration filtering method and L. Alvarez method. In terms of time, the proposed method is 1.3246 seconds slower than the original vibration filtering method and 17.5796 seconds faster than the L. Alvarez method. Conclusion. The new model is not only stable but also has strong ability of contour extraction and fast convergence.

Construction of Computer Microscope Image Segmentation Model Based on Fourth-Order Partial Differential Equation Smoothing.

In order to solve the problem of image noise, the author proposes a computer microscope image segmentation model based on the smoothing of fourth-order partial differential equations. On the basis of the functional describing the smoothness of the image by the directional curvature modulus, the author deduces a fourth-order partial differential equation (PDE) image noise reduction model, while effectively reducing noise, the edges are well preserved. The processing result of this method is a piecewise linear image, and there is a step in the gradient at the edge of the target. Taking advantage of this feature of the noise reduction results, the author proposes a new geodesic active contour model. The experimental results show that the reference method directly segments the results, iterates 10 times, and takes 160.721 seconds. Using the noise reduction model in the paper to preprocess and then using the reference method to segment the result, iterating 8 times, it takes 32.347 seconds. Conclusion. The new model is not only stable but also has strong contour extraction ability and fast convergence speed.

Using the Split Bregman Algorithm to Solve the Self-repelling Snakes Model

Preserving contour topology during image segmentation is useful in many practical scenarios. By keeping the contours isomorphic, it is possible to prevent over-segmentation and under-segmentation, as well as to adhere to given topologies. The Self-repelling Snakes model (SR) is a variational model that preserves contour topology by combining a non-local repulsion term with the geodesic active contour model. The SR is traditionally solved using the additive operator splitting (AOS) scheme. In our paper, we propose an alternative solution to the SR using the Split Bregman method. Our algorithm breaks the problem down into simpler sub-problems to use lower-order evolution equations and a simple projection scheme rather than re-initialization. The sub-problems can be solved via fast Fourier transform or an approximate soft thresholding formula which maintains stability, shortening the convergence time, and reduces the memory requirement. The Split Bregman and AOS algorithms are compared theoretically and experimentally.

Improvement and Handling of the Segmentation Model with an Inflation Term

Abstract The use of balloon models to address the problems of “snakes” based models was introduced by Laurent D. Cohen. This paper presents a geodesic active contours model with a modified external force term that includes a balloon model. This balloon model makes the segmentation surface to behave like a balloon inflated by the external forces. In this paper, we show an automatic way to control the behaviour of the external force with respect to the segmentation evolution. The external forces, comprised of edge and inflation terms, push the segmentation surface to edges, while curvature regularizes the evolution. As segmentation evolves, the influence of the applied inflation force is determined by how close we are to the edges. With this setup, the initial segmentation does not need to be close to the object’s edges, instead it is inflated by the balloon model towards the edges. Closer to the edges, the influence of the inflation force is adjusted accordingly. The force’s influence is completely turned off when the evolution is stable (reached the edges), then only the curvature and edge information is used to evolve the segmentation. This approach solves the issues associated with inclusion of balloon model. These issues are that the inflation force can overpower forces from weak edges, or they can cause the contour to be slightly larger than the actual minima. We present examples of the improved model for segmentation of human bladder images. Weak edges are more prevalent in medical images, and the automated handling of the inflation forces gives promising results for this kind of images.

MATrix LABoratory Algorithm in Ultrasound Image-Guided General Drug Anesthesia along with Lumbar and Sacral Plexus Block in Hip Replacement under

Objective. The study aimed to explore the application of ultrasound image-guided general drug anesthesia combined with lumbar and sacral plexus block based on MATrix LABoratory (MATLAB) algorithm in hip arthroplasty and to study its clinical effect. Methods. The classic geodesic active contour (GAC) algorithm and the improved fuzzy clustering level set algorithm were used to segment ultrasound images of waist plexus, and then their segmentation effects were compared. Both algorithms are from the MATrix LABoratory (MATLAB) platform. A total of 60 patients undergoing hip arthroplasty were selected and randomly enrolled into control and experimental groups. The control group accepted general drug anesthesia, and the experimental group accepted ultrasound-guided lumbar and sacral plexus block combined with general anesthesia. The mean arterial pressure and heart rate at t0 (before anesthesia), t1 (before ventilation), t2 (when the skin was incised), t3 (when the prosthesis was implanted), t4 (when the incision was closed), and t5 (at the end of ventilation) were observed, and the intraoperative sufentanil dosage and 24 h analgesic dosage, the incidence of postoperative delirium, and the incidence of cognitive dysfunction were recorded. Results. The improved fuzzy clustering level set algorithm was better than the GAC model algorithm in image segmentation and running time. In contrast with the control group, the average arterial pressure and heart rate of the experimental group at the four time points of t1, t2, t3, and t5 were obviously reduced ( P < 0.05). In contrast with the control group, the amount of sufentanil and analgesics in the experimental group was obviously reduced ( P < 0.05), and the incidence of postoperative cognitive dysfunction and delirium was obviously reduced ( P < 0.05). Conclusion. The improved fuzzy clustering level set algorithm is superior to the GAC model in image segmentation and running time. Under its guidance, the lumbar and sacral plexus block combined with general anesthesia has a good clinical effect in hip arthroplasty, which is better than simple general anesthesia.

A method for giant aneurysm segmentation using Euler’s elastica

Computed Tomography Angiography (CTA) is a medical modality having the advantage to reveal anatomical accuracy essential for delivering a precise diagnosis and an appropriate patient’s management for treating a cerebral aneurysm. Segmentation of aneurysm shapes through CTA medical images is an important step for geometrical quantification and assessment of rupture risk of cerebral aneurysms. Despite intensive researches in image processing applied to image sequences, aneurysm segmentation remains a major challenge that depends on the geometry and positioning of the aneurysm into the brain. In this paper, the segmentation analysis is performed by using GAC and Euler’s elastica models. With Geodesic Active Contour model (GAC) giant aneurysms (Size > 25 mm) are segmented in high-contrast region, while Euler’s elastica model estimates the missing boundaries caused for instance by the low contrast of a thrombus (clot within the cavity during endovascular aneurysm repair) with respect to the neighboring tissues. The experiments indicate that our original model is relevant for segmenting the aneurysm cavity and thrombus both with clear and distinct edges well providing a valuable tool for biological mechanisms understanding such as thrombosis into giant aneurysms, and medical validation.

A morphological approach to piecewise constant active contour model incorporated with the geodesic edge term

Traditional level set-based image segmentation method has to solve the level set evolution equation which is the Euler–Lagrange equation of the energy functional defined on the image domain. Solving level set evolution equation is very time-consuming, and reinitialization is usually needed. The level set evolution equation can also be solved by mathematical morphology. The morphological implementation is very simple, fast and stable. The piecewise constant active contour model incorporated with the geodesic edge term is a hybrid active contour model which combines two active contour models which are active contour model without edges and geodesic active contour model. In this paper, the mathematical morphology-based level set evolution method is applied to the piecewise constant active contour model incorporated with the geodesic edge term. The curvature morphological operator is also improved. Experimental results show that, compared with the original piecewise constant active contour model incorporated the geodesic edge term, the new mathematical morphology-based model can segment images more accurately and there are significant gains in simplicity, speed and stability. The new mathematical morphology-based model is also compared to morphological piecewise constant active contour model, morphological geodesic active contour model, traditional piecewise constant active contour model and two other active contour models. Results show that the proposed method gets the segmentation result with faster speed and higher accuracy.

3D Model Visualization for Brain Tumour using MRI Images

The inaccurate prediction of tumour is because of the 2D images do not present the complete natural tumour representation as in 3D visualization. In order to construct the 3D model, the contour of 2D MRI images must be merged together. In this work, the edge detection of brain tumour on 2D images is done using the Geodesic Active Contour (GAC) model based on Additive Operator Splitting (AOS), then 3D model is visualized using Image Manifold (IM) and Volume Estimation (VE) methods. The comparison of performance for both methods is calculated. In conclusion, the execution time for VE method is higher than IM method since more images are used in VE method to calculate the volume of the tumour accurately. In terms of iteration number, Volume Estimation has a higher number of iterations, but for error and root mean square error, both methods have roughly the same value.

Land use Detection in Nusajaya using Higher-Order Modified Geodesic Active Contour Model

Urban development is a global phenomenon. In Johor, especially Nusajaya is one of the most rapidly developing cities. This is due to the increase of land demand and population growth. Moreover, land-use changes are considered to be one of the major components of current environmental monitoring strategies. In this context, image segmentation and mathematical model offers essential tools that can be used to analyze land use detection. The image segmentation process is known as the most important and difficult task in image analysis. Nonlinear fourth-order models had shown to have a good achievement in recovering smooth regions. Therefore, these motivate us to propose a fourth-order modified geodesic active contour (GAC) model. In the proposed model, a modified signed pressure force (SPF) function has been defined to segment the inhomogeneous satellite images. The simulations of the fourth-order modified GAC model through some numerical methods based on the higher-order finite difference method (FDM) have been illustrated. Matlab R2015a software in Windows 7 Ultimate on Intel (R) Core (TM) i5-3230M @ 2.60GHz CPU with 8 GB RAM has been considered as a computational platform for the simulation. Qualitative and quantitative differences between modified SPF functions and other SPF functions have been shown as a comparison. Hence land use detection is very useful for local governments and urban planners to enhance the future sustainable development plans of Nusajaya.

A Level Set Method for Infrared Image Segmentation Using Global and Local Information

Infrared image segmentation plays a significant role in many burgeoning applications of remote sensing, such as environmental monitoring, traffic surveillance, air navigation and so on. However, the precision is limited due to the blurred edge, low contrast and intensity inhomogeneity caused by infrared imaging. To overcome these challenges, a level set method using global and local information is proposed in this paper. In our method, a hybrid signed pressure function is constructed by fusing a global term and a local term adaptively. The global term is represented by the global average intensity, which effectively accelerates the evolution when the evolving curve is far away from the object. The local term is represented by a multi-feature-based signed driving force, which accurately guides the curve to approach the real boundary when it is near the object. Then, the two terms are integrated via an adaptive weight matrix calculated based on the range value of each pixel. Under the framework of geodesic active contour model, a new level set formula is obtained by substituting the proposed signed pressure function for the edge stopping function. In addition, a Gaussian convolution is applied to regularize the level set function for the purpose of avoiding the computationally expensive re-initialization. By iteration, the object of interest can be segmented when the level set function converges. Both qualitative and quantitative experiments verify that our method outperforms other state-of-the-art level set methods in terms of accuracy and robustness with the initial contour being set randomly.

3-D segmentation of lung nodules using hybrid level sets

Lung nodule segmentation in CT images and its subsequent volume analysis can help determine the malignancy status of a lung nodule. While several efficient segmentation schemes have been proposed, only a few studies evaluated the segmentation's performance for large nodules. In this research, we contribute a semi-automatic system which is capable of performing robust 3-D segmentations on both small and large nodules with good accuracy. The target CT volume is de-noised with an anisotropic diffusion filter and a region of interest is selected around the target nodule on a reference slice. The proposed model performs nodule segmentation by incorporating a mean intensity based threshold in Geodesic Active Contour model in level sets. We also devise an adaptive technique using image intensity histogram to estimate the desired mean intensity of the nodule. The proposed system is validated on both lung nodules and phantoms collected from publicly available diverse databases. Quantitative and visual comparative analysis of the proposed work with the Chan-Vese algorithm and statistic active contour model of 3D Slicer platform is also presented. The resulting mean spatial overlap between segmented nodules and reference nodules is 0.855, the mean volume bias is 0.10±0.2 ml and the algorithm repeatability is 0.060 ml. The achieved results suggest that the proposed method can be used for volume estimations of small as well as large-sized nodules.

Objective estimation of tropical cyclone innercore surface wind structure using infrared satellite images

An objective technique is presented for estimating tropical cyclone (TC) innercore two-dimensional (2-D) surface wind field structure using infrared satellite imagery and machine learning. For a TC with eye, the eye contour is first segmented by a geodesic active contour model, based on which the eye circumference is obtained as the TC eye size. A mathematical model is then established between the eye size and the radius of maximum wind obtained from the past official TC report to derive the 2-D surface wind field within the TC eye. Meanwhile, the composite information about the latitude of TC center, surface maximum wind speed, TC age, and critical wind radii of 34- and 50-kt winds can be combined to build another mathematical model for deriving the innercore wind structure. After that, least squares support vector machine (LSSVM), radial basis function neural network (RBFNN), and linear regression are introduced, respectively, in the two mathematical models, which are then tested with sensitivity experiments on real TC cases. Verification shows that the innercore 2-D surface wind field structure estimated by LSSVM is better than that of RBFNN and linear regression.

Some numerical methods for solving geodesic active contour model on image segmentation process

In this paper, we present an edge-based image segmentation technique using modified geodesic active contour model to detect the desired objects from an image. The stopping function of the proposed model has been modified from the usual geodesic active contour model. The modified geodesic active contour model is discretized using finite difference method based on the central difference formula. Then, some numerical methods such as RBGS and Jacobi methods are used for solving the linear system of equation. The accuracy and effectiveness of the proposed algorithm have been illustrated by applied to different images and some numerical methods.

New normalized nonlocal hybrid level set method for image segmentation

This article introduces a new normalized nonlocal hybrid level set method for image segmentation. Due to intensity overlapping, blurred edges with complex backgrounds, simple intensity and texture information, such kind of image segmentation is still a challenging task. The proposed method uses both the region and boundary information to achieve accurate segmentation results. The region information can help to identify rough region of interest and prevent the boundary leakage problem. It makes use of normalized nonlocal comparisons between pairs of patches in each region, and a heuristic intensity model is proposed to suppress irrelevant strong edges and constrain the segmentation. The boundary information can help to detect the precise location of the target object, it makes use of the geodesic active contour model to obtain the target boundary. The corresponding variational segmentation problem is implemented by a level set formulation. We use an internal energy term for geometric active contours to penalize the deviation of the level set function from a signed distance function. At last, experimental results on synthetic images and real images are shown in the paper with promising results.

Iterative image segmentation with feature driven heuristic four-color labeling

Multilabel segmentation is an important research branch in image segmentation field. In our previous work, Multiphase Multiple Piecewise Constant and Geodesic Active Contour (MMPC-GAC) model was proposed, which can effectively describe multiple objects and background with intensity inhomogeneity. It can be approximately solved with Multiple Layer Graph (MLG) methods. To make the optimization more efficient and limit the approximate error, four-color labeling theorem was further introduced which can limit the MLG within three layers (representing four phases). However, the adopted random four-color labeling method usually provides chaotic color maps with obvious inhomogeneity for those semantic consistent regions. For this case, a new and alternative method named heuristic four-color labeling is proposed in this paper, which aims to generate more reasonable color maps with a global view of the whole image. And compared with the random four-color labeling strategy, the whole iterative algorithm based on our method usually produces better segmentations with faster convergence, particularly for images with clutters and complicated structures. This strategy is a good substitute for random coloring method when the latter produces unsatisfactory messy segmentation. Experiments conducted on public dataset demonstrate the effectiveness of the proposed method.

A novel level set method for image segmentation by combining local and global information

A novel level set method integrating local and global statistical information is proposed in this paper. In our method, a new signed pressure force (SPF) function is constructed by two parts. One is the global average intensity of the image, which can accelerate the evolution of the curve when the contour far away from the object boundaries. The other is the intensity average of difference image between the averaging convolution image and the original image, which can guide the evolving curve to catch the boundaries of the objects. In addition, an adaptive weighting function is utilized to adjust the ratio between the global and local terms, which can eliminate the inconvenient selection of weighting parameter. By substituting the new SPF function for the edge stopping function of the geodesic active contour model, we obtain a novel adaptive hybrid segmentation model, which is capable of segmenting the images with intensity inhomogeneity. What is more, in our method, the level set function is initialized with a binary function, which reduces the computational cost for the re-initialization step. The experimental results and comparisons with several popular models on synthetic and real images indicate that our method achieves superior performance in segmenting images with noise, low contrast and intensity inhomogeneity.