Concavity Convergence Research Articles

Image segmentation using active contours with image structure adaptive gradient vector flow external force

IntroductionGradient vector flow (GVF) has been proven as an effective external force for active contours. However, its smoothness constraint does not take the image structure into account, such that the GVF diffusion is isotropic and cannot preserve weak edges well.MethodsIn this article, an image structure adaptive gradient vector flow (ISAGVF) external force is proposed for active contours. In the proposed ISAGVF model, the smoothness constraint is first reformulated in matrix form, and then the image structure tensor is incorporated. As the structure tensor characterizes the image structure well, the proposed ISAGVF model can be adaptive to image structure, and the ISAGVF snake performs well on weak edge preservation and deep concavity convergence while possessing some other desirable properties of the GVF snake, such as enlarged capture range and insensitivity to initialization.ResultsExperiments on synthetic and real images manifest these properties of the ISAGVF snake.

Image segmentation using active contours with modified convolutional virtual electric field external force with an edge-stopping function.

The gradient vector flow (GVF) is an effective external force to deform the active contours. However, it suffers from high computational cost. For efficiency, the virtual electric field (VEF) model has been proposed, which can be implemented in real time thanks to fast Fourier transform (FFT). The VEF model has large capture range and low computation cost, but it has the limitations of sensitivity to noise and leakage on weak edge. The recently proposed CONVEF (Convolutional Virtual Electric Field) model takes the VEF model as a convolutional operation and employed another convolution kernel to overcome the drawbacks of the VEF model. In this paper, we employ an edge stopping function similar to that in the anisotropic diffusion to further improve the CONVEF model, and the proposed model is referred to as MCONVEF (Modified CONVEF) model. In addition, a piecewise constant approximation algorithm is borrowed to accelerate the calculation of the MCONVEF model. The proposed MCONVEF model is compared with the GVF and VEF models, and the experimental results are presented to demonstrate its superiority in terms of noise robustness, weak edge preserving and deep concavity convergence.

GVFOM: a novel external force for active contour based image segmentation

The GVF snake is effective on converging into concave areas and being insensitive to initialization. However, it fails to converge to areas with deep and narrow concavities or preserve weak edges. In this paper, a novel external force called gradient vector flow over manifold (GVFOM) is proposed for active contours. The proposed model takes the GVF vector as a 2D manifold embedded into a 4D Euclidean space, leading to the generalization of the Laplacian operator in Euclidean Space to that over manifold, and the two components of the external force are couples with each other to improve the properties of the GVF snake. The GVFOM snake has been tested with different kinds of images, and experimental results and comparison manifest that the GVFOM snake has better performance than the GVF and other state-of-the-art snakes on object separation, deep and narrow concavity convergence, weak edge protection, noise robustness while keeping some desirable properties of the GVF model such as initialization insensitivity and large capture range.

Extension of the virtual electric field model using bilateral-like filter for active contours

The gradient vector flow (GVF) model has been proven as an effective external force for active-contour-based image segmentation. However, it suffers from high computation cost since there are two PDEs to be solved in an iterative manner. As a remedy, the virtual electric field (VEF) model is proposed, which can be implemented in real time using the fast Fourier transform. However, the VEF model cannot preserve weak edges since it employs linear kernels. In this work, we extend the VEF model by using bilateral-like filters, and a fast algorithm is also employed for the proposed model. The proposed model is referred to as bilateral-filter-based VEF (BVEF) model. Experimental results on synthetic and real images demonstrate that the BVEF snake possesses some desired properties of the GVF, CNGGVF and VEF snakes such as large capture range and concavity convergence, and the BVEF model can be implemented in near real time, and its computation cost is comparable to that of the VEF model and much shorter than that of the GVF and CNGGVF models; it also can preserve weak edges, thanks to the bilateral-like nonlinear kernels.

Guide filter-based gradient vector flow module for infrared image segmentation.

Infrared image segmentation is a challenging topic since infrared images are characterized by high noise, low contrast, and weak edges. Active contour models, especially gradient vector flow (GVF), have better segmentation performance for clear images. However, the GVF model has the drawbacks of sensitivity to noise and adaptability of the parameters, decreasing the effect of infrared image segmentation significantly. To address these problems, this paper proposes a guide filter-based gradient vector flow module for infrared image segmentation (GFGVF). First, a guide filter is exploited to construct a novel edge map, providing characteristics of the image edge while excluding the effects of noise. This alleviates the possibility of edge leakage caused by using the traditional edge map. Then, a novel weighting function is constructed to effectively handle the extended capture range and preserving the edge even with noise existing. The experimental results demonstrate that the GFGVF model possesses good properties such as large capture range, concavity convergence, noise robustness, and alleviative boundary leakage.

Convolutional virtual electric field for image segmentation using active contours.

Gradient vector flow (GVF) is an effective external force for active contours; however, it suffers from heavy computation load. The virtual electric field (VEF) model, which can be implemented in real time using fast Fourier transform (FFT), has been proposed later as a remedy for the GVF model. In this work, we present an extension of the VEF model, which is referred to as CONvolutional Virtual Electric Field, CONVEF for short. This proposed CONVEF model takes the VEF model as a convolution operation and employs a modified distance in the convolution kernel. The CONVEF model is also closely related to the vector field convolution (VFC) model. Compared with the GVF, VEF and VFC models, the CONVEF model possesses not only some desirable properties of these models, such as enlarged capture range, u-shape concavity convergence, subject contour convergence and initialization insensitivity, but also some other interesting properties such as G-shape concavity convergence, neighboring objects separation, and noise suppression and simultaneously weak edge preserving. Meanwhile, the CONVEF model can also be implemented in real-time by using FFT. Experimental results illustrate these advantages of the CONVEF model on both synthetic and natural images.

Adaptive diffusion flow active contours for image segmentation

Gradient vector flow (GVF) active contour model shows good performance at concavity convergence and initialization insensitivity, yet it is susceptible to weak edges as well as deep and narrow concavity. This paper proposes a novel external force, called adaptive diffusion flow (ADF), with adaptive diffusion strategies according to the characteristics of an image region in the parametric active contour model framework for image segmentation. We exploit a harmonic hypersurface minimal functional to substitute smoothness energy term in GVF for alleviating the possible leakage. We make use of the p(x) harmonic maps, in which p(x) ranges from 1 to 2, such that the diffusion process of the flow field can be adjusted adaptively according to image characteristics. We also incorporate an infinity laplacian functional to ADF active contour model to drive the active contours onto deep and narrow concave regions of objects. The experimental results demonstrate that ADF active contour model possesses several good properties, including noise robustness, weak edge preserving and concavity convergence.

Method for Segmentation of the Endocardium and Epicardium of the Left Ventricle in Cardiac Magnetic Resonance Images

为了充分利用心脏核磁共振图像(magnetic resonance image,简称MRI)中关于左心室的解剖和功能信息,必须先分割左室壁内、外膜.提出一种基于Snake模型的左室壁内、外膜分割方法.首先提出了Snake模型的卷积虚拟静电场外力模型CONVEF(convolutional virtual electric field),该外力场捕捉范围大、抗噪能力强、在C形凹陷区域等问题上性能突出,而且基于卷积运算,采用快速Fourier变换可以实时计算.就左室壁内膜的分割而言,考虑到左室壁的形状近似为圆形,引入基于圆形约束的能量项.对于左室壁外膜的分割,充分挖掘了左室壁内、外膜形状上的相似性和位置上的相关性,构造了形状相似性内能和一个新的边缘图,该边缘图用来计算新的外力场.基于所有这些策略并采用内膜的分割结果初始化,可以自动、准确地分割外膜.通过对一套活体心脏MR(magnetic resonance)图像进行分割并和手工分割结果和GGVF(generalized gradient vector flow) Snake模型的分割结果进行比较,结果表明该方法是有效的.;In order to make a thorough use of the anatomical and functional information derived from cardiac magnetic resonance images, the epicardium and endocardium of the left ventricle should be extracted in advance. This paper presents a method for segmentation of the endocardium and epicardium of the left ventricle in cardiac magnetic resonance images using Snake models. It first proposes an external force for active contours, which is called convolutional virtual electric field (CONVEF). This CONVEF external force possesses the advantages of enlarged capture range, noise resistance and C-shape concavity convergence and can be implemented in real time by using fast Fourier transform since it is based on convolution. Considering that the left ventricle is roughly a circle, a shape constraint based on circle is adopted for segmentation of the endocardium. As to locating the epicardium, an internal energy based on shape similarity is proposed, and an edge map is coined to calculate the new external force by exploiting the resemblance between the endocardium and epicardium in shape and position. With these strategies, taking the final contour for endocardium as initialization, the Snake contour is reactivated to locate the epicardium automatically and accurately. This paper demonstrates the proposed approach on an in vivo dataset and compare the segmented contours with that of the GGVF (generalized gradient vector flow) Snake and manual collections. The results show its effectiveness.

Analysis of the Critical Point of the Gradient Vector Flow Snake Model

Gradient vector flow (GVF) snake shows high performance at capture-range enlarging and boundary concavity convergence, however, the initial contours encounter a so-called critical point problem (CPP). The initial contour must contain the critical points inside the object and exclude those outside the object, otherwise, the final result would be far from the expected. This paper investigates the CPP of the GVF snake and points out that, serving as an external force field for snake models, gradient vector flow could be effective only under some restrictions. Also, it is proved that the theoretical foundation, the Navier-Stokes equation for viscous fluid flow, for the solution to this CPP in literatures is incorrect. Finally, an empirical solution to the CPP is presented and its performance is validated by experiments.