Snakes, shapes, and gradient vector flow

Snakes, or active contours, are used extensively in computer vision and image processing applications, particularly to locate object boundaries. Problems associated with initialization and poor convergence to boundary concavities, however, have limited their utility. This paper presents a new external force for active contours, largely solving both problems. This external force, which we call gradient vector flow (GVF), is computed as a diffusion of the gradient vectors of a gray-level or binary edge map derived from the image. It differs fundamentally from traditional snake external forces in that it cannot be written as the negative gradient of a potential function, and the corresponding snake is formulated directly from a force balance condition rather than a variational formulation. Using several two-dimensional (2-D) examples and one three-dimensional (3-D) example, we show that GVF has a large capture range and is able to move snakes into boundary concavities.     

Active contour external force using vector field convolution for image segmentation.

Snakes, or active contours, have been widely used in image processing applications. Typical roadblocks to consistent performance include limited capture range, noise sensitivity, and poor convergence to concavities. This paper proposes a new external force for active contours, called vector field convolution (VFC), to address these problems. VFC is calculated by convolving the edge map generated from the image with the user-defined vector field kernel. We propose two structures for the magnitude function of the vector field kernel, and we provide an analytical method to estimate the parameter of the magnitude function. Mixed VFC is introduced to alleviate the possible leakage problem caused by choosing inappropriate parameters. We also demonstrate that the standard external force and the gradient vector flow (GVF) external force are special cases of VFC in certain scenarios. Examples and comparisons with GVF are presented in this paper to show the advantages of this innovation, including superior noise robustness, reduced computational cost, and the flexibility of tailoring the force field.     

External force of snake: virtual electric field

Gradient vector flow (GVF) is an external force of snake that overcomes traditional snake's problems: limited capture range and poor convergence to concave boundaries. A new external force with the same properties as the GVF is proposed. The proposed method has much shorter computational time than the GVF.     

R-Snake:一种基于边缘与区域信息的图像主动轮廓提取模型

 传统Snake模型存在着对轮廓的初始化敏感,对高噪声图像易陷入局部极小值,以及对具有狭长深度凹陷区域的图像无法获得正确轮廓等问题.本文提出了一种基于边缘与区域信息的主动轮廓模型R-Snake(Region Snake).该模型通过文中设计的图像变换算子,并结合区域积分与曲线积分间转化的Green公式,导出了包含目标图像区域信息的区域力.然后由力平衡方程将该区域信息自然直接地引入到主动轮廓提取模型中,从而实现图像的轮廓提取.由于该模型同时利用了图像的区域信息和梯度信息来引导轮廓曲线的演化,使得本文方法不仅扩大了轮廓初始化的范围,降低了对图像噪声的敏感性,而且还增加了轮廓曲线收敛到真实边界的能力.实验结果表明,本文方法具有很强的适应性和鲁棒性,尤其是对高噪声图像和具有狭长深度凹陷的图像获得了优于传统Snake模型的结果.     

Dynamic directional gradient vector flow for snakes.

Snakes, or active contour models, have been widely used in image segmentation. However, most present snake models do not discern between positive and negative step edges. In this paper, a new type of dynamic external force for snakes named dynamic directional gradient vector flow (DDGVF) is proposed that uses this information for better performance. It makes use of the gradients in both x and y directions and deals with the external force field for the two directions separately. In snake deformation, the DDGVF field is utilized dynamically according to the orientation of snake in each iteration. Experimental results demonstrate that the DDGVF snake provides a much better segmentation than GVF snake in situations when edges of different directions are present which pose confusion for segmentation.     

Automatic active model initialization via Poisson inverse gradient

Active models have been widely used in image processing applications. A crucial stage that affects the ultimate active model performance is initialization. This paper proposes a novel automatic initialization approach for parametric active models in both 2-D and 3-D. The PIG initialization method exploits a novel technique that essentially estimates the external energy field from the external force field and determines the most likely initial segmentation. Examples and comparisons with two state-of-the- art automatic initialization methods are presented to illustrate the advantages of this innovation, including the ability to choose the number of active models deployed, rapid convergence, accommodation of broken edges, superior noise robustness, and segmentation accuracy.     

一种新的用于医学图像分割的几何活动轮廊模型

提出一种新的几何活动轮廊模型对医学图像进行分割．首先，我们对几何活动轮廊模型中吸引力场进行正则化，扩大目标轮廊边缘对的轮廊曲线的吸引力范围，增加轮廊曲线搜寻凹轮廊的能力．然后，采用多尺度模型增加对边缘提取的精确度．将正则化方法与多尺度方法相结合，能够很好的抑制医学图像中的噪声和虚假边缘的干扰，这一方法能够在不采用任何附加拓扑控制的情况下自动控制轮廊曲线的拓扑结构变化，同时提取多个解剖结构，对来自不同成像技术的医学图像的分割，结果表明该方法是一种有效的医学图像分割方法。     

Detection of the carpal bone contours from 3-D MR images of the wrist using a planar radial scale-space snake

In this paper we consider the problems encountered when applying snake models to detect the contours of the carpal bones in 3-D MR images of the wrist. In order to improve the performance of the original snake model introduced by Kass [1], we propose a new image force based on one-dimensional (1-D) second-order Gaussian filtering and contrast equalization. The improved snake is less sensitive to model initialization and has no tendency to cut off contour sections of high curvature, because 1-D radial scale-space relaxation is used. Contour orientation is used to minimize the influence of neighboring image structures. Due to 1-D contrast equalization an intensity insensitive measure of external energy is obtained. As a consequence a good balance between internal and external energetic contributions of the snake is established, which also improves convergence. By incorporating this new image force into the snake model, we succeed in accurate contour detection, even when relatively high noise levels are present and when the contrast varies along the contours of the bones.     

基于GVF Snake的运动目标跟踪方法

针对Snake不能收敛于凹形边缘和收敛速度慢的缺点,结合帧间差分和梯度矢量流主动轮廓模型（GVF Snake）,提出了一种运动目标跟踪方法。首先通过帧间差分得到不同时刻的灰度差异图像,然后用形态方法得到的运动目标粗略轮廓作为Snake的初始轮廓,最后利用GVF Snake的特性,准确地收敛到目标边界。实验证明该方法运算速度快、能够快速地收敛到目标轮廓、准确地跟踪目标,并具有一定的抗噪能力。     

Robust B-spline Snakes For Ultrasound Image Segmentation

Snake-based methods are commonly used to segment ultrasound images. However, their performance is generally limited because of the specific properties of this kind of images. This paper addresses the sensitivity of parametric active contours to speckle within ultrasound images. We propose a new B-spline snake model, founded on two original external energies specifically tailored for the segmentation of biomedical speckled images. First, the curve is attracted from a wide capture range with an expansion energy that facilitates the snake initialization. Then, it is accurately fitted on the region boundaries with an energy that allows precise positioning of the curve along edges in ultrasound images. A mutual inhibition function is designed to control the two energies. Results on real ultrasound images are presented and quantitatively compared to the boundaries manually outlined by experts. Our method improves the precision of heart cavities segmentation.     

基于图像引力和Mumford-Shah模型的曲线演化算法

提出了一种图像引力和Mumford—Shah（M—S）模型的快速曲线演化算法,该算法分两步实现：首先利用图像引力,对参数主动轮廓线模型中的控制点进行寻优,使控制点能快速地收敛到图像的边缘附近;然后利用插值算法,得到目标较粗糙的大致轮廓,再使用M—S模型和窄带方法得到准确的轮廓。该算法避免了参数主动轮廓线模型不能收敛到物体凹陷的边缘和对初始位置敏感等问题,也避免了M—S模型需要对所有图像数据进行计算,计算量大等问题,实现了对参数和几何主动轮廓线模型进行了有效结合。     

Inertial snake for contour detection in ultrasonography images

Snakes, or active contour models are used extensively for image segmentation in varied fields. However, some major challenges restrict their use in many fields. The authors propose a new inertial snake model, that introduces an inertial effect of the control points into the snake framework. The proposed inertial force along with the first- and second-order continuity forces controls the spline motion through the concavities and also against weak edge forces. This smart force field, added to the inertial energy framework, posses the ability to adaptively reduce its effect near the true edges, so that the energy minimising spline converges into the edges. A greedy snake has been used for computation of the energy minimising spline. The algorithm has been tested on phantoms and ultrasound images as well. It is shown in the results that the proposed algorithm classifies the object from the background class in most of the images perfectly. Ultrasound images of a lower limb artery of an adult woman have been tested with this algorithm, and also extended for motion tracking.     

Fluid Vector Flow and Applications in Brain Tumor Segmentation

In this paper, we propose a new approach that we call the ldquofluid vector flowrdquo (FVF) active contour model to address problems of insufficient capture range and poor convergence for concavities. With the ability to capture a large range and extract concave shapes, FVF demonstrates improvements over techniques like gradient vector flow, boundary vector flow, and magnetostatic active contour on three sets of experiments: synthetic images, pediatric head MRI images, and brain tumor MRI images from the Internet brain segmentation repository.     

Surface extraction and thickness measurement of the articular cartilage from MR images using directional gradient vector flow snakes

The accuracy of the surface extraction of magnetic resonance images of highly congruent joints with thin articular cartilage layers has a significant effect on the percentage errors and reproducibility of quantitative measurements (e.g., thickness and volume) of the articular cartilage. Traditional techniques such as gradient-based edge detection are not suitable for the extraction of these surfaces. This paper studies the extraction of articular cartilage surfaces using snakes, and a gradient vector flow (GVF)-based external force is proposed for this application. In order to make the GVF snake more stable and converge to the correct surfaces, directional gradient is used to produce the gradient vector flow. Experimental results show that the directional GVF snake is more robust than the traditional GVF snake for this application. Based on the newly developed snake model, an articular cartilage surface extraction algorithm is developed. Thickness is computed based on the surfaces extracted using the proposed algorithm. In order to make the thickness measurement more reproducible, a new thickness computation approach, which is called T-norm, is introduced. Experimental results show that the thickness measurement obtained by the new thickness computation approach has better reproducibility than that obtained by the existing thickness computation approaches.     

A hand tracking algorithm with particle filter and improved GVF snake model

To solve the problem that the accurate information of hand cannot be obtained by particle filter, a hand tracking algorithm based on particle filter combined with skin-color adaptive gradient vector flow (GVF) snake model is proposed. Adaptive GVF and skin color adaptive external guidance force are introduced to the traditional GVF snake model, guiding the curve to quickly converge to the deep concave region of hand contour and obtaining the complex hand contour accurately. This algorithm realizes a real-time correction of the particle filter parameters, avoiding the particle drift phenomenon. Experimental results show that the proposed algorithm can reduce the root mean square error of the hand tracking by 53%, and improve the accuracy of hand tracking in the case of complex and moving background, even with a large range of occlusion. This work has been supported by the National Natural Sciencal Foundation of China (No.61403274), and the Tianjin Technology Project of Intelligent Manufacturing (No.15ZXZNGX00160). E-mail:agwu@tju.edu.cn      

Harmonic gradient vector flow external force for snake model

Gradient vector flow (GVF), an external force for the snake model, is reformulated by replacing the smoothness constraint with a harmonic one, which is related to the divergence and the curl of the vector field. The proposed formulation provides some new insights into the nature of the GVF.     

基于边缘吸引力场正则化的短程线主动轮廓模型

短程线主动轮廓模型是近几年提出的一种有效的多目标轮廓提取算法 .本文在详细分析其动力学过程的基础上 ,针对该模型中存在的局限性和不足 ,提出对边缘吸引力场进行正则化的方法 ,并采用多尺度模型 ,有效的改善了该模型不能对存在断裂轮廓的目标进行正确提取和凹边缘搜索能力弱的缺点 ,增强了抗噪声和虚假边缘干扰的能力 ,使该算法具有更好的鲁棒性和实用性 .     

适应于图像复原的无参考图像质量评价方法

由于图像降质过程的复杂性、成像获取条件限制,以及图像本身的复杂性和图像复原过程的病态性,图像复原解大多都是近似的或畸变的,一种适应于图像复原质量评价的计算方法将大大提升图像复原的应用范围。针对图像复原过程的病态性,提出了一种针对图像复原图像质量评价的计算方法,该算法通过在图像质量算子中引入图像相似矩阵和图像复原趋势矩阵,使其能适应复原对于图像结构或噪声结构的变化。该图像质量评价算子计算无需参考图像,可以很好地反映图像的模糊程度和噪声程度,并且计算简单。实验证明了该图像质量评价算子的有效性。     

基于小波相位保持校正GVF snake模型的B超心脏边缘提取

针对B超图像噪声过大引起的边缘提取问题,本文采用基于小波相位保持校正GVF snake模型的边缘提取 提取方法,在保持视觉效果的同时,达到了对伪像的去除、削弱和对边缘的更精确识别。     

基于变化检测和改进的GVF snake模型的运动目标轮廓提取

为了解决当前目标跟踪中目标轮廓提取不精确的问 题,在对传统GVF (gradient vector flow)snake活动轮廓模型改进的基础上,提 出一种基于变化检测和改进的GVF snake活动轮廓模型的视频目标轮廓提取算法。首先,通 过 基于t显著性检验的变化检测方 法消除背景边界的影响,并获取初始运动变化区域的临界四边形作为GVF snake的初始轮廓 。然后,对初始轮廓应用改进 的GVF snake模型以获得精确的轮廓边界。改进模型采用4方向各项异性扩散,并采用下降速 度较快的保真项系数以增强 GVF snake进入凹陷的能力,且保持对弱边界的收敛。本文方法克服了手动绘制初始轮廓的 缺点,对传统GVF snake方法进 行了改进,且空间准确度(SA)有很大提高。实验表明 ,本文方法成功分割出目标凹陷部分并对弱边界有较好的收敛效果,提高了轮廓提取的精确 度。