Sobolev Active Contours

All previous geometric active contour models that have been formulated as gradient flows of various energies use the same L ²-type inner product to define the notion of gradient. Recent work has shown that this inner product induces a pathological Riemannian metric on the space of smooth curves. However, there are also undesirable features associated with the gradient flows that this inner product induces. In this paper, we reformulate the generic geometric active contour model by redefining the notion of gradient in accordance with Sobolev-type inner products. We call the resulting flows Sobolev active contours. Sobolev metrics induce favorable regularity properties in their gradient flows. In addition, Sobolev active contours favor global translations, but are not restricted to such motions; they are also less susceptible to certain types of local minima in contrast to traditional active contours. These properties are particularly useful in tracking applications. We demonstrate the general methodology by reformulating some standard edge-based and region-based active contour models as Sobolev active contours and show the substantial improvements gained in segmentation.     

基于全局最小化活动轮廓的多目标检测跟踪

为了在噪声干扰以及目标和背景颜色相近情况下实现多目标跟踪,提出一种基于快速全局最小化的活动轮廓模型的目标检测跟踪算法。该算法结合了基于边缘的活动轮廓模型和基于区域的活动轮廓模型,对能量泛函进行全局最小化来检测目标活动轮廓,用卡尔曼滤波预测目标下一帧的特征信息,然后用改进的最近邻法进行多目标跟踪。对图像序列的实验结果表明该算法能有效地对运动背景下多目标进行跟踪。     

结合全局与局部信息活动轮廓的非同质图像分割

目的 通过对现有基于区域的活动轮廓模型能量泛函的Euler-Lagrange方程进行变形,建立其与K-means方法的等价关系,提出一种新的基于K-means活动轮廓模型,该模型能有效分割灰度非同质图像。方法 结合图像全局和局部信息,根据交互熵的特性,提出新的局部自适应权重,它根据像素点所在邻域的局部统计信息自适应地确定各个像素点的分割阈值,排除灰度非同质分割目标的影响。结果 采用Jaccard相似系数-JS(Jaccard similarity)和Dice相似系数-DSC(Dice similarity coefficient)两个指标对自然以及合成图像的分割结果进行定量分析,与传统及最新经典的活动轮廓模型相比,新模型JS和DSC的值最接近1,且迭代次数不多于50次。提出的模型具有较高的计算效率和准确率。结论 通过大量实验发现,新模型结合图像全局和局部信息,利用交互熵特性得到自适应权重,对初始曲线位置具有稳定性,且对灰度非同质图像具有较好地分割效果。本文算法主要适用于分割含有噪声及灰度非同质的医学图像,而且分割结果对初始轮廓具有鲁棒性。     

融合区域和测地线的活动轮廓模型与图割相结合的自然图像分割

针对活动轮廓模型利用水平集函数演化来分割图像时,只能分割灰度均匀的图像 问题以及容易陷入能量泛函局部极小值的缺点,提出一种新的图像分割模型。模型将区域中的 局部和全局信息融合的活动轮廓模型与边界模型相结合,然后利用图切割进行优化。实验表明, 该方法对初始曲线不敏感,能分割灰度不均的自然图像,避免陷入局部极小,并能有效提高图 像分割的速度和精度。     

Multiple piecewise constant with geodesic active contours (MPC-GAC) framework for interactive image segmentation using graph cut optimization

This paper proposes an improved variational model, multiple piecewise constant with geodesic active contour (MPC-GAC) model, which generalizes the region-based active contour model by Chan and Vese, 2001 [11] and merges the edge-based active contour by Caselles et al., 1997 [7] to inherit the advantages of region-based and edge-based image segmentation models. We show that the new MPC-GAC energy functional can be iteratively minimized by graph cut algorithms with high computational efficiency compared with the level set framework. This iterative algorithm alternates between the piecewise constant functional learning and the foreground and background updating so that the energy value gradually decreases to the minimum of the energy functional. The k-means method is used to compute the piecewise constant values of the foreground and background of image. We use a graph cut method to detect and update the foreground and background. Numerical experiments show that the proposed interactive segmentation method based on the MPC-GAC model by graph cut optimization can effectively segment images with inhomogeneous objects and background.     

“Brownian strings”: Segmenting images withstochastically deformable contours

This paper describes an image segmentation technique in which an arbitrarily shaped contour was deformed stochastically until it fitted around an object of interest. The evolution of the contour was controlled by a simulated annealing process which caused the contour to settle into the global minimum of an image-derived “energy” function. The nonparametric energy function was derived from the statistical properties of previously segmented images, thereby incorporating prior experience. Since the method was based on a state space search for the contour with the best global properties, it was stable in the presence of image errors which confound segmentation techniques based on local criteria, such as connectivity. Unlike “snakes” and other active contour approaches, the new method could handle arbitrarily irregular contours in which each interpixel crack represented an independent degree of freedom. Furthermore, since the contour evolved toward the global minimum of the energy, the method was more suitable for fully automatic applications than the snake algorithm, which frequently has to be reinitialized when the contour becomes trapped in local energy minima. High computational complexity was avoided by efficiently introducing a random local perturbation in a time independent of contour length, providing control over the size of the perturbation, and assuring that resulting shape changes were unbiased. The method was illustrated by using it to find the brain surface in magnetic resonance head images and to track blood vessels in angiograms     

Nonlocal variational image segmentation models on graphs using the Split Bregman

Variational functionals such as Mumford-Shah and Chan-Vese methods have a major impact on various areas of image processing. After over 10 years of investigation, they are still in widespread use today. These formulations optimize contours by evolution through gradient descent, which is known for its overdependence on initialization and the tendency to produce undesirable local minima. In this paper, we propose an image segmentation model in a variational nonlocal means framework based on a weighted graph. The advantages of this model are twofold. First, the convexity global minimum (optimum) information is taken into account to achieve better segmentation results. Second, the proposed global convex energy functionals combine nonlocal regularization and local intensity fitting terms. The nonlocal total variational regularization term based on the graph is able to preserve the detailed structure of target objects. At the same time, the modified local binary fitting term introduced in the model as the local fitting term can efficiently deal with intensity inhomogeneity in images. Finally, we apply the Split Bregman method to minimize the proposed energy functional efficiently. The proposed model has been applied to segmentation of real medical and remote sensing images. Compared with other methods, the proposed model is superior in terms of both accuracy and efficient.     

Active contour model combining region and edge information

A novel active contour model is proposed by combining region and edge information. Its level set formulation consists of the edge-related term, the region-based term and the regularization term. The edge-related term is derived from the image gradient, and facilitates the contours evolving into object boundaries. The region-based term is constructed using both local and global statistical information, and related to the direction and velocity of the contour propagation. The last term ensures stable evolution of the contours. Finally, a Gaussian convolution is used to regularize the level set function. In addition, a new quantitative metric named modified root mean squared error is defined, which can be used to evaluate the final contour more accurately. Experimental results show that the proposed method is efficient and robust, and can segment homogenous images and inhomogenous images with the initial contour being set freely.     

An integrated two-stage approach for image segmentation via active contours

A novel integrated two-stage approach is proposed for image segmentation, where the edge, global and local region information of images are in turn incorporated to define the intensity fitting energy. In the first stage, the Chan-Vese model flexibly assimilates the edge indicator function in the beginning, and then the Laplace operator is introduced to regularize the level set function when minimizing the energy functional. As an edge-based and global region-based active contour, it can be inclined to rapidly produce a coarse segmentation result. In the second stage, we further segment the image by absorbing the local region fitting energy, where its initialization is acquired by the final active contour of the first stage. In addition, we present a generalized level set regularization term, which efficiently eliminates the periodically re-initialization procedure of traditional level set methods and maintains the corresponding signed distance property. Compared with the first stage, the local object details are accurately segmented in the second stage, which can acquire an accurate segmentation result. Qualitative and quantitative experimental results demonstrate the accuracy, robustness and efficiency of our approach with applications to some synthetical and real-world images.

     

Hybrid geodesic region-based active contours for image segmentation

In this paper, we propose novel hybrid edge and region based active contour models. First, we consider geodesic curve and region-based model, and evolve contours based on global information to segment images with intensity homogeneity. Second, we extend the global model to the local intensity fitting energy for segmenting the images with intensity inhomogeneity. Moreover, the level set regularization term is added to the energy functional to ensure accurate computation and avoid expensive re-initialization of the evolving level set function. Experimental results indicate the proposed method has advantage over the geodesic active contour (GAC) model, the Chan–Vese (C–V) model, the Lankton’s method and the local binary fitting (LBF) model in terms of efficiency and robustness.     

Isophotes Selection and Reaction-Diffusion Model for Object Boundaries Estimation

This paper investigates generic region-based segmentation schemes using area-minimization constraint and background modeling, and develops a computationally efficient framework based on level lines selection coupled with biased anisotropic diffusion. A common approach to image segmentation is to construct a cost function whose minima yield the segmented image. This is generally achieved by competition of two terms in the cost function, one that punishes deviations from the original image and another that acts as a regularization term. We propose a variational framework for characterizing global minimizers of a particular segmentation energy that can generates irregular object boundaries in image segmentation. Our motivation comes from the observation that energy functionals are traditionally complex, for which it is usually difficult to precise global minimizers corresponding to best segmentations. In this paper, we prove that the set of curves that minimizes the basic energy model under concern is a subset of level lines or isophotes, i.e. the boundaries of image level sets. The connections of our approach with region-growing techniques, snakes and geodesic active contours are also discussed. Moreover, it is absolutely necessary to regularize isophotes delimiting object boundaries and to determine piecewise smooth or constant approximations of the image data inside the objects boundaries for vizualization and pattern recognition purposes. Thus, we have constructed a reaction-diffusion process based on the Perona-Malik anisotropic diffusion equation. In particular, a reaction term has been added to force the solution to remain close to the data inside object boundaries and to be constant in non-informative regions, that is the background region. In the overall approach, diffusion requires the design of the background and foreground regions obtained by segmentation, and segmentation of the adaptively smoothed image is performed after each iteration of the diffusion process. From an application point of view, the sound initialization-free algorithm is shown to perform well in a variety of imaging contexts with variable texture, noise and lighting conditions, including optical imaging, medical imaging and meteorological imaging. Depending on the context, it yields either a reliable segmentation or a good pre-segmentation that can be used as initialization for more sophisticated, application-dependent segmentation models.     

Lip segmentation using localized active contour model with automatic initial contour

Lip-reading is one of important approaches for human–computer interaction (HCI). Its development would have a large range of applications, especially in augmented reality. Lip segmentation is the first and foremost step in the lip-reading system. Conventional method of region-based active contour model adopts the global information of image and is unable to perform well. In this paper, from a localized perspective, we introduce the methodology of localized active contour model (LACM) and, meanwhile, propose the method that using LACM to perform the lip segmentation with the initial contour automatically generated. The scope for active contour model is reduced to the local region that reduces the disturbances of unrelated factors. The experimental results demonstrate the method adopts this model would dramatically improve the robustness for lip segmentation. On this basis, we analyze the influence of initial contours and local radiuses, study the efficiencies under different initial contours and compare it with the conventional active contour model which adopts the global information.

     

A Bayesian approach to dynamic contours through stochastic samplingand simulated annealing

In many applications of image analysis, simply connected objects are to be located in noisy images. During the last 5-6 years active contour models have become popular for finding the contours of such objects. Connected to these models are iterative algorithms for finding the minimizing energy curves making the curves behave dynamically through the iterations. These approaches do however have several disadvantages. The numerical algorithms that are in use constrain the models that can be used. Furthermore, in many cases only local minima can be achieved. In this paper, the author discusses a method for curve detection based on a fully Bayesian approach. A model for image contours which allows the number of nodes on the contours to vary is introduced. Iterative algorithms based on stochastic sampling is constructed, which make it possible to simulate samples from the posterior distribution, making estimates and uncertainty measures of specific quantities available. Further, simulated annealing schemes making the curve move dynamically towards the global minimum energy configuration are presented. In theory, no restrictions on the models are made. In practice, however, computational aspects must be taken into consideration when choosing the models. Much more general models than the one used for active contours may however be applied. The approach is applied to ultrasound images of the left ventricle and to magnetic resonance images of the human brain, and show promising results     

A Review of Statistical Approaches to Level Set Segmentation: Integrating Color,Texture, Motion and Shape

Since their introduction as a means of front propagation and their first application to edge-based segmentation in the early 90’s, level set methods have become increasingly popular as a general framework for image segmentation. In this paper, we present a survey of a specific class of region-based level set segmentation methods and clarify how they can all be derived from a common statistical framework. Region-based segmentation schemes aim at partitioning the image domain by progressively fitting statistical models to the intensity, color, texture or motion in each of a set of regions. In contrast to edge-based schemes such as the classical Snakes, region-based methods tend to be less sensitive to noise. For typical images, the respective cost functionals tend to have less local minima which makes them particularly well-suited for local optimization methods such as the level set method. We detail a general statistical formulation for level set segmentation. Subsequently, we clarify how the integration of various low level criteria leads to a set of cost functionals. We point out relations between the different segmentation schemes. In experimental results, we demonstrate how the level set function is driven to partition the image plane into domains of coherent color, texture, dynamic texture or motion. Moreover, the Bayesian formulation allows to introduce prior shape knowledge into the level set method. We briefly review a number of advances in this domain.     

A robust snake implementation; a dual active contour

A conventional active contour formulation suffers difficulty in appropriate choice of an initial contour and values of parameters. Recent approaches have aimed to resolve these problems but can compromise other performance aspects. To relieve the problem in initialization, we use a dual active contour, which is combined with a local shape model to improve the parameterization. One contour expands from inside the target feature, the other contracts from the outside. The two contours are interlinked to provide a balanced technique with an ability to reject “weak” local energy minima     

An active contour model driven by anisotropic region fitting energy for image segmentation

A novel region active contour model (ACM) for image segmentation is proposed in this paper. In order to perform an accurate segmentation of images with non-homogeneous intensity, the original region fitting energy in the general region-based ACMs is improved by an anisotropic region fitting energy to evolve the contour. Using the local image information described by the structure tensor, this new region fitting energy is defined in terms of two anisotropic fitting functions that approximate the image intensity along the principal directions of variation of the intensity. Therefore, the anisotropic fitting functions extract intensity information more precisely, which enable our model to cope with the boundaries with low-contrast and complicated structures. It is incorporated into a variational formula with a total variation (TV) regularization term with respect to level set function, from which the segmentation process is performed by minimizing this variational energy functional. Experiments on the vessel and brain magnetic resonance images demonstrate the advantages of the proposed method over Chan–Vese (CV) active contours and local binary active contours (LBF) in terms of both efficiency and accuracy.     

DREAM2S: Deformable Regions Driven by an Eulerian Accurate Minimization Method for Image and Video Segmentation

This paper deals with image and video segmentation using active contours. We propose a general form for the energy functional related to region-based active contours. We compute the associated evolution equation using shape derivation tools and accounting for the evolving region-based terms. Then we apply this general framework to compute the evolution equation from functionals that include various statistical measures of homogeneity for the region to be segmented. Experimental results show that the determinant of the covariance matrix appears to be a very relevant tool for segmentation of homogeneous color regions. As an example, it has been successfully applied to face segmentation in real video sequences.     

改进K-means活动轮廓模型

目的 通过对C-V模型能量泛函的Euler-Lagrange方程进行变形,建立其与K-means方法的等价关系,提出一种新的基于水平集函数的改进K-means活动轮廓模型。方法 该模型包含局部自适应权重矩阵函数,它根据像素点所在邻域的局部统计信息自适应地确定各个像素点的分割阈值,排除灰度非同质对分割目标的影响,进而实现对灰度非同质图像的精确分割。结果 通过分析对合成以及自然图像的分割结果,与传统及最新经典的活动轮廓模型相比,新模型不仅能较准确地分割灰度非同质图像,而且降低了对初始曲线选取的敏感度。结论 提出了包含权重矩阵函数的新活动轮廓模型,根据分割目的和分割图像性质,制定不同的权重函数,该模型具有广泛的适用性。文中给出的一种具有局部统计特性的权重函数,对灰度非同质图像的效果较好,且对初始曲线位置具有稳定性。     

Novel fuzzy active contour model with kernel metric for image segmentation

In this paper, a novel region-based fuzzy active contour model with kernel metric is proposed for a robust and stable image segmentation. This model can detect the boundaries precisely and work well with images in the presence of noise, outliers and low contrast. It segments an image into two regions – the object and the background by the minimization of a predefined energy function. Due to the kernel metric incorporated in the energy and the fuzziness of the energy, the active contour evolves very stably without the reinitialization for the level set function during the evolution. Here the fuzziness provides the model with a strong ability to reject local minima and the kernel metric is employed to construct a nonlinear version of energy function based on a level set framework. This new fuzzy and nonlinear version of energy function makes the updating of region centers more robust against the noise and outliers in an image. Theoretical analysis and experimental results show that the proposed model achieves a much better balance between accuracy and efficiency compared with other active contour models.