Image segmentation using active contours driven by the Bhattacharyya gradient flow.

This paper addresses the problem of image segmentation by means of active contours, whose evolution is driven by the gradient flow derived from an energy functional that is based on the Bhattacharyya distance. In particular, given the values of a photometric variable (or of a set thereof), which is to be used for classifying the image pixels, the active contours are designed to converge to the shape that results in maximal discrepancy between the empirical distributions of the photometric variable inside and outside of the contours. The above discrepancy is measured by means of the Bhattacharyya distance that proves to be an extremely useful tool for solving the problem at hand. The proposed methodology can be viewed as a generalization of the segmentation methods, in which active contours maximize the difference between a finite number of empirical moments of the "inside" and "outside" distributions. Furthermore, it is shown that the proposed methodology is very versatile and flexible in the sense that it allows one to easily accommodate a diversity of the image features based on which the segmentation should be performed. As an additional contribution, a method for automatically adjusting the smoothness properties of the empirical distributions is proposed. Such a procedure is crucial in situations when the number of data samples (supporting a certain segmentation class) varies considerably in the course of the evolution of the active contour. In this case, the smoothness properties of the empirical distributions have to be properly adjusted to avoid either over- or underestimation artifacts. Finally, a number of relevant segmentation results are demonstrated and some further research directions are discussed.     

Boundary detection in medical images using edge following algorithm based on intensity gradient and texture gradient features

Finding the correct boundary in noisy images is still a difficult task. This paper introduces a new edge following technique for boundary detection in noisy images. Utilization of the proposed technique is exhibited via its application to various types of medical images. Our proposed technique can detect the boundaries of objects in noisy images using the information from the intensity gradient via the vector image model and the texture gradient via the edge map. The performance and robustness of the technique have been tested to segment objects in synthetic noisy images and medical images including prostates in ultrasound images, left ventricles in cardiac magnetic resonance (MR) images, aortas in cardiovascular MR images, and knee joints in computerized tomography images. We compare the proposed segmentation technique with the active contour models (ACM), geodesic active contour models, active contours without edges, gradient vector flow snake models, and ACMs based on vector field convolution, by using the skilled doctors' opinions as the ground truths. The results show that our technique performs very well and yields better performance than the classical contour models. The proposed method is robust and applicable on various kinds of noisy images without prior knowledge of noise properties.     

Robust real-time segmentation of images and videos using a smooth-spline snake-based algorithm.

This paper deals with fast image and video segmentation using active contours. Region-based active contours using level sets are powerful techniques for video segmentation, but they suffer from large computational cost. A parametric active contour method based on B-Spline interpolation has been proposed in to highly reduce the computational cost, but this method is sensitive to noise. Here, we choose to relax the rigid interpolation constraint in order to robustify our method in the presence of noise: by using smoothing splines, we trade a tunable amount of interpolation error for a smoother spline curve. We show by experiments on natural sequences that this new flexibility yields segmentation results of higher quality at no additional computational cost. Hence, real-time processing for moving objects segmentation is preserved.     

Curve evolution implementation of the Mumford-Shah functional forimage segmentation, denoising, interpolation, and magnification

We first address the problem of simultaneous image segmentation and smoothing by approaching the Mumford-Shah (1989) paradigm from a curve evolution perspective. In particular, we let a set of deformable contours define the boundaries between regions in an image where we model the data via piecewise smooth functions and employ a gradient flow to evolve these contours. Each gradient step involves solving an optimal estimation problem for the data within each region, connecting curve evolution and the Mumford-Shah functional with the theory of boundary-value stochastic processes. The resulting active contour model offers a tractable implementation of the original Mumford-Shah model (i.e., without resorting to elliptic approximations which have traditionally been favored for greater ease in implementation) to simultaneously segment and smoothly reconstruct the data within a given image in a coupled manner. Various implementations of this algorithm are introduced to increase its speed of convergence. We also outline a hierarchical implementation of this algorithm to handle important image features such as triple points and other multiple junctions. Next, by generalizing the data fidelity term of the original Mumford-Shah functional to incorporate a spatially varying penalty, we extend our method to problems in which data quality varies across the image and to images in which sets of pixel measurements are missing. This more general model leads us to a novel PDE-based approach for simultaneous image magnification, segmentation, and smoothing, thereby extending the traditional applications of the Mumford-Shah functional which only considers simultaneous segmentation and smoothing.     

An integrated region-, boundary-, shape-based active contour for multiple object overlap resolution in histological imagery

Active contours and active shape models (ASM) have been widely employed in image segmentation. A major limitation of active contours, however, is in their 1) inability to resolve boundaries of intersecting objects and to 2) handle occlusion. Multiple overlapping objects are typically segmented out as a single object. On the other hand, ASMs are limited by point correspondence issues since object landmarks need to be identified across multiple objects for initial object alignment. ASMs are also are constrained in that they can usually only segment a single object in an image. In this paper, we present a novel synergistic boundary and region-based active contour model that incorporates shape priors in a level set formulation with automated initialization based on watershed. We demonstrate an application of these synergistic active contour models using multiple level sets to segment nuclear and glandular structures on digitized histopathology images of breast and prostate biopsy specimens. Unlike previous related approaches, our model is able to resolve object overlap and separate occluded boundaries of multiple objects simultaneously. The energy functional of the active contour is comprised of three terms. The first term is the prior shape term, modeled on the object of interest, thereby constraining the deformation achievable by the active contour. The second term, a boundary-based term detects object boundaries from image gradients. The third term drives the shape prior and the contour towards the object boundary based on region statistics. The results of qualitative and quantitative evaluation on 100 prostate and 14 breast cancer histology images for the task of detecting and segmenting nuclei and lymphocytes reveals that the model easily outperforms two state of the art segmentation schemes (geodesic active contour and Rousson shape-based model) and on average is able to resolve up to 91% of overlapping/occluded structures in the images.     

An Active Contour Algorithm for Continuous-Time Cellular Neural Networks

A CNN-based algorithm for image segmentation by active contours is proposed here. The algorithm is based on an iterative process of expansion of the contour and its subsequent thinning guided by external and internal energy. The proposed strategy allows for a high level of control over contour evolution making their topologic transformations easier. Therefore processing of multiple contours for segmenting several objects can be carried out simultaneously.     

Integrating local distribution information with level set for boundary extraction

This paper presents a general object boundary extraction model for piecewise smooth images, which incorporates local intensity distribution information into an edge-based implicit active contour. Unlike traditional edge-based active contours that use gradient to detect edges, our model derives the neighborhood distribution and edge information with two different region-based operators: a Gaussian mixture model (GMM)-based intensity distribution estimator and the Hueckel operator. We propose the local distribution fitting model for more accurate segmentation, which incorporates the operator outcomes into the recent local binary fitting (LBF) model. The GMM and the Hueckel model parameters are estimated before contour evolution, which enables the use of the proposed model without the need for initial contour selection, i.e., the level set function is initialized with a random constant instead of a distance map. Thus our model essentially alleviates the initialization sensitivity problem of most active contours. Experiments on synthetic and real images show the improved performance of our approach over the LBF model.     

Multiple contour extraction from graylevel images using an artificial neural network.

For active contour modeling (ACM), we propose a novel self-organizing map (SOM)-based approach, called the batch-SOM (BSOM), that attempts to integrate the advantages of SOM- and snake-based ACMs in order to extract the desired contours from images. We employ feature points, in the form of an edge-map (as obtained from a standard edge-detection operation), to guide the contour (as in the case of SOM-based ACMs) along with the gradient and intensity variations in a local region to ensure that the contour does not "leak" into the object boundary in case of faulty feature points (weak or broken edges). In contrast with the snake-based ACMs, however, we do not use an explicit energy functional (based on gradient or intensity) for controlling the contour movement. We extend the BSOM to handle extraction of contours of multiple objects, by splitting a single contour into as many subcontours as the objects in the image. The BSOM and its extended version are tested on synthetic binary and gray-level images with both single and multiple objects. We also demonstrate the efficacy of the BSOM on images of objects having both convex and nonconvex boundaries. The results demonstrate the superiority of the BSOM over others. Finally, we analyze the limitations of the BSOM.     

基于C-V模型的红外图像自动分割方法研究

为解决红外图像分割中背景噪声及边界轮廓的影响,引入了基于曲线演化理论、水平集方法和M-S分割函数的C-V模型。通过将图像表达为分段常量函数来建立适当的能量函数模型,引入水平集的表示方法,在整个图像域中依据最小化分割寻找全局极小值,可令活动轮廓最终到达目标边缘。由MATLAB实现的仿真结果表明采用C-V模型对红外图像进行自动分割不受边界轮廓线连续性限制,对初始轮廓线位置不敏感,对图像噪声具有很强的鲁棒性,对均匀灰度目标分割效果良好。     

Robust contour tracking based on a coupling between geodesic active contours and conditional random fields

This paper presents a new general framework for contour tracking based on the synergy of two powerful segmentation tools, namely, spatial temporal conditional random fields (CRFs) and geodesic active contours (GACs). The contours of targets are modeled using a level set representation. The evolution of the level sets toward the target contours is formulated as one of the joint region-based (CRF) and boundary-based (GAC) segmentations under a unified Bayesian framework. A variational inference technique is used to solve this otherwise intractable inference problem, leading to approximate MAP solutions of both the new 3D spatial temporal CRF and the GAC model. The tracking result of the previous frame is used to initialize the curve in the current frame. Typical contour tracking problems are considered and experimental results are given to illustrate the robustness of the method against noise and its accurate performance in moving objects boundary localization.     

彩色图像序列中运动目标外轮廓的自动提取

该文提出了一种新的多运动目标精确外轮廓自动提取算法。算法的主要创新点是：采用指数滤波计算彩色图像的梯度强度,改善了彩色图像梯度局部极值点的定位精度,所得到的梯度强度和运动边缘位置信息供随后的轮廓迭代中使用,成功地避免了动态轮廓的过收缩。此外,充分利用轮廓的方向信息,又有效地克服了动态轮廓迭代中的外扩展。从而,算法自动地提取出一个真正紧贴的目标外轮廓。分析和实验表明,该算法抗干扰能力强,对复杂背景及不重叠物体,可以精确定位并提取出各个运动目标的外轮廓。     

Geometric attraction-driven flow for image segmentation and boundary detection

Novel forces in image segmentation based on active contours models are proposed for capturing objects in the image. Contemplating the common functionality of forces in previous active contours models, we propose the geometric attraction-driven flow (GADF), the binary edge function, and the binary balloon forces to detect objects in difficult cases such as varying illumination and complex shapes. The orientation of GADF is orthogonally aligned with the boundary of object and has the opposite direction across the boundary. It prevents the leakage through weak edges of objects, which occur due to illumination. To reduce the interference from other forces, we design the binary edge function using the property of the orientation in the GADF. We also design the binary balloon force based on the four-color theorem. Combining with initial dual level set functions, the proposed model captures holes in objects and multiple junctions from different colors. The result does not depend on positions of initial contours.     

基于SVM能量模型的改进主动轮廓图像分割算法研究

为克服经典主动轮廓模型曲线内外区域能量定义在复杂目标与背景分布情况下的不足,本文将高效的支持向量机有监督学习分类器引入基于Mumford-shah模型的主动轮廓图像分割算法中,提出了基于SVM能量模型的改进主动轮廓图像分割方法.该方法首先利用支持向量机的分类结果对于封闭曲线的内外区域分别构造了一种新的图像能量表示方法,因为分割过程充分利用了有监督学习策略,使得本文提出的算法具有更高的稳定性和更加广泛的适用范围,特别是对目标灰度分布不均或存在多纹理的目标也可以得到较好的分割结果.分割时,首先利用SVM实现粗分割得到目标初始轮廓,然后利用改进的Mumford-shah主动轮廓模型进行精确分割,采用粗分割策略一方面可以大大提高分割速度,另一方面也可以提高了算法的自动化程度.对比实验结果表明本文提出的算法具有更大灵活性和更好的分割性能.     

Image segmentation and selective smoothing by using Mumford-Shah model.

Recently, Chan and Vese developed an active contour model for image segmentation and smoothing by using piecewise constant and smooth representation of an image. Tsai et al. also independently developed a segmentation and smoothing method similar to the Chan and Vese piecewise smooth approach. These models are active contours based on the Mumford-Shah variational approach and the level-set method. In this paper, we develop a new hierarchical method which has many advantages compared to the Chan and Vese multiphase active contour models. First, unlike previous works, the curve evolution partial differential equations (PDEs) for different level-set functions are decoupled. Each curve evolution PDE is the equation of motion of just one level-set function, and different level-set equations of motion are solved in a hierarchy. This decoupling of the motion equations of the level-set functions speeds up the segmentation process significantly. Second, because of the coupling of the curve evolution equations associated with different level-set functions, the initialization of the level sets in Chan and Vese's method is difficult to handle. In fact, different initial conditions may produce completely different results. The hierarchical method proposed in this paper can avoid the problem due to the choice of initial conditions. Third, in this paper, we use the diffusion equation for denoising. This method, therefore, can deal with very noisy images. In general, our method is fast, flexible, not sensitive to the choice of initial conditions, and produces very good results.     

A robust hybrid active contour model based on pre-fitting bias field correction for fast image segmentation

An array of existing active contour models is prone to suffering from the deficiencies of poor anti-noise ability, initialization sensitivity, and slow convergence. In order to handle these problems, a robust hybrid active contour method based on bias correction is proposed in this research paper The energy functional is formulated through incorporating the adaptive edge indicator function and level set formulation driven by bias field correction. The adaptive edge indicator function, which is formulated based on image gradient information, is utilized to detect object boundaries and accelerate the segmentation in the homogeneous region. The level set formulation is constructed based on an improved criterion function, in which bias field information is considered. Specifically, the bias field distribution is approximated through the local mean gray value algorithm as a prior. Moreover, a new regularized function is proposed so as to maintain the stability of curve evolution. The segmentation process is implemented by the optimized energy function and the novel regularized term. Compared to previous active contour models, the modified active contour method can yield more precise, stable, and efficient segmentation results on some challenging images.     

Global regularizing flows with topology preservation for active contours and polygons.

Active contour and active polygon models have been used widely for image segmentation. In some applications, the topology of the object(s) to be detected from an image is known a priori, despite a complex unknown geometry, and it is important that the active contour or polygon maintain the desired topology. In this work, we construct a novel geometric flow that can be added to image-based evolutions of active contours and polygons in order to preserve the topology of the initial contour or polygon. We emphasize that, unlike other methods for topology preservation, the proposed geometric flow continually adjusts the geometry of the original evolution in a gradual and graceful manner so as to prevent a topology change long before the curve or polygon becomes close to topology change. The flow also serves as a global regularity term for the evolving contour, and has smoothness properties similar to curvature flow. These properties of gradually adjusting the original flow and global regularization prevent geometrical inaccuracies common with simple discrete topology preservation schemes. The proposed topology preserving geometric flow is the gradient flow arising from an energy that is based on electrostatic principles. The evolution of a single point on the contour depends on all other points of the contour, which is different from traditional curve evolutions in the computer vision literature.     

基于自适应扩散梯度矢量流的图像分割算法

为了提高活动轮廓分割图像的精度,解决传统活 动轮廓不能够收敛到深凹陷和弱边界对象分割效果不佳等问 题,提出了自适应扩散梯度矢量流(AD-GGVF)算法。首先,在外部力场中,使用基于分量的 归一化方法代替传统的基于矢量的归一化方 法,提高活动轮廓曲线进入深凹陷的能力;然后,将拉普拉斯算子分解为切向和法向分量, 并增加两个互相关的自适应权重 函数,使轮廓曲线能够根据图像的局部特征自适应调节扩散过程;最后,以分割结果的量化 误差为评价标准,和传统的活动 轮廓分割效果进行对比和分析。实验结果表明,本文算法针对两幅不同的弱 边界图像,量化误差分别降低到0.08和0.09,活动轮廓曲线能够收敛到深凹陷的底部;分割 效果较为准确。     

Watershed segmentation based on gradient relief modification using variant structuring element

Watershed segmentation is suitable for producing closed region contour and providing an accurate localization of object boundary. However, it is usually prone to over-segmentation due to the noise and irregular details within the image. For the purpose of reducing over-segmentation while preserving the location of object contours, the watershed segmentation based on morphological gradient relief modification using variant structuring element （SE） is proposed. Firstly, morphological gradient relief is decomposed into multi-level according to the gradient values. Secondly, morphological closing action using variant SE is employed to each level image, where the low gradient level sets use the large SE, while the high gradient level sets use the small one. Finally, the modified gradient image is recomposed by the superposition of the closed level sets, and watershed transform to the modified gradient image is done to implement the final segmentation. Experimental results show that this method can effectively reduce the over-segmentation and preserve the location of the obiect contours.     

应用分层MRF/GRF模型的立体图像视差估计及分割

视差估计与分割是立体图像编码及立体视觉匹配的核心问题,本文提出一种基于分层MRF/GRF模型和交叠块匹配(HMOM)视差估计算法以及结合主动轮廓模型的视差分割提取算法.该混合视差估计方法,可得到光滑准确,且具有清晰边缘的视差场;并便于用主动轮廓模型提取感兴趣对象(OOI)的视差轮廓.与通常的变尺寸块匹配(VSBM)相比,本算法得到的视差补偿图像的峰值信噪比可提高2.5dB左右.本文得到的视差场及对应的轮廓可进一步用于立体图像编码以及视频对象分割.