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.     

基于水平集接力的图像自动分割方法

为了实现图像的完全分割,基于无须重新初始化的水平集方法提出了一种接力水平集方法.该方法在待分割图像中自动交替地创建嵌套子区域和相应的初始水平集函数,使水平集函数在其中演化并收敛,然后重复这个过程直到子区域面积为0.与原始算法及经典的基于区域的水平集方法相比,该方法具有如下优点:1) 自动完成,无须交互式的初始化;2) 多次分割图像,能够比原始算法检测到更多的边缘;3) 对于非匀质的图像,能够取得比经典的基于区域的水平集方法更好的分割效果;4) 提供一个开放的分割算法框架,其他单水平集方法稍作修改后也可替换这里所使用的单水平集方法.实验结果表明,此算法对人造图像和医学影像实现了无须交互的完全分割,对非匀质图像分割表现出更好的鲁棒性.     

Fast level set image and video segmentation using new evolution indicator operators

We propose an effective level set evolution method for robust object segmentation in real images. We construct an effective region indicator and an multiscale edge indicator, and use these two indicators to adaptively guide the evolution of the level set function. The multiscale edge indicator is defined in the gradient domain of the multiscale feature-preserving filtered image. The region indicator is built on the similarity map between image pixels and user specified interest regions, where the similarity map is computed using Gaussian Mixture Models (GMM). Then we combine these two methods to develop a new mixing edge stop function, which makes the level set method more robust to initial active contour setting, and forces the level set to evolve adaptively based on the image content. Furthermore, we apply an acceleration approach to speed up our evolution process, which yields real time segmentation performance. Finally, we extend the proposed approach to video segmentation for achieving effective target tracking results. As the results show, our approach is effective for image and video segmentation and works well to accurately detect the complex object boundaries in real-time.     

一种基于水平集的图像快速多区域分割方法

提出了一种新的基于水平集的图像快速多区域分割方法。首先,在经典水平集分割算法的基础上,通过使用新的水平集初始化函数,有效地改善了水平集分割算法的时间性能;其次,通过引入区域分割控制条件控制水平集函数的收敛过程,实现多区域分割。实验结果表明,提出的多区域分割方法具有较好的分割性能,并且时间耗费少。     

基于T-prim模型的肺气管分割算法

针对现有高阶支气管分割算法计算成本过大或分割精度不足等问题,提出一种基于T-prim模型的肺气管树分割算法。通过形态学灰度重建对CT图像进行初步处理,使用区域生长算法得到主支气管;从马尔可夫随机场的角度对分水岭算法分割框架进行优化,得到优化的分割框架;利用主气管骨架提取自动获得种子节点,算法迭代构造出T-prim模型,利用优化的分割框架得到完整的肺气管树。通过与两种EXACT09竞赛算法的对比实验证明了该算法在不依赖于种子点的人工选择,不需要训练集的条件下,能以极低的泄漏量获得更完整的分割结果。     

A Multiphase Dynamic Labeling Model for Variational Recognition-driven Image Segmentation

We propose a variational framework for the integration of multiple competing shape priors into level set based segmentation schemes. By optimizing an appropriate cost functional with respect to both a level set function and a (vector-valued) labeling function, we jointly generate a segmentation (by the level set function) and a recognition-driven partition of the image domain (by the labeling function) which indicates where to enforce certain shape priors. Our framework fundamentally extends previous work on shape priors in level set segmentation by directly addressing the central question of where to apply which prior. It allows for the seamless integration of numerous shape priors such that—while segmenting both multiple known and unknown objects—the level set process may selectively use specific shape knowledge for simultaneously enhancing segmentation and recognizing shape.     

Multiphase Soft Segmentation with Total Variation and <Emphasis Type="Italic">H</Emphasis><Superscript>1</Superscript> Regularization

In this paper, we propose a variational soft segmentation framework inspired by the level set formulation of multiphase Chan-Vese model. We use soft membership functions valued in [0,1] to replace the Heaviside functions of level sets (or characteristic functions) such that we get a representation of regions by soft membership functions which automatically satisfies the sum to one constraint. We give general formulas for arbitrary N-phase segmentation, in contrast to Chan-Vese’s level set method only 2 ^m -phase are studied. To ensure smoothness on membership functions, both total variation (TV) regularization and H ¹ regularization used as two choices for the definition of regularization term. TV regularization has geometric meaning which requires that the segmentation curve length as short as possible, while H ¹ regularization has no explicit geometric meaning but is easier to implement with less parameters and has higher tolerance to noise. Fast numerical schemes are designed for both of the regularization methods. By changing the distance function, the proposed segmentation framework can be easily extended to the segmentation of other types of images. Numerical results on cartoon images, piecewise smooth images and texture images demonstrate that our methods are effective in multiphase image segmentation.     

A Multiphase Level Set Framework for Image Segmentation Using the Mumford and Shah Model

We propose a new multiphase level set framework for image segmentation using the Mumford and Shah model, for piecewise constant and piecewise smooth optimal approximations. The proposed method is also a generalization of an active contour model without edges based 2-phase segmentation, developed by the authors earlier in T. Chan and L. Vese (1999. In Scale-Space'99, M. Nilsen et al. (Eds.), LNCS, vol. 1682, pp. 141–151) and T. Chan and L. Vese (2001. IEEE-IP, 10(2):266–277). The multiphase level set formulation is new and of interest on its own: by construction, it automatically avoids the problems of vacuum and overlap; it needs only log n level set functions for n phases in the piecewise constant case; it can represent boundaries with complex topologies, including triple junctions; in the piecewise smooth case, only two level set functions formally suffice to represent any partition, based on The Four-Color Theorem. Finally, we validate the proposed models by numerical results for signal and image denoising and segmentation, implemented using the Osher and Sethian level set method.     

基于Generalized Region Loss的代价函数及在图像分割中的应用

针对图像分割中的困难样本,提出了一种对像素区域细分计算的Generalized Region Loss的新的代价函数;首先通过引入一项参数,改变了以往代价函数主要通过设置权重或Focal等关注困难样本的方法,其次通过对标签图像和预测图像进行区域划分,并且对划分四区域的困难样本分类关注,最后分别计算其四区域绝对损失,进而进行加权组合;为验证算法性能,使用CamVid数据集作为实验数据,该代价函数在FCN和U-Net两种图像分割网络上得到验证,同当前图像分割领域常用的12种代价函相比,IoU指标分别提高1.93%和2.99%,由此证明此代价函数优于大多数图像分割代价函数;最终实验结果表明,提出的基于像素区域细分计算的代价函数能够有效提高图像分割精度,为图像分割的研究提供借鉴。     

Kernel Density Estimation and Intrinsic Alignment for Shape Priors in Level Set Segmentation

In this paper, we make two contributions to the field of level set based image segmentation. Firstly, we propose shape dissimilarity measures on the space of level set functions which are analytically invariant under the action of certain transformation groups. The invariance is obtained by an intrinsic registration of the evolving level set function. In contrast to existing approaches to invariance in the level set framework, this closed-form solution removes the need to iteratively optimize explicit pose parameters. The resulting shape gradient is more accurate in that it takes into account the effect of boundary variation on the object’s pose. Secondly, based on these invariant shape dissimilarity measures, we propose a statistical shape prior which allows to accurately encode multiple fairly distinct training shapes. This prior constitutes an extension of kernel density estimators to the level set domain. In contrast to the commonly employed Gaussian distribution, such nonparametric density estimators are suited to model aribtrary distributions. We demonstrate the advantages of this multi-modal shape prior applied to the segmentation and tracking of a partially occluded walking person in a video sequence, and on the segmentation of the left ventricle in cardiac ultrasound images. We give quantitative results on segmentation accuracy and on the dependency of segmentation results on the number of training shapes. Electronic supplementary material Electronic supplementary material is available for this article at and accessible for authorised users.     

A novel multi-scale level set method for SAR image segmentation based on a statistical model

To overcome the problems of large data volumes and strong speckle noise in synthetic aperture radar (SAR) images, a multi-scale level set approach for SAR image segmentation is proposed in this article. Because the multi-scale analysis of SAR images preserves their highest resolution features while additionally making use of sets of images at lower resolutions to improve specific functions, the proposed method is useful for removing the influence of speckle and, at the same time, preserving important structural information. The Gamma distribution is one of the most commonly used models employed to represent the statistical characteristics of speckle noise in a SAR image and it is introduced to define the energy functional. Moreover, based on the multi-scale level set framework, an improved multi-layer approach is introduced for multi-region segmentation. To obtain a fast and more accurate result, a novel threshold segmentation result is used to represent the initial segmentation curve. The experiments with synthetic and real SAR images demonstrate the effectiveness of the new method.     

高分辨率极化SAR图像水平集分割

目的 传统的极化SAR图像分割方法中,由于采用的统计分布模型不能较好地描述高分辨率的图像纹理特征,导致高分辨率极化SAR图像分割效果较差。针对这个问题,本文将具有广泛适用性的KummerU分布嵌入到水平集极化SAR图像分割方法中,提出了一种新的极化SAR图像分割算法。方法 将KummerU分布作为高分辨率极化SAR图像的统计模型,定义一种适用于极化SAR图像分割的能量泛函;利用最大似然法对各个区域的KummerU分布进行参数估计,并通过数值偏微分方程的方法求解水平集函数,实现极化SAR图像的区域分割。结果 分别对仿真全极化数据,真实全极化数据进行分割实验,结果表明本文提出的方法其分割精度高于传统方法,分割精度高于95%,从而验证了新方法的有效性。结论 本文算法能够对各向同质区和各向异质区的极化SAR图像都能取得良好的分割效果,并适应于多种场景,有效地分割出背景和目标。     

A novel active contour model for image segmentation using local and global region-based information

In this paper, we propose a novel level set geodesic model for image segmentation. In our model, we define a hybrid signed pressure force (SPF) function integrating local and global region-based information to segment inhomogeneous images. The local region-based SPF utilizes mean values on local circular regions centered in each pixel. By introducing the local image information, the images with intensity inhomogeneity can be effectively segmented. In order to reduce the dependency on complex initialization, we incorporate a global region-based SPF into this model to develop a hybrid SPF. The global SPF and the local SPF are adaptively balanced by an adaptive weight. In addition, we also extend this model to four-phase level set formulation for brain MR image segmentation. Finally, a truncated Gaussian kernel is used to regularize the level set function, which not only regularizes it but also removes the need for computationally expensive re-initialization. Experimental results indicate that the proposed method achieves superior segmentation performance in terms of accuracy and robustness.     

Semi-automatic computer aided lesion detection in dental X-rays using variational level set

A semi-automatic lesion detection framework is proposed to detect areas of lesions from periapical dental X-rays using level set method. In this framework, first, a new proposed competitive coupled level set method is used to segment the image into three pathologically meaningful regions using two coupled level set functions. Tailored for the dental clinical setting, a two-stage clinical segmentation acceleration scheme is used. The method uses a trained support vector machine (SVM) classifier to provide an initial contour for two coupled level sets. Then, based on the segmentation results, an analysis scheme is applied. Firstly, the scheme builds an uncertainty map from which those areas with radiolucent will be automatically emphasized by a proposed color emphasis scheme. Those radiolucent in the teeth or jaw usually suggested possible lesions. Secondly, the scheme employs a method based on the average intensity profile to isolate the teeth and locate two types of lesions: periapical lesion (PL) and bifurcation lesion (BL). Experimental results show that our proposed segmentation method is able to segment the image into pathological meaningful regions for further analysis; our proposed framework is able to automatically provide direct visual cues for the lesion detection; and when given the orientation of the teeth, it is able to automatically locate the PL and BL with a seriousness level marked for further dental diagnosis. When used in the clinical setting, the framework enables dentist to improve interpretation and to focus their attention on critical areas.     

图像局部交互熵分割模型的两步快速优化

目的 针对LCK（local correntropy-based K-means）模型收敛速度慢,提出新的基于LCK模型的两步快速分割模型。方法 两步快速分割模型包括粗分割和细分割。1）粗分割：先将待分割的原始图像下采样,减少数据量;然后使用LCK模型对采样后的粗尺度图像进行分割,得到粗分割结果及其相应的粗水平集函数。由于数据量的减少,粗分割步骤可以快速得到近似分割结果。2）细分割：在水平集函数光滑性约束下,将粗分割结果及其对应的粗水平集函数上采样到原始图像的尺度,然后将上采样后的粗水平集函数作为细分割的初始值,利用LCK模型对原始图像进行精细分割。因初始值与真实目标边界很接近,所以只需很少迭代次数就能得到最终分割结果。结果 采用F-score评价方法分析自然以及合成图像的分割结果,并与LCK模型作比较,新的模型F-score数值最大,且迭代次数不大于50。结论 粗分割步骤能在小数据量的情况下,快速分割出粗略的目标;细分割步骤在较好的初始值条件下,能够快速收敛到最终的分割结果,从而有效提高了模型的计算效率和精确性。本文算法主要适用于分割含有未知噪声及灰度非同质的医学图像,且分割效率高。     

Nonlinear Dynamical Shape Priors for Level Set Segmentation

The introduction of statistical shape knowledge into level set based segmentation methods was shown to improve the segmentation of familiar structures in the presence of noise, clutter or partial occlusions. While most work has been focused on shape priors which are constant in time, it is clear that when tracking deformable shapes certain silhouettes may become more or less likely over time. In fact, the deformations of familiar objects such as the silhouettes of a walking person are often characterized by pronounced temporal correlations. In this paper, we propose a nonlinear dynamical shape prior for level set based image segmentation. Specifically, we propose to approximate the temporal evolution of the eigenmodes of the level set function by means of a mixture of autoregressive models. We detail how such shape priors “with memory” can be integrated into a variational framework for level set segmentation. As an application, we experimentally validate that the nonlinear dynamical prior drastically improves the tracking of a person walking in different directions, despite large amounts of clutter and noise.     

Adaptive active contour model driven by image data field for image segmentation with flexible initialization

In this paper, a novel adaptive active contour model based on image data field for image segmentation with robust and flexible initializations is proposed. We firstly construct a new external energy term deduced from the image data field that drives the level set function to move in the opposite direction along the boundaries of object and an adaptive length regularization term based on the image local entropy. The designed external energy and length regularization term are then incorporated into a variationlevel set framework with an additional penalizing energy term. Due to the adaptive sign–changing property of the external energy and the adaptive length regularization term, the proposed model can tackle images with clutter background and noise, the level set function can be initialized as any bounded functions (e.g., constant function), which implies the proposed model is robust to initialization of contours. Experimental results on both synthetic and real images from different modalities confirm the effectiveness and competivive performance of the proposed method compared with other representative models.

     

基于多层水平集函数的三维多相图像分割

多相图像分割通常利用多个水平集函数分别定义不同区域的特征函数,其极值求解问题需要对多个函数分别求极值,计算效率较低。针对三维多相图像,提出一种改进的变分水平集模型,采用一个多层水平集函数的n层水平集隐式曲面,将图像划分为n个区域,通过对一个水平集函数求极值,实现三维多相分段常值图像的快速分割与重建。将能量泛函表达为数据项和规则项,借助规则化Heaviside函数设计区域划分的通用特征函数,采用Split-Bregman投影方法进行能量最小化求解。实验结果表明,该模型可以有效地实现三维多相图像分割,与Chan-Vese模型相比,其迭代步数较少,分割速度较快。     

Use of Spectral Clustering Combined with Normalized Cuts (N-Cuts) in an Iterative k-Means Clustering Framework (NKSC) for Superpixel Segmentation with Contour Adherence

Superpixel segmentation methods are generally used as a pre-processing step to speed up image processing tasks. They group the pixels of an image into homogeneous regions while trying to respect existing contours. In this paper, we propose a fast Superpixels segmentation algorithm with Contour Adherence using spectral clustering, combined with normalized cuts in an iterative k-means clustering framework. It produces compact and uniform superpixels with low computational costs. Normalized cut is adapted to measure the color similarity and space proximity between image pixels. We have used a kernel function to estimate the similarity metric. Kernel function maps the pixel values and coordinates into a high dimensional feature space. The objective functions of weighted K-means and normalized cuts share the same optimum point in this feature space. So it is possible to optimize the cost function of normalized cuts by iteratively applying simple K-means clustering algorithm. The proposed framework produces regular and compact superpixels that adhere to the image contours. On segmentation comparison benchmarks it proves to be equally well or better than the state-of-the-art super pixel segmentation algorithms in terms of several commonly used evaluation metrics in image segmentation. In addition, our method is computationally very efficient and its computational complexity is linear.     

Mumford-Shah on the Move: Region-Based Segmentation on Deforming Manifolds with Application to 3-D Reconstruction of Shape and Appearance from Multi-View Images

We address the problem of estimating the shape and appearance of a scene made of smooth Lambertian surfaces with piecewise smooth albedo. We allow the scene to have self-occlusions and multiple connected components. This class of surfaces is often used as an approximation of scenes populated by man-made objects. We assume we are given a number of images taken from different vantage points. Mathematically this problem can be posed as an extension of Mumford and Shah’s approach to static image segmentation to the segmentation of a function defined on a deforming surface. We propose an iterative procedure to minimize a global cost functional that combines geometric priors on both the shape of the scene and the boundary between smooth albedo regions. We carry out the numerical implementation in the level set framework.