Incorporating shape prior into geodesic active contours for detecting partially occluded object

A new method to incorporate shape prior knowledge into geodesic active contours for detecting partially occluded object is proposed in this paper. The level set functions of the collected shapes are used as training data. They are projected onto a low dimensional subspace using PCA and their distribution is approximated by a Gaussian function. A shape prior model is constructed and is incorporated into the geodesic active contour formulation to constrain the contour evolution process. To balance the strength between the image gradient force and the shape prior force, a weighting factor is introduced to adaptively guide the evolving curve to move under both forces. The curve converges with due consideration of both local shape variations and global shape consistency. Experimental results demonstrate that the proposed method makes object detection robust against partial occlusions.     

结合先验形状和Mumford-Shah模型的活动轮廓分割

基于先验形状和Mumford-Shah模型的活动轮廓分割是一种抗噪声干扰、稳定的图像分割方法。该模型采用水平集方法,并结合活动轮廓模型、先验形状和Mumford-Shah模型来控制曲线演化。特定目标的先验知识可以有效地指导目标准确分割,经过主成分分析（PCA）法可以得到感兴趣对象形状的主要信息。通过对不同图片分割实验表明,针对特定的形状,该方法对杂乱背景、部分遮挡、缺失和强噪声的图片依然能得到满意的结果。     

Image segmentation with one shape prior — A template-based formulation

Image segmentation with one shape prior is an important problem in computer vision. Most algorithms not only share a similar energy definition, but also follow a similar optimization strategy. Therefore, they all suffer from the same drawbacks in practice such as slow convergence and difficult-to-tune parameters. In this paper, by reformulating the energy cost function, we establish an important connection between shape-prior based image segmentation with intensity-based image registration. This connection enables us to combine advanced shape and intensity modeling techniques from segmentation society with efficient optimization techniques from registration society. Compared with the traditional regularization-based approach, our framework is more systematic and more efficient, able to converge in a matter of seconds. We also show that user interaction (such as strokes and bounding boxes) can easily be incorporated into our algorithm if desired. Through challenging image segmentation experiments, we demonstrate the improved performance of our algorithm compared to other proposed approaches.     

基于先验形状的混杂活动轮廓模型及其在图像分割中的应用

提出了一种新颖的基于先验形状学习的混杂活动轮廓(SHAC)模型,该模型采用变分水平集方法,融合自适应区域信息与边界信息,运用主成分分析的方法从给定的含有目标物体轮廓的训练集学习得到最佳形状信息,并将其作为先验形状。将自适应区域特征和轮廓特征作为局部信息,先验形状作为全局信息,在迭代过程中结合全局和局部信息实现对演化曲线的形变进行指导和约束,达到分割目标物体的目的。通过定量和定性地分析低对比度的乳腺核磁共振图像中的乳腺轮廓的分割,以及具有复杂背景的自然图像中感兴趣区域的分割结果,验证了SHAC模型比传统活动轮廓模型具有更高的准确率,表明了该模型不仅提高了图像分割中对弱边界的识别度,减弱了非目标轮廓的干扰,而且具有良好的抗噪能力。     

Multiphase segmentation using an implicit dual shape prior: Application to detection of left ventricle in cardiac MRI

Cardiac magnetic resonance imaging (MRI) has been extensively used in the diagnosis of cardiovascular disease and its quantitative evaluation. Cardiac MRI techniques have been progressively improved, providing high-resolution anatomical and functional information. One of the key steps in the assessment of cardiovascular disease is the quantitative analysis of the left ventricle (LV) contractile function. Thus, the accurate delineation of LV boundary is of great interest to improve diagnostic performance. In this work, we present a novel segmentation algorithm of LV from cardiac MRI incorporating an implicit shape prior without any training phase using level sets in a variational framework. The segmentation of LV still remains a challenging problem due to its subtle boundary, occlusion, and inhomogeneity. In order to overcome such difficulties, a shape prior knowledge on the anatomical constraint of LV is integrated into a region-based segmentation framework. The shape prior is introduced based on the anatomical shape similarity between endocardium and epicardium. The shape of endocardium is assumed to be mutually similar under scaling to the shape of epicardium. An implicit shape representation using signed distance function is introduced and their discrepancy is measured in a probabilistic way. Our shape constraint is imposed by a mutual similarity of shapes without any training phase that requires a collection of shapes to learn their statistical properties. The performance of the proposed method has been demonstrated on fifteen clinical datasets, showing its potential as the basis in the clinical diagnosis of cardiovascular disease.     

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.     

Individual tooth segmentation from CT images using level set method with shape and intensity prior

3D visualization of teeth from CT images provides important assistance for dentists performing orthodontic surgery and treatment. However, dental CT images present several major challenges for the segmentation of tooth, which touches with adjacent teeth as well as surrounding periodontium and jaw bones. Moreover, tooth contour suffers from topological changes and splits into several branches. In this work, we focus on the segmentation of individual teeth with complete crown and root parts. To this end, we propose adaptive active contour tracking algorithms: single level set method tracking for root segmentation to handle the complex image conditions as well as the root branching problem, and coupled level set method tracking for crown segmentation in order to separate the touching teeth and create the virtual common boundaries between them. Furthermore, we improve the variational level set method in several aspects: gradient direction is introduced into the level set framework to prevent catching the surrounding object boundaries; in addition to the shape prior, intensity prior is introduced to provide adaptive shrinking or expanding forces in order to deal with the topological changes. The test results for both tooth segmentation and 3D reconstruction show that the proposed method can visualize individual teeth with high accuracy and efficiency.     

A novel active contour model for image segmentation using distance regularization term

In this paper, a novel active contour model (R-DRLSE model) based on level set method is proposed for image segmentation. The R-DRLSE model is a variational level set approach that utilizes the region information to find image contours by minimizing the presented energy functional. To avoid the time-consuming re-initialization step, the distance regularization term is used to penalize the deviation of the level set function from a signed distance function. The numerical implementation scheme of the model can significantly reduce the iteration number and computation time. The results of experiments performed on some synthetic and real images show that the R-DRLSE model is effective and efficient. In particular, our method has been applied to MR kidney image segmentation with desirable results.     

Adaptive shape prior for recognition and variational segmentation of degraded historical characters

We propose a variational method for model based segmentation of gray-scale images of highly degraded historical documents. Given a training set of characters (of a certain letter), we construct a small set of shape models that cover most of the training set's shape variance. For each gray-scale image of a respective degraded character, we construct a custom made shape prior using those fragments of the shape models that best fit the character's boundary. Therefore, we are not limited to any particular shape in the shape model set. In addition, we demonstrate the application of our shape prior to degraded character recognition. Experiments show that our method achieves very accurate results both in segmentation of highly degraded characters and both in recognition. When compared with manual segmentation, the average distance between the boundaries of respective segmented characters was 0.8 pixels (the average size of the characters was 70*70 pixels).     

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。     

先验模型约束的抗干扰轮廓跟踪

目的 基于水平集的轮廓提取方法被广泛用于运动物体的轮廓跟踪。针对传统方法易受局部遮挡、复杂背景等因素影响的问题,提出一种先验模型约束的抗干扰（AC-PMC）轮廓跟踪算法。方法 首先,选取图像序列的前5帧进行跟踪训练,将每帧图像基于颜色特征分割成若干超像素块,利用均值聚类组建簇集合,并通过该集合建立目标的先验模型。然后,利用水平集分割方法提取目标轮廓,并提出决策判定算法,判断是否需要引入形状先验模型加以约束,避免遮挡、复杂背景等影响。最后,提出一种在线模型更新算法,在特征集中加入适当特征补偿,使得更新的目标模型更为准确。结果 本文算法与多种优秀的轮廓跟踪算法相比,可以达到相同甚至更高的跟踪精度,在Fish、Face1、Face2、Shop、Train以及Lemming视频图像序列下的平均中心误差分别为3.46、7.16、3.82、13.42、14.72、12.47,算法的跟踪重叠率分别为0.92、0.74、0.85、0.77、0.73、0.82,算法的平均运行速度分别为4.27 帧/s、4.03 帧/s、3.11 帧/s、2.94 帧/s、2.16 帧/s、1.71 帧/s。结论 利用目标的先验模型约束以及提取轮廓过程中的决策判定,使本文算法在局部遮挡、目标形变、目标旋转、复杂背景等条件下具有跟踪准确、适应性强的特点。     

A robust active contour model driven by fuzzy c-means energy for fast image segmentation

In this paper, we propose a robust region-based active contour model driven by fuzzy c-means energy that draws upon the clustering intensity information for fast image segmentation. The main idea of fuzzy c-means energy is to quickly compute the two types of cluster center functions for all points in image domain by fuzzy c-means algorithm locally with a proper preprocessing procedure before the curve starts to evolve. The time-consuming local fitting functions in traditional models are substituted with these two functions. Furthermore, a sign function and a Gaussian filtering function are utilized to replace the penalty term and the length term in most models, respectively. Experiments on several synthetic and real images have proved that the proposed model can segment images with intensity inhomogeneity efficiently and precisely. Moreover, the proposed model has a good robustness on initial contour, parameters and different kinds of noise.     

形状约束下活动轮廓模型冠脉血管图像多尺度分割

目的 由于计算机断层血管造影(CTA)图像的复杂性,临床诊断冠脉疾病往往需要经验丰富的医师对冠状动脉进行手动分割,快速、准确自动分割出冠状动脉对提高冠脉疾病诊断效率具有重要意义。针对双源CT图像特点以及传统单一基于区域或边界的活动轮廓模型的不足,研究了心脏冠脉3维分割算法,提出一种基于血管形状约束的活动轮廓模型分割方法。方法 首先,利用改进的FCM(fuzzy C-means)对心脏CT图像感兴趣区域初分割,其结果用于初始化C-V模型水平集演化曲线及控制参数,提取感兴趣区域轮廓。接着,由3维心脏图像数据获取多尺度梯度矢量信息构造边界型能量泛函,然后利用基于Hessian矩阵的多尺度血管函数对心脏感兴趣区域3维体数据增强滤波,获取血管先验形状信息用于约束能量泛函。最后融合边界、区域能量泛函并利用变分原理及水平集方法得到适合冠脉血管分割的水平集演化方程。结果 由于血管图像的灰度不均匀,血管末端区域更为细小,所以上述算法的实施是面向被划分多个子区域的血管,在缩小的范围内进行轮廓的演化。相比于传统的血管分割方法,该方法充分融合血管图像的先验信息及梯度场信息,能够从灰度及造影剂分布不均匀的冠脉血管图像中准确分割出冠状动脉,对于细小的血管结构亦能获得较好的分割效果。实验结果表明,该方法只需在给定初始轮廓前提下,有效提取3维冠脉血管。结论 对多组心脏CT图像进行分割,本文基于血管先验形状约束的活动轮廓模型可以准确分割出冠脉结构完整轮廓,并且人工交互简单。该方法在双源CT冠脉图像自动分割方面具有较好的正确率与优越性。     

ORACM: Online region-based active contour model

A new online region-based active contour model (ORACM) is proposed in this paper. The classical geodesic active contour (GAC) model has only local segmentation property, although the Chan–Vese (C–V) model possesses global. An up-to-date active contour model (ACM with SBGFRLS) proposed in Zhang, Zhang, Song, and Zhou (2010) both has the properties of global/local segmentation and incorporates the GAC and the C–V models to raise active contours’ performance on image segmentation. However it has two major disadvantages. First, it deforms the active contour model just using the gradient of current level set iteratively and so works too slowly. Second, it needs a parameter α which plays major impact on the results and to be tuned according to input images. The proposed model ORACM eliminates these two disadvantages by using a new binary level set formula and a new regularization operation such as morphological opening and closing. Without changing segmentation accuracy, ORACM requires no parameter and less time over the traditional ACMs. Experiments on synthetic and real images demonstrate that the computational cost of ORACM with the morphological operations is 3.75 times less than the traditional ACMs on average.     

Geometric active contours without re-initialization for image segmentation

A geometric active contour model without re-initialization that can be used for grey and color image segmentation is presented in this paper. It combines directional information about edge location based on Cumani operator as a part of driving force, with the improved geodesic active contours containing Bays error based statistical region information. Moreover, an extra term that penalizes the deviation of the level set function from a signed distance function is also included in the model, thus the costly re-initialization procedure can be completely eliminated and all these measures are integrated in a unified frame. Experimental results on real grey and color images have shown that our model can precisely extract contours of images and its performance is much better and faster than the geodesic-aided C-V (GACV) model.     

基于改进活动轮廓模型和视觉特性的图像分割方法

提出一种基于改进活动轮廓模型和视觉显著性分析的图像分割方法。与传统的水平集模型不同,改进的活动轮廓模型不需要进行初始化和计算符号距离函数,从而有效地提高曲线演化效率。在此基础上,提出了基于标记的多相水平集分割方法,有效地解决了复杂图像存在的灰度不均性问题。另外,为避免初始轮廓位置对分割结果的影响,采用视觉显著图获取水平集初始轮廓位置,通过对该显著图进行OSTU分割提取初始轮廓。通过实验分析,提出的方法在分割结果、速度和复杂度上较之传统的CV模型都有明显的改进。     

一种全局LBF主动轮廓模型

LBF模型的能量函数对于水平集函数是非凸的,从而导致应用LBF模型分割的最终结果对水平集函数的初始化非常敏感。通过凸化LBF模型的能量函数,提出一种全局的LBF模型(GLBF)。该模型针对水平集函数是凸的,从而可以通过任意初始化水平集函数得到全局最优解。此外,该模型不必重新初始化水平集函数为符号距离函数,从而极大地提高运算效率。对灰度不均匀医学图像的分割结果表明,GLBF模型对水平集函数的初始化不敏感,优于传统的LBF模型以及目前具有代表性的LIF模型。     

A moving object segmentation algorithm for static camera via active contours and GMM

Moving object segmentation is one of the most challenging issues in computer vision. In this paper, we propose a new algorithm for static camera foreground segmentation. It combines Gaussian mixture model (GMM) and active contours method, and produces much better results than conventional background subtraction methods. It formulates foreground segmentation as an energy minimization problem and minimizes the energy function using curve evolution method. Our algorithm integrates the GMM background model, shadow elimination term and curve evolution edge stopping term into energy function. It achieves more accurate segmentation than existing methods of the same type. Promising results on real images demonstrate the potential of the presented method. Supported by National Basic Research Program of China (Grant No. 2006CB303105), the Chinese Ministry of Education Innovation Team Fund Project (Grant No. IRT0707), the National Natural Science Foundation of China (Grant Nos. 60673109 and 60801053), Beijing Excellent Doctoral Thesis Program (Grant No. YB20081000401), Beijing Municipal Natural Science Foundation (Grant No. 4082025), and Doctoral Foundation of China (Grant No. 20070004037)     

一种区域自适应主动轮廓模型的图像分割方法

为了有效地分割灰度不均匀图像,提出了一种区域自适应主动轮廓模型,在该模型中,定义了一个包含全局能量项和局部能量项的能量泛函。在算法的初期,全局能量项占主导地位,它具有收敛速度快、对初始轮廓不敏感的优点。在算法的后期,局部能量项占主导地位,它具有定位精度高的优点。理论分析和实验结果表明,该模型具有收敛速度快、分割精度高、对初始轮廓不敏感等优点。     

基于多尺度统计形状模型的Levelset分割方法

提出并建立了一种基于小波分析的多尺度统计模型,将该统计模型作为先验知识引入Mumford-Shah能量约束函数,从而指导水平集函数进行图像分割。实验表明,当对拓扑结构复杂的医学图像进行分割时,该方法具有明显的效果,同时分割速度和精度都得到了明显改善。