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.     

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.     

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.     

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.     

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).     

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。     

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。     

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)     

Adaptive diffusion flow active contours for image segmentation

Gradient vector flow (GVF) active contour model shows good performance at concavity convergence and initialization insensitivity, yet it is susceptible to weak edges as well as deep and narrow concavity. This paper proposes a novel external force, called adaptive diffusion flow (ADF), with adaptive diffusion strategies according to the characteristics of an image region in the parametric active contour model framework for image segmentation. We exploit a harmonic hypersurface minimal functional to substitute smoothness energy term in GVF for alleviating the possible leakage. We make use of the p(x) harmonic maps, in which p(x) ranges from 1 to 2, such that the diffusion process of the flow field can be adjusted adaptively according to image characteristics. We also incorporate an infinity laplacian functional to ADF active contour model to drive the active contours onto deep and narrow concave regions of objects. The experimental results demonstrate that ADF active contour model possesses several good properties, including noise robustness, weak edge preserving and concavity convergence.     

Probability density difference-based active contour for ultrasound image segmentation

Because of its low signal/noise ratio, low contrast and blurry boundaries, ultrasound (US) image segmentation is a difficult task. In this paper, a novel level set-based active contour model is proposed for breast ultrasound (BUS) image segmentation. At first, an energy function is formulated according to the differences between the actual and estimated probability densities of the intensities in different regions. The actual probability densities are calculated directly. For calculating the estimated probability densities, the probability density estimation method and background knowledge are utilized. The energy function is formulated with level set approach, and a partial differential equation is derived for finding the minimum of the energy function. For performing numerical computation, the derived partial differential equation is approximated by the central difference and non-re-initialization approach. The proposed method was operated on both the synthetic images and clinical BUS images for studying its characteristics and evaluating its performance. The experimental results demonstrate that the proposed method can model the BUS images well, be robust to noise, and segment the BUS images accurately and reliably.     

Active contours with selective local or global segmentation: A new formulation and level set method

A novel region-based active contour model (ACM) is proposed in this paper. It is implemented with a special processing named Selective Binary and Gaussian Filtering RegularizedLevel Set(SBGFRLS) method, which first selectively penalizes the level set function to be binary, and then uses a Gaussian smoothing kernel to regularize it. The advantages of our method are as follows. First, a new region-based signed pressure force (SPF) function is proposed, which can efficiently stop the contours at weak or blurred edges. Second, the exterior and interior boundaries can be automatically detected with the initial contour being anywhere in the image. Third, the proposed ACM with SBGFRLS has the property of selective local or global segmentation. It can segment not only the desired object but also the other objects. Fourth, the level set function can be easily initialized with a binary function, which is more efficient to construct than the widely used signed distance function (SDF). The computational cost for traditional re-initialization can also be reduced. Finally, the proposed algorithm can be efficiently implemented by the simple finite difference scheme. Experiments on synthetic and real images demonstrate the advantages of the proposed method over geodesic active contours (GAC) and Chan–Vese (C–V) active contours in terms of both efficiency and accuracy.     

单位法向量引导的自适应医学图像分割新算法

水平集方法已经广泛应用于图像分割,ChunmingLi等人早期的模型通过在能量方程中引入惩罚项可以避免重新初始化。但惩罚项中的函数会引起扩散率趋于无穷大的问题,因此ChumningLi等人通过改进惩罚项中的函数,解决了扩散率的问题。针对新模型采用高斯滤波去除图像噪声使图像边缘变模糊的问题,采用正则化的P-M方程滤波,去除噪声的同时保护图像边缘信息。同时,新模型仍然不能实现自适应分割。通过初始曲线内外梯度模值的信息改变曲线内法向量的方向,从而使曲线自适应地向内或者向外演化。最后,用改进的算法准确地提取出了医学图像的轮廓,算法的效率也有很大的提高。     

A new graph cut-based multiple active contour algorithm without initial contours and seed points

This paper presents a new graph cut-based multiple active contour algorithm to detect optimal boundaries and regions in images without initial contours and seed points. The task of multiple active contours is framed as a partitioning problem by assuming that image data are generated from a finite mixture model with unknown number of components. Then, the partitioning problem is solved within a divisive graph cut framework where multi-way minimum cuts for multiple contours are efficiently computed in a top-down way through a swap move of binary labels. A split move is integrated into the swap move within that framework to estimate the model parameters associated with regions without the use of initial contours and seed points. The number of regions is also estimated as a part of the algorithm. Experimental results of boundary and region detection of natural images are presented and analyzed with precision and recall measures to demonstrate the effectiveness of the proposed algorithm.     

Graph cut segmentation with a statistical shape model in cardiac MRI

Segmenting the right ventricle (RV) in magnetic resonance (MR) images is required for cardiac function assessment. The segmentation of the RV is a difficult task due to low contrast with surrounding tissues and high shape variability. To overcome these problems, we introduce a segmentation method based on a statistical shape model obtained with a principal component analysis (PCA) on a set of representative shapes of the RV. Shapes are not represented by a set of points, but by distance maps to their contour, relaxing the need for a costly landmark detection and matching process. A shape model is thus obtained by computing a PCA on the shape variations. This prior is registered onto the image via a very simple user interaction and then incorporated into the well-known graph cut framework in order to guide the segmentation. Our semi-automatic segmentation method has been applied on 248 MR images of a publicly available dataset (from MICCAI’12 Right Ventricle Segmentation Challenge). We show that encouraging results can be obtained for this challenging application.