Semiautomatic segmentation with compact shape prior

In recent years, interactive methods for segmentation are increasing in popularity due to their success in different domains such as medical image processing, photo editing, etc. We present an interactive segmentation algorithm that can segment an object of interest from its background with minimum guidance from the user, who just has to select a single seed pixel inside the object of interest. Due to minimal requirements from the user, we call our algorithm semiautomatic. To obtain a reliable and robust segmentation with such low user guidance, we have to make several assumptions. Our main assumption is that the object to be segmented is of compact shape, or can be approximated by several connected roughly collinear compact pieces. We base our work on the powerful graph cut segmentation algorithm of Boykov and Jolly, which allows straightforward incorporation of the compact shape constraint. In order to make the graph cut approach suitable for our semiautomatic framework, we address several well-known issues of graph cut segmentation technique. In particular, we counteract the bias towards shorter segmentation boundaries and develop a method for automatic selection of parameters. We demonstrate the effectiveness of our approach on the challenging industrial application of transistor gate segmentation in images of integrated chips. Our approach produces highly accurate results in real-time.     

An optimal graph theoretic approach to data clustering: theory andits application to image segmentation

A novel graph theoretic approach for data clustering is presented and its application to the image segmentation problem is demonstrated. The data to be clustered are represented by an undirected adjacency graph 𝒢 with arc capacities assigned to reflect the similarity between the linked vertices. Clustering is achieved by removing arcs of 𝒢 to form mutually exclusive subgraphs such that the largest inter-subgraph maximum flow is minimized. For graphs of moderate size (~ 2000 vertices), the optimal solution is obtained through partitioning a flow and cut equivalent tree of 𝒢, which can be efficiently constructed using the Gomory-Hu algorithm (1961). However for larger graphs this approach is impractical. New theorems for subgraph condensation are derived and are then used to develop a fast algorithm which hierarchically constructs and partitions a partially equivalent tree of much reduced size. This algorithm results in an optimal solution equivalent to that obtained by partitioning the complete equivalent tree and is able to handle very large graphs with several hundred thousand vertices. The new clustering algorithm is applied to the image segmentation problem. The segmentation is achieved by effectively searching for closed contours of edge elements (equivalent to minimum cuts in 𝒢), which consist mostly of strong edges, while rejecting contours containing isolated strong edges. This method is able to accurately locate region boundaries and at the same time guarantees the formation of closed edge contours     

Object segmentation using graph cuts based active contours

In this paper we present a graph cuts based active contours (GCBAC) approach to object segmentation. GCBAC approach is a combination of the iterative deformation idea of active contours and the optimization tool of graph cuts. It differs from traditional active contours in that it uses graph cuts to iteratively deform the contour and its cost function is defined as the summation of edge weights on the cut. The resulting contour at each iteration is the global optimum within a contour neighborhood (CN) of the previous result. Since this iterative algorithm is shown to converge, the final contour is the global optimum within its own CN. The use of contour neighborhood alleviates the well-known bias of the minimum cut in favor of a shorter boundary. GCBAC approach easily extends to the segmentation of three and higher dimensional objects, and is suitable for interactive correction. Experimental results on selected data sets and performance analysis are provided.     

Two graph theory based methods for identifying the pectoral muscle in mammograms

Two image segmentation methods based on graph theory are used in conjunction with active contours to segment the pectoral muscle in screening mammograms. One method is based on adaptive pyramids (AP) and the other is based on minimum spanning trees (MST). The algorithms are tested on a public data set of mammograms and results are compared with previously reported methods. In 80% of the images, the boundary of the segmented regions has average error less than 2 mm. In 82 of 84 images, the boundary of the pectoral muscle found by the AP algorithm has average error less than 5 mm.     

Object segmentation in hyperspectral images using active contours and graph cuts

The interest in object segmentation on hyperspectral images is increasing and many approaches have been proposed to deal with this area. In this project, we developed an algorithm that combines both the active contours and the graph cut approaches for object segmentation in hyperspectral images. The active contours approach has the advantage of producing subregions with continuous boundaries. The graph cut approach has emerged as a technique for minimizing energy functions while avoiding the problems of local minima. Additionally, it guarantees continuity and produces smooth contours, free of self-crossing and uneven spacing problems. The algorithm uses the complete spectral signature of a pixel and also considers spatial neighbourhood for graph construction, thereby combining both spectral and spatial information present in the image. The algorithm is tested using real hyperspectral images taken from a variety of sensors, such as Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) and Hyperspectral Data Imagery Collection Experiment (HYDICE), and also taken by the SOC hyperspectral camera. This approach can segment different objects in an image. This algorithm can be applied in many fields and it should represent an important advance in the field of object segmentation.     

Cell tracking in microscopic video using matching and linking of bipartite graphs

Automated visual tracking of cells from video microscopy has many important biomedical applications. In this paper, we track human monocyte cells in a fluorescent microscopic video using matching and linking of bipartite graphs. Tracking of cells over a pair of frames is modeled as a maximum cardinality minimum weight matching problem for a bipartite graph with a novel cost function. The tracking results are further refined using a rank-based filtering mechanism. Linking of cell trajectories over different frames are achieved through composition of bipartite matches. The proposed solution does not require any explicit motion model, is highly scalable, and, can effectively handle the entry and exit of cells. Our tracking accuracy of (97.97 ± 0.94)% is superior than several existing methods [(95.66 ± 2.39)% [11], (94.42 ± 2.08)% [20], (81.22 ± 5.75)% [13], (78.31 ± 4.70)% [14]] and is highly comparable (98.20 ± 1.22)% to a recently published algorithm [26].     

Dynamic graph cuts for efficient inference in Markov Random Fields

Abstract-In this paper we present a fast new fully dynamic algorithm for the st-mincut/max-flow problem. We show how this algorithm can be used to efficiently compute MAP solutions for certain dynamically changing MRF models in computer vision such as image segmentation. Specifically, given the solution of the max-flow problem on a graph, the dynamic algorithm efficiently computes the maximum flow in a modified version of the graph. The time taken by it is roughly proportional to the total amount of change in the edge weights of the graph. Our experiments show that, when the number of changes in the graph is small, the dynamic algorithm is significantly faster than the best known static graph cut algorithm. We test the performance of our algorithm on one particular problem: the object-background segmentation problem for video. It should be noted that the application of our algorithm is not limited to the above problem, the algorithm is generic and can be used to yield similar improvements in many other cases that involve dynamic change.     

Liver segmentation in MRI: A fully automatic method based on stochastic partitions

There are few fully automated methods for liver segmentation in magnetic resonance images (MRI) despite the benefits of this type of acquisition in comparison to other radiology techniques such as computed tomography (CT). Motivated by medical requirements, liver segmentation in MRI has been carried out. For this purpose, we present a new method for liver segmentation based on the watershed transform and stochastic partitions. The classical watershed over-segmentation is reduced using a marker-controlled algorithm. To improve accuracy of selected contours, the gradient of the original image is successfully enhanced by applying a new variant of stochastic watershed. Moreover, a final classifier is performed in order to obtain the final liver mask. Optimal parameters of the method are tuned using a training dataset and then they are applied to the rest of studies (17 datasets). The obtained results (a Jaccard coefficient of 0.91 ± 0.02) in comparison to other methods demonstrate that the new variant of stochastic watershed is a robust tool for automatic segmentation of the liver in MRI.     

Approximating Maximum Weight Cycle Covers in Directed Graphs with Weights Zero and One

A cycle cover of a graph is a spanning subgraph, each node of which is part of exactly one simple cycle. A k-cycle cover is a cycle cover where each cycle has length at least k. Given a complete directed graph with edge weights zero and one, Max-k-DDC(0,1) is the problem of finding a k-cycle cover with maximum weight. We present a 2/3 approximation algorithm for Max-k-DDC(0,1) with running time O(n ^5/2). This algorithm yields a 4/3 approximation algorithm for Max-k-DDC(1,2) as well. Instances of the latter problem are complete directed graphs with edge weights one and two. The goal is to find a k-cycle cover with minimum weight. We particularly obtain a 2/3 approximation algorithm for the asymmetric maximum traveling salesman problem with distances zero and one and a 4/3 approximation algorithm for the asymmetric minimum traveling salesman problem with distances one and two. As a lower bound, we prove that Max-k-DDC(0,1) for k 3 and Max-k-UCC(0,1) (finding maximum weight cycle covers in undirected graphs) for k 7 are \APX-complete.     

基于K-means和图割的脑部MRI分割算法

为了克服原始图割算法在用户选定的像素种子点较少情况下,目标边界容易出现错分这一现象,本文提出了基于K-means和图割(Graph cut,GC)算法相结合的交互式K-均值图割（K-means and graph cut,KMGC）算法,对脑部核磁共振图像（Magnetic resonance image,MRI） 进行交互式操作,该算法通过K-means聚类,对脑部MRI的灰度不均匀性进行了处理,在此基础上,再使用图割算法进一步对脑部MRI进行细化,从而达到有效地分割脑白质和脑 灰质的目的。本文分别在仿真和真实的脑部MRI数据上进行了大量的实验,分别从定量分析和定性分析两个角度对实验结果进行了分析,并与其他分割算法进行了对比,对比实验结果标明,KMGC算法能够有效地对脑部MRI进行分割,并在分割效果上优于其他算法。     

A Simple and Fast Min-Cut Algorithm

We present an algorithm which calculates a minimum cut and its weight in an undirected graph with nonnegative real edge weights, n vertices and m edges, in time O(max(log n, min(m/n,δ_G/ε)) n²), where ε is the minimal edge weight, and δ_G is the minimal weighted degree. For integer edge weights this time is further improved to O(δ_G n²) and O(λ_G n²). In both cases these bounds are improvements of the previously known best bounds of deterministic algorithms. These were O(nm + n² log n) for real edge weights and O(nM + n²) and O(M + λ_G n²) for integer weights, where M is the sum of all edge weights.     

一种基于图的交互式目标分割算法

静态图片的编辑中,交互式背景、前景分割的高效性研究有着重大的实际意义。传统的分割方法或是应用图片的纹理(色彩)信息,如Magic Wand,或是利用边界(对比度)信息,如Intelligent Scissors。最近提出的Graph cuts分割算法很好地结合了以上的两种信息。该文将介绍Graph cuts算法以及在该算法基础上改进得到的Grab cut算法。Grab cut算法堪称目前交互式分割方法中分割效果较好的方法,其分割精度高,交互工作少,具有较好的应用前景。文章结合作者当前的研究课题,把Grab cut算法应用在医学图像器官分割中得到了令人满意的效果。     

NP-completeness of maximum-cut and cycle-covering problems for a planar graph

We consider problems of finding the maximum cut and a cycle covering for a planar graph with edge weights of arbitrary sign. Methods that find the maximum cut in graphs with only positive edge weights are shown to be inapplicable in this case. NP-completeness of the problem is proved.Translated from Kibernetika, No. 1, pp. 13–16, January–February, 1991.     

A hybrid semi-automatic method for liver segmentation based on level-set methods using multiple seed points

The present study developed a hybrid semi-automatic method to extract the liver from abdominal computerized tomography (CT) images. The proposed hybrid method consists of a customized fast-marching level-set method for detection of an optimal initial liver region from multiple seed points selected by the user and a threshold-based level-set method for extraction of the actual liver region based on the initial liver region. The performance of the hybrid method was compared with those of the 2D region growing method implemented in OsiriX using abdominal CT datasets of 15 patients. The hybrid method showed a significantly higher accuracy in liver extraction (similarity index, SI = 97.6 ± 0.5%; false positive error, FPE = 2.2 ± 0.7%; false negative error, FNE = 2.5 ± 0.8%; average symmetric surface distance, ASD = 1.4 ± 0.5 mm) than the 2D (SI = 94.0 ± 1.9%; FPE = 5.3 ± 1.1%; FNE = 6.5 ± 3.7%; ASD = 6.7 ± 3.8 mm) region growing method. The total liver extraction time per CT dataset of the hybrid method (77 ± 10 s) is significantly less than the 2D region growing method (575 ± 136 s). The interaction time per CT dataset between the user and a computer of the hybrid method (28 ± 4 s) is significantly shorter than the 2D region growing method (484 ± 126 s). The proposed hybrid method was found preferred for liver segmentation in preoperative virtual liver surgery planning.     

图像分割的自适应交互核图割模型

为了克服图割模型算法在实现图像分割时需要人为选定参数,以及图割模型可能会陷入局部最小值的不足,考虑到交互图割是一种灵活的全局最优算法,提出了基于EM方法的交互核图割算法。数据映射到核空间,构造了新的目标函数,这样可以更有效地解决分类分割问题;为了估计交互图割所需要的参数以及图割算法所需要的各种阈值,采用EM算法来估计这些参数,避免人为随机选取可能造成的不利影响,因而该方法是一种自适应的分割算法。实验结果表明,相对于交互图割算法,该算法分割合成图像时具有更低的误分率,处理光学等图像时,分割结果更准确,保留图像细节信息的能力更强。     

基于图割及均值漂移的合成孔径雷达图像强散射目标分割

针对合成孔径雷达(SAR)图像的特点及标准图割分割算法计算量较大等问题,提出了一种基于图割及均值漂移(Mean Shift)的高效的SAR图像强散射目标分割方法。该方法利用均值漂移算法对SAR图像进行预处理,将原图像表示为基于过分割区域的图结构;然后,以这些过分割图像区域为节点建立区域邻接图,运用图割分割算法得到SAR强散射目标的分割结果。与标准图割算法中以单像素为节点构建邻接图相比,参与图割算法的节点和边的数目减少了两个数量级,计算效率大幅提高。另外,根据SAR图像中目标的强散射特性,自动定义终端节点,减少了人工交互量。实验表明,该方法充分利用均值漂移及图割的优点,能够在背景杂波的干扰下有效地提取SAR强散射目标。     

Segmentation and detection of breast cancer in mammograms combining wavelet analysis and genetic algorithm

In Brazil, the National Cancer Institute (INCA) reports more than 50,000 new cases of the disease, with risk of 51 cases per 100,000 women. Radiographic images obtained from mammography equipments are one of the most frequently used techniques for helping in early diagnosis. Due to factors related to cost and professional experience, in the last two decades computer systems to support detection (Computer-Aided Detection – CADe) and diagnosis (Computer-Aided Diagnosis – CADx) have been developed in order to assist experts in detection of abnormalities in their initial stages. Despite the large number of researches on CADe and CADx systems, there is still a need for improved computerized methods. Nowadays, there is a growing concern with the sensitivity and reliability of abnormalities diagnosis in both views of breast mammographic images, namely cranio-caudal (CC) and medio-lateral oblique (MLO). This paper presents a set of computational tools to aid segmentation and detection of mammograms that contained mass or masses in CC and MLO views. An artifact removal algorithm is first implemented followed by an image denoising and gray-level enhancement method based on wavelet transform and Wiener filter. Finally, a method for detection and segmentation of masses using multiple thresholding, wavelet transform and genetic algorithm is employed in mammograms which were randomly selected from the Digital Database for Screening Mammography (DDSM). The developed computer method was quantitatively evaluated using the area overlap metric (AOM). The mean ± standard deviation value of AOM for the proposed method was 79.2 ± 8%. The experiments demonstrate that the proposed method has a strong potential to be used as the basis for mammogram mass segmentation in CC and MLO views. Another important aspect is that the method overcomes the limitation of analyzing only CC and MLO views.     

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.     

A marker-based watershed method for X-ray image segmentation

Digital X-ray images are the most frequent modality for both screening and diagnosis in hospitals. To facilitate subsequent analysis such as quantification and computer aided diagnosis (CAD), it is desirable to exclude image background. A marker-based watershed segmentation method was proposed to segment background of X-ray images. The method consisted of six modules: image preprocessing, gradient computation, marker extraction, watershed segmentation from markers, region merging and background extraction. One hundred clinical direct radiograph X-ray images were used to validate the method. Manual thresholding and multiscale gradient based watershed method were implemented for comparison. The proposed method yielded a dice coefficient of 0.964 ± 0.069, which was better than that of the manual thresholding (0.937 ± 0.119) and that of multiscale gradient based watershed method (0.942 ± 0.098). Special means were adopted to decrease the computational cost, including getting rid of few pixels with highest grayscale via percentile, calculation of gradient magnitude through simple operations, decreasing the number of markers by appropriate thresholding, and merging regions based on simple grayscale statistics. As a result, the processing time was at most 6 s even for a 3072 × 3072 image on a Pentium 4 PC with 2.4 GHz CPU (4 cores) and 2G RAM, which was more than one time faster than that of the multiscale gradient based watershed method. The proposed method could be a potential tool for diagnosis and quantification of X-ray images.