A novel region-based active contour model based on kernel function for image segmentation

It is a difficult task to accurately segment images with intensity inhomogeneity, because most of existing algorithms are based upon the assumption of the homogeneity of image intensity. In this paper, we propose a novel region-based active contour model, referred to as the K-GLIF, which utilizes both global and local image intensity fittings with kernel functions. The model consists of an intensity fitting term and a new regularization term. The intensity fitting term of the level set function is the gradient descent flow that minimizes the global binary fitting energy functional. The local intensity fitting value based on the generalized Gaussian kernel function is then incorporated into the global intensity fitting value to form the weighted intensity fitting value on the two sides of the contour. Owing to the kernel function, the intensity information in local regions is extracted to guide the motion of the contour, which enables the model to effectively segment images with intensity inhomogeneity and smooth noise. A new regularization term is used to control the smoothness of the level set function and avoid complicated re-initialization. Experimental results and comparisons with other models of inhomogeneous images, synthetic images, medical images, multi-object images, natural and infrared images show that the proposed K-GLIF model improves the quality of image segmentation in terms of accuracy and robustness of initial contours.

     

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.

     

An active contour model driven by anisotropic region fitting energy for image segmentation

A novel region active contour model (ACM) for image segmentation is proposed in this paper. In order to perform an accurate segmentation of images with non-homogeneous intensity, the original region fitting energy in the general region-based ACMs is improved by an anisotropic region fitting energy to evolve the contour. Using the local image information described by the structure tensor, this new region fitting energy is defined in terms of two anisotropic fitting functions that approximate the image intensity along the principal directions of variation of the intensity. Therefore, the anisotropic fitting functions extract intensity information more precisely, which enable our model to cope with the boundaries with low-contrast and complicated structures. It is incorporated into a variational formula with a total variation (TV) regularization term with respect to level set function, from which the segmentation process is performed by minimizing this variational energy functional. Experiments on the vessel and brain magnetic resonance images demonstrate the advantages of the proposed method over Chan–Vese (CV) active contours and local binary active contours (LBF) in terms of both efficiency and accuracy.     

Robust global and local fuzzy energy based active contour for image segmentation

Though various image segmentation techniques have been developed, it is still a very challenging task to design a robust and efficient algorithm to segment (noisy, blurred or even discontinuous edged) images having high intensity inhomogeneity or non-homogeneity. In this article, a robust fuzzy energy based active contour, using both global and local information, is proposed to detect objects in a given image based on curve evolution. The local energy is generated by considering both local spatial and gray level/color information. The proposed model can better deal with images having high intensity inhomogeneity or non-homogeneity, noise and blurred boundary or discontinuous edges by incorporating local energy term in the proposed active contour energy function. The global energy term is used to avoid unsatisfactory results due to bad initialization. In this article, instead of solving the Euler–Lagrange equation, a level set based optimization is used for the convergence. We show a realization of the proposed method and demonstrate its performance (both qualitatively and quantitatively) with respect to state-of-the-art techniques on several images having such kind of artifacts. Analysis of results concludes that the proposed method can detect objects from given images in a better way than the existing ones.     

结合MRF能量和模糊速度的乳腺癌图像分割方法

乳腺癌灶的精确分割是乳腺癌计算机辅助诊断的重要前提. 在动态对比增强核磁共振成像(Dynamic contrast-enhanced magnetic resonance imaging, DCE-MRI)的图像中, 乳腺癌灶具有对比度低、边界模糊及亮度不均匀等特点, 传统的活动轮廓模型方法很难取得准确的分割结果. 本文提出一种结合马尔科夫随机场(Markov random field, MRF)能量和模糊速度函数的活动轮廓模型的半自动分割方法来完成乳腺癌灶的分割, 相对于专业医生的手动分割, 本文方法具有速度快、可重复性高和分割结果相对客观等优点. 首先, 计算乳腺DCE-MRI图像的MRF能量, 以增强目标区域与周围背景的差异. 其次, 在能量图中计算每个像素点的后验概率, 建立基于后验概率驱动的活动轮廓模型区域项. 最后, 结合Gabor纹理特征、DCE-MRI时域特征和灰度特征构建模糊速度函数, 将其引入到活动轮廓模型中作为边缘检测项. 在乳腺癌灶边界处, 该速度函数趋向于零, 活动轮廓曲线停止演变, 完成对乳腺癌灶的分割. 实验结果表明, 所提出的方法有助于乳腺癌灶在DCE-MRI图像中的准确分割.     

自适应尺度的局部强度聚类图像分割模型

针对传统活动轮廓模型无法精确分割强度不均匀图像，并且对尺度参数比较敏感的问题，提出了一种基于区域信息的自适应尺度的活动轮廓模型。根据图像的局部熵构建自适应尺度算子，利用图像的局部强度聚类性质构建能量函数。使用一组平滑基函数的线性组合来表示偏移场，这样可以增加模型的稳定性。通过最小化该能量，所提模型能够同时分割图像和估计偏移场，并且估计的偏移场可以用于强度不均匀校正。实验结果表明，与其它4种模型相比，该模型拥有更高的分割精确度，且分割结果对水平集函数的初始化和噪声具有鲁棒性。     

Novel fuzzy active contour model with kernel metric for image segmentation

In this paper, a novel region-based fuzzy active contour model with kernel metric is proposed for a robust and stable image segmentation. This model can detect the boundaries precisely and work well with images in the presence of noise, outliers and low contrast. It segments an image into two regions – the object and the background by the minimization of a predefined energy function. Due to the kernel metric incorporated in the energy and the fuzziness of the energy, the active contour evolves very stably without the reinitialization for the level set function during the evolution. Here the fuzziness provides the model with a strong ability to reject local minima and the kernel metric is employed to construct a nonlinear version of energy function based on a level set framework. This new fuzzy and nonlinear version of energy function makes the updating of region centers more robust against the noise and outliers in an image. Theoretical analysis and experimental results show that the proposed model achieves a much better balance between accuracy and efficiency compared with other active contour models.     

Fast automatic medical image segmentation based on spatial kernel fuzzy c-means on level set method

Fast two-cycle (FTC) model is an efficient and the fastest Level set image segmentation. But, its performance is highly dependent on appropriate manual initialization. This paper proposes a new algorithm by combining a spatially constrained kernel-based fuzzy c-means (SKFCM) algorithm and an FTC model to overcome the mentioned problem. The approach consists of two successive stages. First, the SKFCM makes a rough segmentation to select the initial contour automatically. Then, a fuzzy membership matrix of the region of interest, which is generated by the SKFCM, is used in the next stage to produce an initial contour. Eventually, the FTC scheme segments the image by a curve evolution based on the level set. Moreover, the fuzzy membership degree from the SKFCM is incorporated into the fidelity term of the Chan–Vese model to improve the robustness and accuracy, and it is utilized for the data-dependent speed term of the FTC. A performance evaluation of the proposed algorithm is carried out on the synthetic and real images. The experimental results show that the proposed algorithm has advantages in accuracy, computational time and robustness against noise in comparison with the KFCM, the SKFCM, the hybrid model of the KFCM and the FTC, and five different level set methods on medical image segmentation.     

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。     

An improved region-based model with local statistical features for image segmentation

In this paper, we propose a new region-based active contour model (ACM) for image segmentation. In particular, this model utilizes an improved region fitting term to partition the regions of interests in images depending on the local statistics regarding the intensity and the magnitude of gradient in the neighborhood of a contour. By this improved region fitting term, images with noise, intensity non-uniformity, and low-contrast boundaries can be well segmented. Integrated with the duality theory and the anisotropic diffusion process based on structure tensor, a new regularization term is defined through the duality formulation to penalize the length of active contour. By this new regularization term, the structural information of images is utilized to improve the ability of capturing the geometric features such as corners and cusps. From a numerical point of view, we minimize the energy function of our model by an efficient dual algorithm, which avoids the instability and the non-differentiability of traditional numerical solutions, e.g. the gradient descent method. Experiments on medical and natural images demonstrate the advantages of the proposed model over other segmentation models in terms of both efficiency and accuracy.     

A novel level set method for image segmentation by incorporating local statistical analysis and global similarity measurement

This paper presents a novel level set method for complex image segmentation, where the local statistical analysis and global similarity measurement are both incorporated into the construction of energy functional. The intensity statistical analysis is performed on local circular regions centered in each pixel so that the local energy term is constructed in a piecewise constant way. Meanwhile, the Bhattacharyya coefficient is utilized to measure the similarity between probability distribution functions for intensities inside and outside the evolving contour. The global energy term can be formulated by minimizing the Bhattacharyya coefficient. To avoid the time-consuming re-initialization step, the penalty energy term associated with a new double-well potential is constructed to maintain the signed distance property of level set function. The experiments and comparisons with four popular models on synthetic and real images have demonstrated that our method is efficient and robust for segmenting noisy images, images with intensity inhomogeneity, texture images and multiphase images.     

局部区域拟合的快速水平集图像分割方法

目的 由于灰度不均匀图像在不同目标区域的灰度分布存在严重的重叠,对其进行分割仍然是一个难题;同时,图像中的噪声严重降低了图像分割的准确性。因此,传统水平集方法无法鲁棒、精确、快速地对具有灰度不均匀性和噪声的图像进行分割。针对这一问题,提出一种基于局部区域信息的快速水平集图像分割方法。方法 灰度不均匀图像通常被描述为一个分段常数图像乘以一个缓慢变化的偏移场。首先,通过一个经过微调的多尺度均值滤波器来估计图像的偏移场,并对图像进行预处理以减轻图像的不均匀性;然后,利用基于偏移场校正的方法和基于局部区域信息拟合的方法分别构建能量项,并利用演化曲线轮廓内外图像灰度分布的重叠程度,构建权重函数自适应调整两个能量项之间的权重;最后,引入全方差规则项对水平集进行约束,增强了数值计算的稳定性和对噪声的鲁棒性,并通过加性算子分裂策略实现水平集快速演化。结果 在具有不同灰度不均匀性和噪声图像上的分割结果表明,所提方法不但对初始轮廓的位置、灰度不均匀性和各种噪声具有较强的鲁棒性,而且具有高达94.5%的分割精度和较高的分割效率,与传统水平集方法相比分割精度至少提高了20.6%,分割效率是LIC（local intensity clustering）模型的9倍;结论 本文提出一种基于局部区域信息的快速水平集图像分割方法。实验结果表明,与传统水平集方法相比具有较高的分割精度和分割效率,可以很好地应用于具有灰度不均匀和噪声的医学、红外和自然图像等的分割。     

显著性驱动的局部相似拟合模型分割算法研究

灰度不均匀和噪声图像的分割是计算机视觉中的难点。现有的活动轮廓模型尽管能够取得较好的分割效果,但仍然对噪声图像分割效果不理想,初始轮廓曲线的选取敏感,优化易陷入局部极小导致演化速度慢等问题。针对该问题,首先使用局部区域灰度的均值和方差拟合高斯分布,构建新的能量泛函,均值和方差随着能量的最小化过程而变化,从而增强了灰度不均匀和噪声图像的分割能力。此外,结合视觉显著性检测算法获取待分割目标的先验形状信息,并自适应地创建水平集函数,从而降低了初始轮廓位置敏感性及计算时间复杂度,实现全自动的图像分割。实验结果证明,提出的算法可以用于灰度不均匀和噪声图像分割,并取得了较好的分割性能,消除了算法对初始轮廓位置敏感性,减少了迭代次数。     

A Modified Fuzzy C-Means Algorithm for Brain MR Image Segmentation and Bias Field Correction

In quantitative brain image analysis, accurate brain tissue segmentation from brain magnetic resonance image (MRI) is a critical step. It is considered to be the most important and difficult issue in the field of medical image processing. The quality of MR images is influenced by partial volume effect, noise, and intensity inhomogeneity, which render the segmentation task extremely challenging. We present a novel fuzzy c-means algorithm (RCLFCM) for segmentation and bias field correction of brain MR images. We employ a new gray-difference coefficient and design a new impact factor to measure the effect of neighbor pixels, so that the robustness of anti-noise can be enhanced. Moreover, we redefine the objective function of FCM (fuzzy c-means) by adding the bias field estimation model to overcome the intensity inhomogeneity in the image and segment the brain MR images simultaneously. We also construct a new spatial function by combining pixel gray value dissimilarity with its membership, and make full use of the space information between pixels to update the membership. Compared with other state-of-the-art approaches by using similarity accuracy on synthetic MR images with different levels of noise and intensity inhomogeneity, the proposed algorithm generates the results with high accuracy and robustness to noise.     

Kernel generalized fuzzy c-means clustering with spatial information for image segmentation

The generalized fuzzy c-means clustering algorithm with improved fuzzy partition (GFCM) is a novel modified version of the fuzzy c-means clustering algorithm (FCM). GFCM under appropriate parameters can converge more rapidly than FCM. However, it is found that GFCM is sensitive to noise in gray images. In order to overcome GFCM?s sensitivity to noise in the image, a kernel version of GFCM with spatial information is proposed. In this method, first a term about the spatial constraints derived from the image is introduced into the objective function of GFCM, and then the kernel induced distance is adopted to substitute the Euclidean distance in the new objective function. Experimental results show that the proposed method behaves well in segmentation performance and convergence speed for gray images corrupted by noise.     

基于局部增强与区域拟合的活动轮廓模型

针对活动轮廓模型在分割弱边缘图像及严重的灰度不均匀图像方面存在轮廓曲线不能很好地演化到目标边界等问题,提出了一种基于局部增强与区域拟合的活动轮廓模型。首先,利用局部区域增强方法将原始图像转换为新图像,以增强图像的对比度。其次,利用统计信息计算图像的区域拟合能量。然后,加入正则项以避免演化轮廓重新初始化,提高图像分割效率。最后,通过灰度不均匀的合成图像和真实图像的实验,验证了该算法的有效性。     

修正局部极小值的局部灰度差异分割模型

针对现有局部模型在分割灰度不均匀图像时容易陷入局部极小值,导致演化曲线停留在背景处或目标内部无法继续演化从而造成分割失败的现象,提出本模型。该模型在能量泛函中增加局部灰度差异项,通过最大化演化曲线上所有点的邻域内目标和背景的差异来驱动演化曲线越过图像背景处或目标内部,直到准确地停留在目标边缘。实验结果表明提出的模型可以有效地解决局部模型因陷入局部极小值而导致的误分割问题,同时提高对分割灰度不均匀等复杂图像的准确性,并减小对初始轮廓的敏感性。     

Strong fuzzy c-means in medical image data analysis

This paper presents a robust fuzzy c-means (FCM) for an automatic effective segmentation of breast and brain magnetic resonance images (MRI). This paper obtains novel objective functions for proposed robust fuzzy c-means by replacing original Euclidean distance with properties of kernel function on feature space and using Tsallis entropy. By minimizing the proposed effective objective functions, this paper gets membership partition matrices and equations for successive prototypes. In order to reduce the computational complexity and running time, center initialization algorithm is introduced for initializing the initial cluster center. The initial experimental works have done on synthetic image and benchmark dataset to investigate the effectiveness of proposed, and then the proposed method has been implemented to differentiate the different region of real breast and brain magnetic resonance images. In order to identify the validity of proposed fuzzy c-means methods, segmentation accuracy is computed by using silhouette method. The experimental results show that the proposed method is more capable in segmentation of medical images than existed methods.     

A framework with modified fast FCM for brain MR images segmentation

Intensity inhomogeneity, noise and partial volume (PV) effect render a challenging task for segmentation of brain magnetic resonance (MR) images. Most of the current MR image segmentation methods focus on only one or two of the effects listed above. In this paper, a framework with modified fast fuzzy c-means for brain MR images segmentation is proposed to take all these effects into account simultaneously and improve the accuracy of image segmentations. Firstly, we propose a new automated method to determine the initial values of the centroids. Secondly, an adaptive method to incorporate the local spatial continuity is proposed to overcome the noise effectively and prevent the edge from blurring. The intensity inhomogeneity is estimated by a linear combination of a set of basis functions. Meanwhile, a regularization term is added to reduce the iteration steps and accelerate the algorithm. The weights of the regularization terms are all automatically computed to avoid the manually tuned parameter. Synthetic and real MR images are used to test the proposed framework. Improved performance of the proposed algorithm is observed where the intensity inhomogeneity, noise and PV effect are commonly encountered. The experimental results show that the proposed method has stronger anti-noise property and higher segmentation precision than other reported FCM-based techniques.     

A multiobjective spatial fuzzy clustering algorithm for image segmentation

This article describes a multiobjective spatial fuzzy clustering algorithm for image segmentation. To obtain satisfactory segmentation performance for noisy images, the proposed method introduces the non-local spatial information derived from the image into fitness functions which respectively consider the global fuzzy compactness and fuzzy separation among the clusters. After producing the set of non-dominated solutions, the final clustering solution is chosen by a cluster validity index utilizing the non-local spatial information. Moreover, to automatically evolve the number of clusters in the proposed method, a real-coded variable string length technique is used to encode the cluster centers in the chromosomes. The proposed method is applied to synthetic and real images contaminated by noise and compared with k-means, fuzzy c-means, two fuzzy c-means clustering algorithms with spatial information and a multiobjective variable string length genetic fuzzy clustering algorithm. The experimental results show that the proposed method behaves well in evolving the number of clusters and obtaining satisfactory performance on noisy image segmentation.