Image segmentation by combining the global and local properties 结合全局和局部特征进行图像分割
Abstract 摘要
Image segmentation plays a fundamental role in many computer vision applications. 图像分割在许多计算机可视化应用中起着至关重要的作用。It is challenging because of the vast variety of images involved and the diverse segmentation requirements in different applications. 由于所涉及的图像种类繁多, 而且不同的应用程序中的细分需求多种多样, 因此具有挑战性。As a result, it remains an open problem after so many years of study by researchers all over the world. 因此, 经过这么多年的研究对于世界各地的研究人员来说它仍然是一个开难题。In this paper, we propose to segment the image by combing its global and local properties. 本文通过对图像的全局和局部性质的结合, 提出了分割图象的方法。The global properties of the image are characterized by the mean values of different pixel classes and the continuous boundary of the object or region. 图像的全局属性是以不同像素类的平均值和对象或区域的连续边界为特征的。The local properties are characterized by the interactions of neighboring pixels and the image edge. 局部属性的特征是相邻像素和图像边缘的相互作用。The proposed approach consists of four basic parts corresponding to the global or local property of the image respectively: 所提出的方法包括与图像的全局或局部性质相对应的四个基本部分: (1) The slope difference distribution that is used to compute the global mean values of different pixel classes;. (1) 用于计算不同像素类的全局均值的斜率差分布; (2) Energy minimization to remove inhomogeneity based on Gibbs distribution that complies with local interactions of neighboring pixels; (2) 基于吉布斯分布的能量最小化消除不均匀性, 符合相邻像素的局部相互作用;(3) The Canny operator that is used to detect the local edge of the object or the region; 3) 用于检测物体或区域局部边缘的Canny算子;((4) The polynomial spline that is used to smooth the boundary of the object or the region(4) 用于平滑对象或区域边界的多项式样条。These four basic parts are applied one by one and each of them is indispensable for the achieved high accuracy. 这四个基本部分一个一个地被应用, 并且为了得到的高准确性它们是不可缺少的。A large variety of images are used to validate the proposed approach and the results are favorable. 大量多种图像被用来验证所提出的方法, 结果是正确，可支持的。
Keywords: Segmentation Histogram Gibbs distribution Slope difference distribution
关键词: 分割 直方图 吉布斯分布 斜率差分布
1.Introduction 引言
Image segmentation algorithms are usually only effective for some specific types of images while they might make great mistakes for other types of images due to four major problems.图像分割算法通常只对某些特定类型的图像有效, 而它们可能会因四大问题而对其他类型的图像造成很大的错误。 (1) The histogram distributions of different pixel classes overlap with each other, which makes the estimation of the global parameters inaccurate.(1) 不同像素类的直方图分布相互重叠, 使得全局参数估计不准确。 (2) The noise that modifies the histogram distribution might cause great errors during global parameter estimation. (2) 在全局参数估计中, 修改直方图分布的噪声可能会造成较大的误差。(3) The local properties of different regions in the image are usually not homogeneous at the same spatial scale, which makes it difficult for modeling-based segmentation methods to estimate the local parameters with satisfactory accuracy. (3) 图像中不同区域的局部性质在同一空间尺度上通常不均匀, 使得基于分割方法难以准确估计局部参数。(4) The overlap of different grayscale distributions makes the boundaries of the labeled regions inaccurate. (4) 不同灰度分布的重叠使得标记区域的边界不准确。
The first two problems persist in the famous expectation maximization (EM) algorithm ( Besag, 1986; Dempster, Laird, amp; Ru- bin, 1977 ) that has been widely used to estimate the means and variances of different pixel classes during image segmentation although its effectiveness has been widely accepted ( Carson, Belongie, Greenspan, amp; Malik, 2002; Won amp; Gray, 2004 ). 前两个问题在著名的期望最大化 (EM) 算法中仍然存在( Carson, Belongie, Greenspan, amp; Malik, 2002; Won amp; Gray, 2004 )。在图像分割中被广泛用于估计不同像素类的平均值和方差, 尽管它的有效性已被广泛接受 ( Carson, Belongie, Greenspan, amp; Malik, 2002; Won amp; Gray, 2004 )。The other popular parameter estimation algorithm, k-means clustering method ( Jain, 2010 ) could not effectively deal with the first problem and the second problem either. 其他常用的参数估计算法, k-均值聚类方法 ( Jain, 2010 ) 不能有效地处理第一个问题或第二个问题。The estimated global parameters by EM or K -means are frequently inaccurate in image segmentation applications.在图像分割应用中, 由 EM 或 k-均值估计的全局参数往往不准确。 For the popular thresholding methods ( Osuna- Encisa, Cuevas, amp; Sossa, 2013 ), their accuracies are also affected by the first two problems. 对于流行的阈值法 ( Osuna- Encisa, Cuevas, amp; Sossa, 2013 )， 他们的准确度也受到前两个问题的影响。Some researchers have tried to solve the second problem by estimating the noise separately and apply the denoising technique to suppress the estimated noise ( Chan, Ese- doglu, amp; Nikolova, 2006; Manjon, Coupe, amp; Buades, 2015; Sagar, Brando, amp; Sambridge, 2014 ), which achieved significant improvement in segmentation accuracy. 一些研究人员试图通过分别估计噪声来解决第二个问题, 并应用降噪技术来抑制估计的噪声 ( Chan, Ese- doglu, amp; Nikolova, 2006; Manjon, Coupe, amp; Buades, 2015; Sagar, Brando, amp; Sambridge, 2014 ), 在分割精度方面取得了显著的提高。However, it is also very difficult to estimate the parameters of the noise model accurately. 然而, 准确地估计噪声模型的参数也非常困难。The overlap of the gray-scale distributions of different pixel classes, the different levels of noise magnitudes and the different forms of noise distributions make it difficult to estimate the parameters with adequate accuracy in most cases.在大多数情况下, 不同像素级的灰度分布、不同的噪声等级和不同的噪声分布形式之间的重叠, 使得在大多数情况下难以对参数进行足够的准确估计。
To address the third problem, the image had been assumed as a Markov Random Field (MRF) that is subject to the Gibbs distribution ( Caillol, Hillon, amp; Pieczynski, 1993; Derin amp; Elliott, 1987; Wang amp; Zhang, 2012 ).为了解决第三个问题, 图像被假设为一个马尔可夫随机场 (MRF), 受吉布斯分布限制 ( Caillol, Hillon, amp; Pieczynski, 1993; Derin amp; Elliott, 1987; Wang amp; Zhang, 2012 )。 Based on this assumption, a lot of effort s have been put into the segmentation research work and many MRF-based segmentation methods have been proposed. 基于这一假设, 在分割研究工作中投入了大量的精力, 并提出了许多基于马尔可夫随机场的分割方法。For instance, some researchers proposed to cluster the texture features with a mixture of Gaussian models for better performance ( Yang, Wright,Ma, amp; Sastry, 2008 ).例如, 一些研究人员建议将纹理特征与高斯模型混合以提高性能 ( Yang, Wright,Ma, amp; Sastry, 2008 )。 Some researchers combined the Maximuma posteriori (MAP), maximum likelihood (ML) and graph cut to achieve the satisfactory segmentation results ( Chen, Cao, Wang,Liu, amp; Tang, 2010 ). 一些研究人员将最大后验概率 (MAP)、最大似然估计(ML) 和图形裁剪相结合, 以达到满意的分割结果 ( Chen, Cao, Wang,Liu, amp; Tang, 2010 )。One merit of the MRF-based method is thatit could distinguish different textured regions, especially for the textures that could be modeled and defined with parameters. 基于马尔可夫随机场方法的一个优点是它可以区分不同的纹理区域, 特别是对于可以用参数建模和定义的纹理。The major drawback of MRF-based methods is that they could not estimatethe parameters of the textures with adequate accuracy in most cases, especially for the natural images.基于马尔可夫随机场方法的主要缺点是, 在大多数情况下, 它们不足以准确估计纹理的参数, 特别是对自然图像。On the other hand, its segmentation accuracy is determined by the accuracy of theparameter estimation. 另一方面, 它的分割精度取决于参数估计的准确度。Consequently, the accuracy of MRF-based methods is only good for a specific class of images whose texture parameters could be estimated robustly. 因此, 基于马尔可夫随机场方法的准确性仅对特定的图像类具有良好的纹理参数估计。Although the parameter of the Gibbs distribution might not be estimated accurately in most cases, it characterizes the interaction of neighboring pixels well and thus could be utilized in the segmentation process. 虽然在大多数情况下, 吉布斯分布的参数可能无法准确估计, 但它能很好地刻画相邻像素之间的相互作用, 从而在分割过程中得到应用。Instead of estimating its parameters, we use the iterative gradient descent method to minimize the energy of the Gibbs distribution until it converges to a steady state.而不是估计其参数, 我们使用迭代梯度下降法, 以尽量减少吉布斯分布的能量, 直到它收敛到一个稳定的状态。
