基于谱聚类的彩色图像分割算法研究
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摘要
图像分割是图像识别领域需要解决的基本问题同时也是图像处理的难题之一。在计算机视觉领域,图像分割是将图像分别表达为不同对象的子区域的过程,图像分割的目的是简化或改变图像的表示形式,使得图像的分析和理解更为容易,它是从图像处理到图像分析的关键步骤。现有的彩色图像分割方法主要由灰度图像分割方法和颜色空间变换的组合构成,其中常见的灰度图像分割方法有：直方图阈值法、特征空间聚类法、基于区域的方法、边缘检测法、模糊方法、神经元网络、物理模型方法以及以上方法的组合,常见的颜色空间变换包括：RGB、YUV、LUV、HSI、LAB及以上空间的组合。而基于聚类的图像分割是近十几年来研究的热点问题,特别是谱聚类算法,因为它不但对于样本空间的分布没有限制而且收敛于全局最优解,并且在彩色图像的分割中也能取得较为理想的分割结果。但是谱聚类算法本身在参数定义、海量数据运算、聚类个数选取等方面还有许多没有解决的问题,因此对于谱聚类方法的研究还仅仅是一个开始。
本文研究基于谱聚类的彩色图像分割算法,主要从上述灰度图像的分割方法和颜色空间的变换两方面对彩色图像的分割进行分析和研究,研究工作主要分为以下几点：(1)谱聚类算法的实质就是把高维空间映射到低维空间中去,并且获得了能够使同类分布更为紧致的新的数据表示。然而在如何自定义参数、如何处理大规模数据以及如何自动确定最终聚类个数等问题中,传统的谱聚类算法都没有给出很好的解决方法。针对这一问题,提出了基于多层次化结构Nystrom方法的自适应谱聚类算法,将谱聚类算法中基于多层次化结构的方法和基于Nystrom采样的方法结合起来,有效减少了运算时间、解决了数据量较大时计算过程中内存溢出的问题,并且在k均值聚类中通过对特征间隙(eigengap)的分析,自适应的选择k值的大小,解决了自动确定聚类数目的问题。实验证明,基于多层次化结构Nystrom方法的自适应谱聚类算法在运算时间和分割结果上都优于基于Nystrom方法的谱聚类算法(Spectral Clustering-Nystrom,SC-N)。
(2)RGB颜色空间是非线性的,三个分量之间存在很强的相关性,并且由于色彩辨别阈(Just Noticeable Difference)的存在使得在RGB颜色空间上处理彩色图像很不方便。引入LUV颜色空间的目的是建立与人的视觉统一的颜色空间,LUV颜色空间具备一致性和均一性且各颜色分量之间不相关,因此它被广泛应用于计算机彩色图像处理领域,并获得了较好的效果。实验结果表明,在LUV颜色空间中进行图像分割,彩色图像的纹理、边缘区域取得了更好的分割效果。
(3)随着图像分辨率的不断增大,传统的基于像素的彩色图像分割算法的运算时间越来越长,如何降低数据运算量变成了彩色图像分割中的一大难题。利用分水岭算法对图像进行过分割,虽然对图像进行了过分割,却很好的保存了图像的边缘信息,将分水岭算法过分割的劣势变成了优势；然后以保存了图像边缘信息的每一个小区域为对象采用谱聚类算法进行聚类,降低了谱聚类算法的数据运算量；同时引入must-link和cannot-link成对约束信息,在K均值算法中加入惩罚项来限制违反成对约束的样本,进一步提高了算法的分割精度。实验证明,基于区域的半监督谱聚类算法有效降低了图像分割的时间,进一步提高了图像分割的精度和稳定性。
Image segmentation is the basic unresolved problem in the field of image recognition, which is' also one of difficulties in the image processing. With regard to the domain of computer vision, image segmentation is a procedure that dividing the image into several sub-regions to express the different objects, which is intended to simplify or change the representation form of image so as to make it easier for the analysis and understanding of image. It is a key step from the image processing to image analysis. Current methods of colored images segmentation are mainly composed of the approaches of gray image segmentation and the combination of alternation of color space, there are several common methods of gray image segmentation, such as the histogram threshold, the clustering method of feature space, the approach based on area, the method of edge detection, fuzzy method, neural network, the method of physical model and combinations of the above-mentioned methods. The common transformation of color space includes the RGB, YUV, LUV, HSI, LAB and combinations of the former spaces. Image segmentation based on clustering is a hot issue in the past decades. In particular, the spectral clustering algorithm not only has no restriction towards the distribution of sample space and converges to the global optimal solution, but also obtains a relatively satisfying segmentation effect in the color image segmentation. However, there are several unresolved problems in the spectral clustering algorithm itself such as definition of parameters, computation of high-throughput data, selection of cluster number and so on. Therefore the study on spectral clustering method is just a start.
With regard to the segmentation methods of color images based on spectral clustering algorithm, this paper mainly analyzes and studies the color image segmentation from the two aspects of segmentation method of above-mentioned gray images and transformation of color space. The research work includes the following points:
(l)Firstly, the essence of spectral clustering algorithm is to project the data from the higher dimensional space to lower dimensional space and obtain the novel data expression which makes the distribution of identical cluster much more compact. However, the traditional spectral clustering algorithm performs not well in dealing with the problems such as self defining parameters, processing the high-throughput data and automatically determining the cluster number. Therefore this paper proposes a self-adaptive spectral clustering algorithm based on the Nystrom method of multi-hierarchical structure, which combines the spectral clustering algorithm based on the method of multi-hierarchical structure with the approach based on the Nystrom sampling in order to effectively reduce the time consumed, solve the problem of out of memory during the computation procedure of high-throughput data, and automatically determine the cluster number by means of the k value of self-adaptive selection through analyzing the eigengap when executing the k-means clustering algorithm. The simulation experiment turns out that the self-adaptive spectral clustering algorithm based on the Nystrom method of multi-hierarchical structure is superior to spectral clustering method based on Nystrom approach in terms of time consumed and segmentation effect.
(2)Secondly, the color space of RGB is non-linear and there are strong relationships among the three components. In addition, the existence of differential threshold of color makes it non-convenient for processing the color images in the RGB color space. Therefore the LUV color space is integrated to build up the coordinating color space with the human vision. Owing to that the LUV color space has the characters of consistency, homogeneity and irrelevances among the color components, it is widely applied to the field of color image processing of computer and obtains the better effect. The experiments prove that image segmentation in the LUV color space performs better from the perspective of both texture and marginal area of color images.
(3)Finally, with the continuous increment of image resolution, the traditional segmentation algorithms of color images based on pixel consume too much time. So it is difficult for the color image segmentation to reduce the computation time of data. Although adopting the watershed algorithm to divide images generate the over segmentation, the marginal information can be better preserved, which transforms the drawback of over segmentation to the advantage in the watershed algorithm. Afterwards regards each small area which contains the marginal information as object to cluster by means of spectral clustering algorithm for the aim of reducing the computation time of data of spectral clustering method. Simultaneously, the coupled restriction information of must-link and cannot-link are introduced and adding the punishing item into k-means algorithm to confine the samples of disobeying the coupled restriction in order to further improve the segmentation accuracy of algorithm. The experiments turn out that the semi-supervising spectral clustering algorithm based on area can effectively reduce the consumed time of image segmentation and meantime improve the accuracy and stability of image segmentation.
本文研究基于谱聚类的彩色图像分割算法,主要从上述灰度图像的分割方法和颜色空间的变换两方面对彩色图像的分割进行分析和研究,研究工作主要分为以下几点：(1)谱聚类算法的实质就是把高维空间映射到低维空间中去,并且获得了能够使同类分布更为紧致的新的数据表示。然而在如何自定义参数、如何处理大规模数据以及如何自动确定最终聚类个数等问题中,传统的谱聚类算法都没有给出很好的解决方法。针对这一问题,提出了基于多层次化结构Nystrom方法的自适应谱聚类算法,将谱聚类算法中基于多层次化结构的方法和基于Nystrom采样的方法结合起来,有效减少了运算时间、解决了数据量较大时计算过程中内存溢出的问题,并且在k均值聚类中通过对特征间隙(eigengap)的分析,自适应的选择k值的大小,解决了自动确定聚类数目的问题。实验证明,基于多层次化结构Nystrom方法的自适应谱聚类算法在运算时间和分割结果上都优于基于Nystrom方法的谱聚类算法(Spectral Clustering-Nystrom,SC-N)。
(2)RGB颜色空间是非线性的,三个分量之间存在很强的相关性,并且由于色彩辨别阈(Just Noticeable Difference)的存在使得在RGB颜色空间上处理彩色图像很不方便。引入LUV颜色空间的目的是建立与人的视觉统一的颜色空间,LUV颜色空间具备一致性和均一性且各颜色分量之间不相关,因此它被广泛应用于计算机彩色图像处理领域,并获得了较好的效果。实验结果表明,在LUV颜色空间中进行图像分割,彩色图像的纹理、边缘区域取得了更好的分割效果。
(3)随着图像分辨率的不断增大,传统的基于像素的彩色图像分割算法的运算时间越来越长,如何降低数据运算量变成了彩色图像分割中的一大难题。利用分水岭算法对图像进行过分割,虽然对图像进行了过分割,却很好的保存了图像的边缘信息,将分水岭算法过分割的劣势变成了优势；然后以保存了图像边缘信息的每一个小区域为对象采用谱聚类算法进行聚类,降低了谱聚类算法的数据运算量；同时引入must-link和cannot-link成对约束信息,在K均值算法中加入惩罚项来限制违反成对约束的样本,进一步提高了算法的分割精度。实验证明,基于区域的半监督谱聚类算法有效降低了图像分割的时间,进一步提高了图像分割的精度和稳定性。
Image segmentation is the basic unresolved problem in the field of image recognition, which is' also one of difficulties in the image processing. With regard to the domain of computer vision, image segmentation is a procedure that dividing the image into several sub-regions to express the different objects, which is intended to simplify or change the representation form of image so as to make it easier for the analysis and understanding of image. It is a key step from the image processing to image analysis. Current methods of colored images segmentation are mainly composed of the approaches of gray image segmentation and the combination of alternation of color space, there are several common methods of gray image segmentation, such as the histogram threshold, the clustering method of feature space, the approach based on area, the method of edge detection, fuzzy method, neural network, the method of physical model and combinations of the above-mentioned methods. The common transformation of color space includes the RGB, YUV, LUV, HSI, LAB and combinations of the former spaces. Image segmentation based on clustering is a hot issue in the past decades. In particular, the spectral clustering algorithm not only has no restriction towards the distribution of sample space and converges to the global optimal solution, but also obtains a relatively satisfying segmentation effect in the color image segmentation. However, there are several unresolved problems in the spectral clustering algorithm itself such as definition of parameters, computation of high-throughput data, selection of cluster number and so on. Therefore the study on spectral clustering method is just a start.
With regard to the segmentation methods of color images based on spectral clustering algorithm, this paper mainly analyzes and studies the color image segmentation from the two aspects of segmentation method of above-mentioned gray images and transformation of color space. The research work includes the following points:
(l)Firstly, the essence of spectral clustering algorithm is to project the data from the higher dimensional space to lower dimensional space and obtain the novel data expression which makes the distribution of identical cluster much more compact. However, the traditional spectral clustering algorithm performs not well in dealing with the problems such as self defining parameters, processing the high-throughput data and automatically determining the cluster number. Therefore this paper proposes a self-adaptive spectral clustering algorithm based on the Nystrom method of multi-hierarchical structure, which combines the spectral clustering algorithm based on the method of multi-hierarchical structure with the approach based on the Nystrom sampling in order to effectively reduce the time consumed, solve the problem of out of memory during the computation procedure of high-throughput data, and automatically determine the cluster number by means of the k value of self-adaptive selection through analyzing the eigengap when executing the k-means clustering algorithm. The simulation experiment turns out that the self-adaptive spectral clustering algorithm based on the Nystrom method of multi-hierarchical structure is superior to spectral clustering method based on Nystrom approach in terms of time consumed and segmentation effect.
(2)Secondly, the color space of RGB is non-linear and there are strong relationships among the three components. In addition, the existence of differential threshold of color makes it non-convenient for processing the color images in the RGB color space. Therefore the LUV color space is integrated to build up the coordinating color space with the human vision. Owing to that the LUV color space has the characters of consistency, homogeneity and irrelevances among the color components, it is widely applied to the field of color image processing of computer and obtains the better effect. The experiments prove that image segmentation in the LUV color space performs better from the perspective of both texture and marginal area of color images.
(3)Finally, with the continuous increment of image resolution, the traditional segmentation algorithms of color images based on pixel consume too much time. So it is difficult for the color image segmentation to reduce the computation time of data. Although adopting the watershed algorithm to divide images generate the over segmentation, the marginal information can be better preserved, which transforms the drawback of over segmentation to the advantage in the watershed algorithm. Afterwards regards each small area which contains the marginal information as object to cluster by means of spectral clustering algorithm for the aim of reducing the computation time of data of spectral clustering method. Simultaneously, the coupled restriction information of must-link and cannot-link are introduced and adding the punishing item into k-means algorithm to confine the samples of disobeying the coupled restriction in order to further improve the segmentation accuracy of algorithm. The experiments turn out that the semi-supervising spectral clustering algorithm based on area can effectively reduce the consumed time of image segmentation and meantime improve the accuracy and stability of image segmentation.
引文
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