支持向量机及其在医学图像分割中的应用
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摘要
医学图像分割始终是医学图像处理中重要的也是非常困难的研究课题。传统的模
式分类方法以经验风险最小化为归纳原则,只有当训练样本数趋于无穷时,其性能才
能达到理论上的最优。然而在医学图像分割中,训练样本通常是有限的,所以传统模
式分类方法通常难以取得很好的结果。本文借助支持向量机方法在小样本、非线性及
高维特征空间中具有良好的分类性能,针对医学图像分割的特点,对支持向量机方法
及其在医学图像分割中的应用进行了深入地研究,主要工作包括:
1、针对在医学图像分割时,采用交互式方式得到的训练样本数通常是有限的,
以致传统模式分类方法对渐进性的前提条件往往得不到满足。本文结合医学图像中目
标具有分散的特点,借助支持向量机良好的分类性能,特别在小样本、非线性及高维
特征空间中具有较好的推广能力,将支持向量机方法应用于医学图像分割。采用仿真
MR 图像进行了脑组织分类,相对于神经网络与模糊 C 均值两种方法,支持向量机方
法具有较小的时间代价,优良的分类性能。并将在不同训练样本数及不同的切片中进
行了对比实验,进一步验证了支持向量机方法在小样本的情况下具有良好的分类性
能。
2、结合磁共振图像中提取的图像特征可用高斯分布较好地近似描述的特点及高
斯核函数在其它领域中成功的应用,本文在利用支持向量机方法对医学图像进行分割
时,选择高斯径向基函数作为核函数。结合支持向量机方法的最优判别函数仅仅与支
持向量有关,并且支持向量为高斯核中心的特点,提出了一种利用支持向量求取高斯
核函数参数的有效方法,解决了高斯核函数参数在实际使用中不易确定的问题。
3、研究了纹理与灰度组合以及区域象素灰度两组图像特征。在提取纹理与灰度
组合特征时,将由灰度共生矩阵提取的 6 种纹理统计特征(对比度、相关性、和均值、
和方差、和熵、差熵)及 3 种灰度特征(象素灰度,象素灰度的中值滤波值及平均值)
作为医学图像脑组织分类时纹理与灰度组合的图像特征。在提取区域象素的灰度特征
时,除了象素本身的灰度,还提取了该象素邻域内所有象素的灰度。针对使用方形窗
口区域的不足,结合医学图像中各种分割目标之间具有相对光滑的特点,提出了一种
基于圆形区域象素灰度特征的提取方法,该组特征具有优良的分类性能,较小的计算
代价。
4、针对传统支持向量机方法中存在对噪声或野值敏感的问题,依据特征空间中
样本之间的紧密度,提出了一种基于紧密度的模糊支持向量机方法。在确定样本的隶
II
属度时,不仅考虑了样本与类中心之间的关系,还考虑了各个样本之间的紧密度,并
提出一种利用包围同一类中样本的最小球半径来度量样本之间紧密度的方法,对分布
在半径内与外的样本分别采用两种不同的方式计算其各自样本的隶属度,有利于将野
值或含噪声样本与有效样本进行区分。仿真图像的实验结果表明,与传统支持向量机
方法及基于线性距离与基于 S 型函数的两种模糊支持向量机方法相比,基于紧密度的
模糊支持向量机方法具有更好的抗噪性能及分类能力。
5、针对传统支持向量机方法不提供后验概率输出的问题,结合医学图像分类时
不确定性的特点,提出一种对传统支持向量机方法进行输出概率建模的直接拟合方
法。在该方法中,从信息熵的角度,提出了一种确定该拟合模型参数的最大熵拟合准
则。在多类分类问题输出概率建模中,提出了加权近似方法与直接求解方法两种输出
概率建模方法,在这两种方法中,在对多个两类支持向量机的概率输出进行组合时,
充分考虑了各个两类支持向量机的差异,并分别提供了不同的权系数。仿真图像的实
验结果表明,本文提出的直接求解方法与近似方法及 Pairwise Coupling 方法相比,不
仅具有较好的分类性能,而且得到的后验概率具有较好的概率分布形态。
6、针对支持向量机在大规模样本学习时,学习速度慢,需要存储空间大等问题,
提出了一种将支持向量机方法与 C 均值方法结合的 SVM-CM 方法。在该方法中,先采
用 C 均值方法对训练样本集进行聚类,然后依据聚类域中样本的类型特点确定样本的
约简方式。仿真图像数据实验结果表明,SVM-CM 方法提高了支持向量机的学习速度,
同时支持向量机的分类精度几乎没有降低,表现出较好的样本约简性能。
7、采用基于紧密度的模糊支持向量机及输出概率建模方法对两个 MR 图像实例分
别进行了正常脑组织分类及脑肿瘤组织的分类与提取。首先对 MR 实例图像进行剔除
非脑组织处理,然后对正常脑组织或脑肿瘤组织进行分类与提取,并由医生对分类结
果采用主观评估方法进行评价。在对脑肿瘤进行提取时,将由基于紧密度的模糊支持
向量机及输出概率建模方法提取出的脑肿瘤区域与由医生参考对应切片的 T2 加权 MR
图像,在原始切片上勾画的脑肿瘤区域进行对比,通过观察和对比,相对于模糊 C 均
值及传统支持向量机方法,采用基于紧密度的模糊支持向量机及输出概率建模方法提
取的脑肿瘤区域与专家手工勾画的脑肿瘤区域比较接近,获得了较好的结果。
Medical image segmentation is an important and difficult issue in medical image processing. The
performance of traditional pattern classification methods, which are based on the principle of
Experiential Risk Minimization, achieve the best, only when the number of training samples approaches
infinity. Unfortunately, the number of training samples is actually limited and the data dimension is high,
thus the performance of traditional pattern classification algorithms is deteriorated in medical image
segmentation. Taken into account the good generalization of support vector machine in small samples,
nonlinearity and high dimension space and features of medical images, this dissertation deeply studies
support vector machine methods and their application in medical image segmentation. The main
contributions of this thesis are given below.
1. For the numbered samples by the interactive mode in medical image segmentation, the
precondition of infinity for traditional pattern classification methods can not be satisfied. Given the
advantages of the good generalization for support vector machine in the small-sample, and the disperse
feature of the segmented objects in medical images, support vector machine is used to perform
segmentation of medical images. The brain tissues are classified from the stimulant MR images.
Experiment results show that the SVM classifier offers lower computational time and better
classification precision than the BP and the FCM methods. The comparative experiments are made using
the different number of training samples and the different scans, and it confirms that SVM method holds
the better classification ability in the small-sample.
2. Considering that the image features extracted from the medical images can be well characterized
by the Gaussian function, and the successful applications of the Gaussian function in other fields, we
choose the Gaussian function as the kernel for segmentation in medical images. Furthermore, given the
fact that the optimal discriminative function is determined by the support vectors, and the support
vectors are centered as the Gaussian function, we put forward an effective algorithm which provides the
parameter of Gaussian kernel using support vectors, and it solves a difficult problem for the parameter of
Gaussian kernel in application.
3. Two groups of image features, the combined features both textures and gray features, and gray
level features based on window region, are studied. 6 textures statistics features based on the
co-occurrence matrix of gray level (namely, contrast, correlation, sum average, sum variance, sum
IV
entropy and difference entropy) and 3 gray features (namely, the pixel intensity, the median filter
intensity and the average intensity of window size of each pixel) are chosen as the image combined
features both texture and gray in the brain tissues classification. The gray level values of the pixels and
the pixel intensities in the neighborhood are used for gray level features extraction. Taking into account
the disadvantage about the square window region in extracting the gray level features, and the slick
surface among the segmented objects in medical images, we design a new method for extracting the gray
level features based on the circle window region. The gray level features own the better classification
ability and the lower time.
4. Since SVM is very sensitive to outliers and noises in the training set and the fuzzy feature exists
in medical images, we hereby studied fuzzy support vector machine based on the affinity among samples.
The fuzzy membership is defined by not only the relation between a sample and its cluster center, but
also the affinity among samples. A method defining the affinity among samples is proposed using a
sphere with minimum volume while containing maximum of the samples. Then, the fuzzy membership
is defined according to the position of samples in sphere space, which distinguished between the val
式分类方法以经验风险最小化为归纳原则,只有当训练样本数趋于无穷时,其性能才
能达到理论上的最优。然而在医学图像分割中,训练样本通常是有限的,所以传统模
式分类方法通常难以取得很好的结果。本文借助支持向量机方法在小样本、非线性及
高维特征空间中具有良好的分类性能,针对医学图像分割的特点,对支持向量机方法
及其在医学图像分割中的应用进行了深入地研究,主要工作包括:
1、针对在医学图像分割时,采用交互式方式得到的训练样本数通常是有限的,
以致传统模式分类方法对渐进性的前提条件往往得不到满足。本文结合医学图像中目
标具有分散的特点,借助支持向量机良好的分类性能,特别在小样本、非线性及高维
特征空间中具有较好的推广能力,将支持向量机方法应用于医学图像分割。采用仿真
MR 图像进行了脑组织分类,相对于神经网络与模糊 C 均值两种方法,支持向量机方
法具有较小的时间代价,优良的分类性能。并将在不同训练样本数及不同的切片中进
行了对比实验,进一步验证了支持向量机方法在小样本的情况下具有良好的分类性
能。
2、结合磁共振图像中提取的图像特征可用高斯分布较好地近似描述的特点及高
斯核函数在其它领域中成功的应用,本文在利用支持向量机方法对医学图像进行分割
时,选择高斯径向基函数作为核函数。结合支持向量机方法的最优判别函数仅仅与支
持向量有关,并且支持向量为高斯核中心的特点,提出了一种利用支持向量求取高斯
核函数参数的有效方法,解决了高斯核函数参数在实际使用中不易确定的问题。
3、研究了纹理与灰度组合以及区域象素灰度两组图像特征。在提取纹理与灰度
组合特征时,将由灰度共生矩阵提取的 6 种纹理统计特征(对比度、相关性、和均值、
和方差、和熵、差熵)及 3 种灰度特征(象素灰度,象素灰度的中值滤波值及平均值)
作为医学图像脑组织分类时纹理与灰度组合的图像特征。在提取区域象素的灰度特征
时,除了象素本身的灰度,还提取了该象素邻域内所有象素的灰度。针对使用方形窗
口区域的不足,结合医学图像中各种分割目标之间具有相对光滑的特点,提出了一种
基于圆形区域象素灰度特征的提取方法,该组特征具有优良的分类性能,较小的计算
代价。
4、针对传统支持向量机方法中存在对噪声或野值敏感的问题,依据特征空间中
样本之间的紧密度,提出了一种基于紧密度的模糊支持向量机方法。在确定样本的隶
II
属度时,不仅考虑了样本与类中心之间的关系,还考虑了各个样本之间的紧密度,并
提出一种利用包围同一类中样本的最小球半径来度量样本之间紧密度的方法,对分布
在半径内与外的样本分别采用两种不同的方式计算其各自样本的隶属度,有利于将野
值或含噪声样本与有效样本进行区分。仿真图像的实验结果表明,与传统支持向量机
方法及基于线性距离与基于 S 型函数的两种模糊支持向量机方法相比,基于紧密度的
模糊支持向量机方法具有更好的抗噪性能及分类能力。
5、针对传统支持向量机方法不提供后验概率输出的问题,结合医学图像分类时
不确定性的特点,提出一种对传统支持向量机方法进行输出概率建模的直接拟合方
法。在该方法中,从信息熵的角度,提出了一种确定该拟合模型参数的最大熵拟合准
则。在多类分类问题输出概率建模中,提出了加权近似方法与直接求解方法两种输出
概率建模方法,在这两种方法中,在对多个两类支持向量机的概率输出进行组合时,
充分考虑了各个两类支持向量机的差异,并分别提供了不同的权系数。仿真图像的实
验结果表明,本文提出的直接求解方法与近似方法及 Pairwise Coupling 方法相比,不
仅具有较好的分类性能,而且得到的后验概率具有较好的概率分布形态。
6、针对支持向量机在大规模样本学习时,学习速度慢,需要存储空间大等问题,
提出了一种将支持向量机方法与 C 均值方法结合的 SVM-CM 方法。在该方法中,先采
用 C 均值方法对训练样本集进行聚类,然后依据聚类域中样本的类型特点确定样本的
约简方式。仿真图像数据实验结果表明,SVM-CM 方法提高了支持向量机的学习速度,
同时支持向量机的分类精度几乎没有降低,表现出较好的样本约简性能。
7、采用基于紧密度的模糊支持向量机及输出概率建模方法对两个 MR 图像实例分
别进行了正常脑组织分类及脑肿瘤组织的分类与提取。首先对 MR 实例图像进行剔除
非脑组织处理,然后对正常脑组织或脑肿瘤组织进行分类与提取,并由医生对分类结
果采用主观评估方法进行评价。在对脑肿瘤进行提取时,将由基于紧密度的模糊支持
向量机及输出概率建模方法提取出的脑肿瘤区域与由医生参考对应切片的 T2 加权 MR
图像,在原始切片上勾画的脑肿瘤区域进行对比,通过观察和对比,相对于模糊 C 均
值及传统支持向量机方法,采用基于紧密度的模糊支持向量机及输出概率建模方法提
取的脑肿瘤区域与专家手工勾画的脑肿瘤区域比较接近,获得了较好的结果。
Medical image segmentation is an important and difficult issue in medical image processing. The
performance of traditional pattern classification methods, which are based on the principle of
Experiential Risk Minimization, achieve the best, only when the number of training samples approaches
infinity. Unfortunately, the number of training samples is actually limited and the data dimension is high,
thus the performance of traditional pattern classification algorithms is deteriorated in medical image
segmentation. Taken into account the good generalization of support vector machine in small samples,
nonlinearity and high dimension space and features of medical images, this dissertation deeply studies
support vector machine methods and their application in medical image segmentation. The main
contributions of this thesis are given below.
1. For the numbered samples by the interactive mode in medical image segmentation, the
precondition of infinity for traditional pattern classification methods can not be satisfied. Given the
advantages of the good generalization for support vector machine in the small-sample, and the disperse
feature of the segmented objects in medical images, support vector machine is used to perform
segmentation of medical images. The brain tissues are classified from the stimulant MR images.
Experiment results show that the SVM classifier offers lower computational time and better
classification precision than the BP and the FCM methods. The comparative experiments are made using
the different number of training samples and the different scans, and it confirms that SVM method holds
the better classification ability in the small-sample.
2. Considering that the image features extracted from the medical images can be well characterized
by the Gaussian function, and the successful applications of the Gaussian function in other fields, we
choose the Gaussian function as the kernel for segmentation in medical images. Furthermore, given the
fact that the optimal discriminative function is determined by the support vectors, and the support
vectors are centered as the Gaussian function, we put forward an effective algorithm which provides the
parameter of Gaussian kernel using support vectors, and it solves a difficult problem for the parameter of
Gaussian kernel in application.
3. Two groups of image features, the combined features both textures and gray features, and gray
level features based on window region, are studied. 6 textures statistics features based on the
co-occurrence matrix of gray level (namely, contrast, correlation, sum average, sum variance, sum
IV
entropy and difference entropy) and 3 gray features (namely, the pixel intensity, the median filter
intensity and the average intensity of window size of each pixel) are chosen as the image combined
features both texture and gray in the brain tissues classification. The gray level values of the pixels and
the pixel intensities in the neighborhood are used for gray level features extraction. Taking into account
the disadvantage about the square window region in extracting the gray level features, and the slick
surface among the segmented objects in medical images, we design a new method for extracting the gray
level features based on the circle window region. The gray level features own the better classification
ability and the lower time.
4. Since SVM is very sensitive to outliers and noises in the training set and the fuzzy feature exists
in medical images, we hereby studied fuzzy support vector machine based on the affinity among samples.
The fuzzy membership is defined by not only the relation between a sample and its cluster center, but
also the affinity among samples. A method defining the affinity among samples is proposed using a
sphere with minimum volume while containing maximum of the samples. Then, the fuzzy membership
is defined according to the position of samples in sphere space, which distinguished between the val
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