基于三维SVMs的肺部CT中的结节检测算法
摘要
计算机辅助肺部CT图像中的结节检测技术属于数字图像处理和医学的交叉课题。可靠的检测结果需凭借有效的图像分割、特征提取和机器学习技术。
候选结节的分割与提取,及其精确识别(去除假阳性)是计算机辅助肺部结节检测的两大主要部分。针对这两个部分,国内外现有算法主要的研究重点可以归纳为：
(1)在候选结节的分割和提取这一环节,研究重点是对因为与正常组织粘连程度较大而被漏检的候选结节的修复。由于某些粘连型结节与周围的正常组织灰度相近,无论用灰度阈值法或基于滤波器的图像增强法都很难加以区别；而由于肺部组织的复杂性,也很难用模板匹配法提取。
(2)在候选结节的精确识别(去除假阳性)这一环节,研究重点是去除一些由于大的血管和支气管的截面造成的假阳性判断。肺部结节通常被定义为一定半径范围内的类圆形,而大的血管和支气管在二维CT断层中的截面通常也为类圆形,很难加以区分；另外,传统的机器学习方法如神经网络等,存在网络不稳定(对初始权值敏感)、维数灾难、过收敛和局部最小化等问题,严重制约识别效果。
针对以上问题,论文的主要研究目标为：在三维矩阵中分析候选结节的三维特性,以存在于连续断层间的候选结节的三维感兴趣体(Volume of Interest, VOI)代替传统方法中的单幅CT图像中的二维感兴趣区(Region of Interest, ROI),作为提取和识别的对象,有效提高检测精确度、抑制假阳性判断。具体内容如下：
(1)为了在三维空间中分析更多的有用信息,以达到有效去除肺部各组织之间的粘连的目的,提出一种基于快速三维主成分分析(Three Dimension Principal Component Analysis,3DPCA)的肺部病灶提取算法。首先用3DPCA法在CT序列构成的三维空间内提取特征点；然后,以提取出的特征点为种子点,进行区域生长以获取完整的疑似病灶区域；最后,根据医学图像具体特征,设计一种高维张量奇异值分解(Higher-order Tensor Singular Value Decomposition, HOSVD)的简化分解算法来降低3DPCA的计算复杂度。3DPCA相比于传统的2DPCA,可在一定程度上提高病灶区的提取精度；另外,快速3DPCA与3DPCA比较,计算次数可降低到约为原来的1/3。
(2)为了有效修复由于与正常组织粘连程度较大而被漏提取的结节,提出一种基于相邻模板限制的区域生长法的候选结节提取算法。首先结合阈值法、圆点滤波器增强法和滚球法对整个CT序列进行逐层地预提取；然后,以所有包含候选结节的断层作为基准层,以候选结节的位置作为基准位置,以基准层的肺区作为限制条件,在相邻层中寻找种子点并进行区域生长,有效修复被漏提取的候选结节,并构成候选结节的三维VOI。通过实验可以证明,该方法的提取效果优于单独的滚球法、区域生长法,以及Snake算法、GVF Snake算法。提取出的三维VOI是下一步的基于三维SVMs精确识别(去除假阳性)的基础。
(3)为了有效提高候选结节的识别精度,考虑以三维VOI作为分类器的识别对象,代替传统算法中的二维ROI,提出基于三维矩阵模式的支持向量机(Support Vector Machines based on 3D matrix, SVMs3Dmatrix)算法,可以处理基于三维矩阵模式的输入样本。
a.展开模式的SVMs3Dmatrix
首先利用高维张量的展开方法(本文中指三维矩阵),将基于三维矩阵模式的输入样本从三维空间的三个方向展成三个不同的二维矩阵；然后,分别对每个二维矩阵进行基于矩阵模式的SVMs (SVMs based on matrix, SVMsmatrix)的识别,得到三个不同的决策函数；最后利用三人投票选举法得到最终决策。
b.非展开模式的SVMs3Dmatrix
利用三维矩阵的乘法法则,改进传统SVMs,使之可以直接处理基于三维矩阵模式的输入样本,而避免了三维矩阵的展开：通过增加右乘向量的方式来重新构造优化条件；然后利用梯度下降法迭代地求解原来的左乘向量和两个新增的右乘向量。
通过实验可以证明,SVMs3Dmatrix与二维线性判别分析(Two Dimension Linear Discrimination Analysis,2D-LDA)、大规模样本训练的神经网络(Mative Training Argificial Nural Network, MTANN)、SVMsmatrix相比,可以更精确地区分结节与非结节。并且,非展开模式的SVMs3Dmatrix与展开模式的SVMs3Dmatrix相比,由于可以直接处理基于三维矩阵模式的输入而避免分别处理三个展开后的大矩阵,在提高分类精确度的基础上进一步减少内存占用。
(4)为了更好地符合肺部结节的复杂性、多样性,在二分类SVMs3Dmatrix基础上,进一步提出多分类的SVMs3Dmatrix (Multi-class SVMs3Dmatrix, MC-SVMs3Dmatrix)。首先分析当前存在的多种MC-SVMs方法,选择一种可以并行处理多分类问题且不存在“不可分类区”这一缺陷的一种基于编码的MC-SVMs,将之与二分类的SVMs3Dmatrix相结合,设计一种基于编码的MC-SVMs3Dmatrix。通过实验可以证明,MC-SVMs3Dmatrix的识别效果更优于二分类SVMs3Dmatrix。
本文数据来自于XX肿瘤医院胸一、胸二、胸三,三个科室从2009.6-2010.6的96组临床病例,每一组均配有专家会诊后的批注。用国际上计算机辅助肺部结节检测中几种较新算法与本文算法做出比较,并用通用的ROC曲线方法分析实验结果,可以证明本文算法的有效性。
Computer-aided Diagnosis (CAD) of lung nodules is the intersecting subject of image processing and medicine. Realible results of lung CAD depend on effective image segmentation, extraction and machine learning technology. Lung CAD usually includes two main parts:extraction and accurate recognition of potential nodules. Major focuses of the two parts by current lung CAD schemes can be summarized as follows:
(1)In the part of segmentation and extraction, researches focus on repairing the lossed nodules which adhere to normal structure seriously. As gray level of these juxta-nodules is usually similar to the surrounding normal structures, they are hard to be distinguished from normal structures by threshold method and image enhancement; On the other hand, as the complex of lung areas, they are hard to be extracted by mask matching.
(2)In the part of accurate recognition, researches focus on removing False Positives (FP) caused by some large vessels and bronchus. Lung nodules usually are defined as sphere with the diameter in a certain range, but cross profiles of some large vessels are also sphere, which would increase FP. In addition, instability, minimization and overfitting of some traditional machine learning methods such as Nerual Network (NN) would affect seriously the performance of recognition.
Aiming at above problems, main purpose in the paper is effectively improving the performance of classifiers. It would be achived by analyzing 3D features of potential nodules in 3D space, and 3D Volum of Interest (VOI) of potential nodules in successive sections are chosen as the identify object instead of 2D ROI. The details are as follows:
(1)In order to analyze more information in 3D space and effectively remove the adhesions between different structures, a fast Three Dimension Principle Component Analysis (3DPCA) is presented. Firstly, feature points in 3D space made up of a CT set are extracted by 3DPCA; Secondly, region grow method is used to obtain the whole suspected lesions by choosing the feature points as the seed points; Lastly, a fast decomposition algorithm of Higher-Order Singular Value Decomposition (HOSVD) is designed in order to reduce computation of 3DPCA. Recognition accuracy of lung lesions is improved by 3DPCA comparing with traditional 2DPCA, and computation is reduced to 1/3 by fast 3DPCA.
(2)In order to repair lossed potential nodules which adhere to normal structure seriously, extraction algorithm based on restrict by successive sections is proposed. Firstly, potential nodules in all sections are extracted respectively by combining of threshold method, image enhancement (by Dot Filter) and rolling ball method; Secondly, let the sections including potential nodules as base sections, locations of potential nodules as base locations and lung area of base sections as restrict conditions; At last, lossed potential nodules are repaired by region grow method. It is proved by experiment that the lossed nodules can be repaired more effectively by above extraction algorithm comparing with rolling ball method, region grow method, Snake and GVF Snake method. And 3D VOI of potential nodules are made for further recognition.
(3)In order to improve performance of recognition,3D VOI of potential nodules are chosen as the identification objects instead of traditional 2D ROI. For above reason, SVMs3Dmatrix which can process the input samples based on 3D matrix patterns is proposed.
a.Unfolding SVMs3Dmatrix
Firstly, unfolding method of high-order tensor is used to unfold the input sample based on 3D matrix into three 2D matrixes; Secondly, SVMsmatnx is used to obtain three decisions of the three 2D matrixes; At last, the three people's voting method is used to obtain the final decision.
b.Non-unfolding SVMs3Dmatrix
Multiplication of 3D matrix is used to design non-unfolding SVMs3Dmatrix, which can process input samples based on 3D matrix patterns directly and avoiding unfolding. Firstly, new optimum codition of SVMs is conducted by increasing two right-vectors; Secondly, the left-vector and two right-vectors can be solved iteratively by the gradient descent method.
It is proved by experiment that the perfomence of SVMs3Dmatrix is better than that of Two Dimension Linear Discrimination Analysis (2D-LDA), Massitive Training Artificial Neural Network (MTANN) and SVMsmatrix. Furthermore, as avoiding the unfolding, memory occupy of non-unfolding SVMs3Dmatrix is effectively reduced comparing with that of unfolding SVMs3Dmatrix.
(4) In order to better meet complex and variety of lung nodules, Multi-class SVMs based on 3D matrix pattern (MC-SVMs3Dmatrix) is further designed on the basis of two-class SVMs3Dmatrix. Firstly, several current MC-SVMs are compared, and sencondly, one based on encoding is chosen to be extended to MC-SVMs3Dmatrix. It is proved by experiment that the performance of MC-SVMs3Dmatrix is better than that of two-class SVMs3Dmatrix.
Data set in the paper is made up of 96 cases form Chest No.1-No.3 in XX Tumor Hospital (2009.6-2010.6). All of them are with expert notations. Other CAD schemes and method in the paper are compared by ROC. The results confirm the availability of the method in the paper.
候选结节的分割与提取,及其精确识别(去除假阳性)是计算机辅助肺部结节检测的两大主要部分。针对这两个部分,国内外现有算法主要的研究重点可以归纳为：
(1)在候选结节的分割和提取这一环节,研究重点是对因为与正常组织粘连程度较大而被漏检的候选结节的修复。由于某些粘连型结节与周围的正常组织灰度相近,无论用灰度阈值法或基于滤波器的图像增强法都很难加以区别；而由于肺部组织的复杂性,也很难用模板匹配法提取。
(2)在候选结节的精确识别(去除假阳性)这一环节,研究重点是去除一些由于大的血管和支气管的截面造成的假阳性判断。肺部结节通常被定义为一定半径范围内的类圆形,而大的血管和支气管在二维CT断层中的截面通常也为类圆形,很难加以区分；另外,传统的机器学习方法如神经网络等,存在网络不稳定(对初始权值敏感)、维数灾难、过收敛和局部最小化等问题,严重制约识别效果。
针对以上问题,论文的主要研究目标为：在三维矩阵中分析候选结节的三维特性,以存在于连续断层间的候选结节的三维感兴趣体(Volume of Interest, VOI)代替传统方法中的单幅CT图像中的二维感兴趣区(Region of Interest, ROI),作为提取和识别的对象,有效提高检测精确度、抑制假阳性判断。具体内容如下：
(1)为了在三维空间中分析更多的有用信息,以达到有效去除肺部各组织之间的粘连的目的,提出一种基于快速三维主成分分析(Three Dimension Principal Component Analysis,3DPCA)的肺部病灶提取算法。首先用3DPCA法在CT序列构成的三维空间内提取特征点；然后,以提取出的特征点为种子点,进行区域生长以获取完整的疑似病灶区域；最后,根据医学图像具体特征,设计一种高维张量奇异值分解(Higher-order Tensor Singular Value Decomposition, HOSVD)的简化分解算法来降低3DPCA的计算复杂度。3DPCA相比于传统的2DPCA,可在一定程度上提高病灶区的提取精度；另外,快速3DPCA与3DPCA比较,计算次数可降低到约为原来的1/3。
(2)为了有效修复由于与正常组织粘连程度较大而被漏提取的结节,提出一种基于相邻模板限制的区域生长法的候选结节提取算法。首先结合阈值法、圆点滤波器增强法和滚球法对整个CT序列进行逐层地预提取；然后,以所有包含候选结节的断层作为基准层,以候选结节的位置作为基准位置,以基准层的肺区作为限制条件,在相邻层中寻找种子点并进行区域生长,有效修复被漏提取的候选结节,并构成候选结节的三维VOI。通过实验可以证明,该方法的提取效果优于单独的滚球法、区域生长法,以及Snake算法、GVF Snake算法。提取出的三维VOI是下一步的基于三维SVMs精确识别(去除假阳性)的基础。
(3)为了有效提高候选结节的识别精度,考虑以三维VOI作为分类器的识别对象,代替传统算法中的二维ROI,提出基于三维矩阵模式的支持向量机(Support Vector Machines based on 3D matrix, SVMs3Dmatrix)算法,可以处理基于三维矩阵模式的输入样本。
a.展开模式的SVMs3Dmatrix
首先利用高维张量的展开方法(本文中指三维矩阵),将基于三维矩阵模式的输入样本从三维空间的三个方向展成三个不同的二维矩阵；然后,分别对每个二维矩阵进行基于矩阵模式的SVMs (SVMs based on matrix, SVMsmatrix)的识别,得到三个不同的决策函数；最后利用三人投票选举法得到最终决策。
b.非展开模式的SVMs3Dmatrix
利用三维矩阵的乘法法则,改进传统SVMs,使之可以直接处理基于三维矩阵模式的输入样本,而避免了三维矩阵的展开：通过增加右乘向量的方式来重新构造优化条件；然后利用梯度下降法迭代地求解原来的左乘向量和两个新增的右乘向量。
通过实验可以证明,SVMs3Dmatrix与二维线性判别分析(Two Dimension Linear Discrimination Analysis,2D-LDA)、大规模样本训练的神经网络(Mative Training Argificial Nural Network, MTANN)、SVMsmatrix相比,可以更精确地区分结节与非结节。并且,非展开模式的SVMs3Dmatrix与展开模式的SVMs3Dmatrix相比,由于可以直接处理基于三维矩阵模式的输入而避免分别处理三个展开后的大矩阵,在提高分类精确度的基础上进一步减少内存占用。
(4)为了更好地符合肺部结节的复杂性、多样性,在二分类SVMs3Dmatrix基础上,进一步提出多分类的SVMs3Dmatrix (Multi-class SVMs3Dmatrix, MC-SVMs3Dmatrix)。首先分析当前存在的多种MC-SVMs方法,选择一种可以并行处理多分类问题且不存在“不可分类区”这一缺陷的一种基于编码的MC-SVMs,将之与二分类的SVMs3Dmatrix相结合,设计一种基于编码的MC-SVMs3Dmatrix。通过实验可以证明,MC-SVMs3Dmatrix的识别效果更优于二分类SVMs3Dmatrix。
本文数据来自于XX肿瘤医院胸一、胸二、胸三,三个科室从2009.6-2010.6的96组临床病例,每一组均配有专家会诊后的批注。用国际上计算机辅助肺部结节检测中几种较新算法与本文算法做出比较,并用通用的ROC曲线方法分析实验结果,可以证明本文算法的有效性。
Computer-aided Diagnosis (CAD) of lung nodules is the intersecting subject of image processing and medicine. Realible results of lung CAD depend on effective image segmentation, extraction and machine learning technology. Lung CAD usually includes two main parts:extraction and accurate recognition of potential nodules. Major focuses of the two parts by current lung CAD schemes can be summarized as follows:
(1)In the part of segmentation and extraction, researches focus on repairing the lossed nodules which adhere to normal structure seriously. As gray level of these juxta-nodules is usually similar to the surrounding normal structures, they are hard to be distinguished from normal structures by threshold method and image enhancement; On the other hand, as the complex of lung areas, they are hard to be extracted by mask matching.
(2)In the part of accurate recognition, researches focus on removing False Positives (FP) caused by some large vessels and bronchus. Lung nodules usually are defined as sphere with the diameter in a certain range, but cross profiles of some large vessels are also sphere, which would increase FP. In addition, instability, minimization and overfitting of some traditional machine learning methods such as Nerual Network (NN) would affect seriously the performance of recognition.
Aiming at above problems, main purpose in the paper is effectively improving the performance of classifiers. It would be achived by analyzing 3D features of potential nodules in 3D space, and 3D Volum of Interest (VOI) of potential nodules in successive sections are chosen as the identify object instead of 2D ROI. The details are as follows:
(1)In order to analyze more information in 3D space and effectively remove the adhesions between different structures, a fast Three Dimension Principle Component Analysis (3DPCA) is presented. Firstly, feature points in 3D space made up of a CT set are extracted by 3DPCA; Secondly, region grow method is used to obtain the whole suspected lesions by choosing the feature points as the seed points; Lastly, a fast decomposition algorithm of Higher-Order Singular Value Decomposition (HOSVD) is designed in order to reduce computation of 3DPCA. Recognition accuracy of lung lesions is improved by 3DPCA comparing with traditional 2DPCA, and computation is reduced to 1/3 by fast 3DPCA.
(2)In order to repair lossed potential nodules which adhere to normal structure seriously, extraction algorithm based on restrict by successive sections is proposed. Firstly, potential nodules in all sections are extracted respectively by combining of threshold method, image enhancement (by Dot Filter) and rolling ball method; Secondly, let the sections including potential nodules as base sections, locations of potential nodules as base locations and lung area of base sections as restrict conditions; At last, lossed potential nodules are repaired by region grow method. It is proved by experiment that the lossed nodules can be repaired more effectively by above extraction algorithm comparing with rolling ball method, region grow method, Snake and GVF Snake method. And 3D VOI of potential nodules are made for further recognition.
(3)In order to improve performance of recognition,3D VOI of potential nodules are chosen as the identification objects instead of traditional 2D ROI. For above reason, SVMs3Dmatrix which can process the input samples based on 3D matrix patterns is proposed.
a.Unfolding SVMs3Dmatrix
Firstly, unfolding method of high-order tensor is used to unfold the input sample based on 3D matrix into three 2D matrixes; Secondly, SVMsmatnx is used to obtain three decisions of the three 2D matrixes; At last, the three people's voting method is used to obtain the final decision.
b.Non-unfolding SVMs3Dmatrix
Multiplication of 3D matrix is used to design non-unfolding SVMs3Dmatrix, which can process input samples based on 3D matrix patterns directly and avoiding unfolding. Firstly, new optimum codition of SVMs is conducted by increasing two right-vectors; Secondly, the left-vector and two right-vectors can be solved iteratively by the gradient descent method.
It is proved by experiment that the perfomence of SVMs3Dmatrix is better than that of Two Dimension Linear Discrimination Analysis (2D-LDA), Massitive Training Artificial Neural Network (MTANN) and SVMsmatrix. Furthermore, as avoiding the unfolding, memory occupy of non-unfolding SVMs3Dmatrix is effectively reduced comparing with that of unfolding SVMs3Dmatrix.
(4) In order to better meet complex and variety of lung nodules, Multi-class SVMs based on 3D matrix pattern (MC-SVMs3Dmatrix) is further designed on the basis of two-class SVMs3Dmatrix. Firstly, several current MC-SVMs are compared, and sencondly, one based on encoding is chosen to be extended to MC-SVMs3Dmatrix. It is proved by experiment that the performance of MC-SVMs3Dmatrix is better than that of two-class SVMs3Dmatrix.
Data set in the paper is made up of 96 cases form Chest No.1-No.3 in XX Tumor Hospital (2009.6-2010.6). All of them are with expert notations. Other CAD schemes and method in the paper are compared by ROC. The results confirm the availability of the method in the paper.
引文
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