0 引言

1 图结构视角下的医学图像

1.1 专业医疗设备的数据采集

1.2 医学图像数据的图结构转换

1.3 基于医学图像特征的图结构重构

2 GCN理论基础

2.1 图卷积层

图卷积层利用图结构信息完成节点特征或边特征的更新。如图 1所示，图卷积的方法可分为两大类：基于频谱的图卷积操作，借助图频谱的理论来实现拓扑图上的卷积操作；基于空间域的图卷积操作，直接将卷积操作定义在每个节点的连接关系上。Bruna等人(2014)首次提出了基于频谱图理论的图卷积方法。此后，基于频谱的图卷积(Defferrard等，2016；Kipf和Welling，2017；Levie等，2019)得到不断改进和优化。基于空间域的图卷积研究始于Micheli(2009)的研究。该方法通过体系结构上的复合非递归层解决图的相互依赖问题，同时继承了GRecNN(graph recursive neural networks)的消息传递思想。

图 1 图卷积基础理论发展时间轴

Fig. 1 Timeline of graph convolution theory development

2.1.1 基于频谱的图卷积操作

2.1.2 基于空间域的图卷积操作

基于空间域的图卷积操作模仿CNN中的卷积运算，根据节点的空间关系定义图卷积操作。该方法摆脱了基于频谱的图卷积操作对拉普拉斯矩阵的依赖，能够将图卷积操作应用于有向图。如图 2所示，基于空间域的图卷积操作是根据边的特征信息对图中的节点与其邻域节点进行特征聚合，得到该节点的新表示。基于空间域的图卷积操作定义为

$ \boldsymbol{h}_{i}^{(l+1)}=\sigma\left(\sum\limits_{j \in \boldsymbol{N}(i)} \frac{1}{c_{i j}} \boldsymbol{W}^{(l)} \boldsymbol{h}_{j}^{(l)}\right) $

(10)

图 2 2D卷积和图卷积的对比(Wu等，2021)

Fig. 2 Comparison of 2D convolution and graph convolution

((a)2D convolution; (b)graph convolution)(Wu et al., 2021)

式中，$\boldsymbol{h}_{j}^{(l)} $表示节点$j $在$l $层的特征矩阵，$c_{i j}= \sqrt{|\boldsymbol{N}(j)|} \cdot \sqrt{|\boldsymbol{N}(i)|}$表示归一化因子，${\boldsymbol{W}}^{(l)} $表示可学习权重矩阵，$ σ(·)$是一个激活函数，$ {\boldsymbol{N}}(i) $表示节点$ i $的所有邻接节点所组成的集合。

在早期的研究中，面向图的神经网络(neural network for graphs，NN4G)(Micheli，2009)与GNN并行提出，是基于空间域GCN的第1个工作。NN4G通过直接求和节点邻域信息来进行图卷积，应用残差连接和跳跃连接存储每一层的信息，其图卷积操作定义为

$ \begin{aligned} &\boldsymbol{h}_{v}^{(l+1)}=\sigma\left(\boldsymbol{W}^{(l+1)^{\mathrm{T}}} \boldsymbol{x}_{v}+\right. \\ &\ \ \left.\sum\limits_{i=1}^{l} \sum\limits_{u \in \boldsymbol{N}(v)} \boldsymbol{\varTheta}^{(i+1)^{\mathrm{T}}} \boldsymbol{h}_{u}^{(i)}\right) \end{aligned} $

(11)

式中，$ \boldsymbol{h}_{v}^{(0)}=\boldsymbol{O} $。

基于NN4G模型，Bacciu等人(2018)提出名为上下文图马尔可夫模型(contextual graph Markov model，CGMM)的概率模型，使得GCN在保持空间局部性的同时具有概率可解释性。

基于递归神经网络的思想，Li等人(2018c)将图卷积视为一个扩散的过程，提出扩散卷积神经网络(diffusion convolutional neural network，DCNN)。该方法通过对递归函数施加约束，使用门递归单元体系对节点进行随机异步更新，直至图节点的潜在表示达到稳态，将图卷积定义为

$ \boldsymbol{H}^{(l)}=f\left(\boldsymbol{W}^{(l)} \odot \boldsymbol{P}^{l} \boldsymbol{X}\right) $

(12)

式中，$ f(\cdot) \text { 是一个激活函数, } \boldsymbol{P}=\boldsymbol{D}^{-1} \boldsymbol{A} $。

Gilmer等人(2017)将图卷积视为一个消息传递的过程，消息沿着边在节点之间进行传递，提出消息传递神经网络(message passing neural network，MPNN)。该方法定义为

$ \boldsymbol{h}_{v}^{(l)}=U_{l}\left(\boldsymbol{h}_{v}^{(l-1)}, \sum\limits_{u \in \boldsymbol{N}(v)} M_{l}\left(\boldsymbol{h}_{v}^{(l-1)}, \boldsymbol{h}_{u}^{(l-1)}, \boldsymbol{x}_{v u}^{\mathrm{e}}\right)\right) $

(13)

式中，$ \boldsymbol{h}_{v}^{(0)}=\boldsymbol{x}_{v}^{0}, U_{l}(\cdot) \text {和} M_{l}(\cdot) $是具有可学习参数的函数。

Xu等人(2019)发现，同构图和非同构图的特征提取结果差异明显，基于MPNN的模型无法区分不同的同构图，于是提出图同构网络(graph isomorphism network，GIN)，即

$ \boldsymbol{h}_{v}^{(l)}=M L P^{(l)}\left(\left(1+\mathrm{e}^{(l)}\right) \boldsymbol{h}_{v}^{(l-1)}+\sum\limits_{u \in \boldsymbol{N}(v)} \boldsymbol{h}_{u}^{(l-1)}\right) $

(14)

式中，$ MLP(·) $表示多元感知器。

总体来看，基于空间域的图卷积操作分为3步。1)每个节点将自身的特征信息传递给邻居节点；2)每个节点将邻居节点及自身的特征信息进行汇集，对局部结构进行融合；3)在图卷积中加入激活函数，对节点的信息做非线性变换，增强模型的表达能力。因此，图卷积网络的关键是学习到一个非线性函数，将当前节点的特征信息与其邻居节点的特征信息进行聚合。

2.2 图池化层

2.3 图正则化层

2.4 图读出层

3 GCN改进

3.1 跳跃连接机制

3.2 inception机制

3.3 图注意力机制

3.4 邻接矩阵重构

4 GCN在医学图像分析上的应用

4.1 结构分割

4.1.1 血管分割

4.1.2 组织分割

Zhang等人(2019)利用改进的简单线性迭代聚类算法从3维MR图像中生成超体素，再通过KNN算法从超体素中构建图结构，最后输入GCN完成脑组织的分割。同时，Tian等人(2020)提出了一种基于GCN的多尺度卷积神经网络编码器，该编码器通过学习具有代表性的特征来获得精确分割前列腺轮廓。Wu等人(2019)利用GCN强大的学习能力，在不需要球面映射的情况下，将大脑皮层直接分割到原始皮层表面，并使用核策略将图卷积扩展到曲面流形，使模型能够克服不同对象间形状差异问题，从而解决大脑局部内在表面斑块上皮质属性模式与分割标签之间的高度非线性映射难题。

Gopinath等人(2019)利用图卷积网络中的频谱坐标去拟合学习算法和几何结构之间的差异。该方法使用频谱过滤器对表面邻域内在表示进行图卷积操作，可以跳过学习大脑皮层表面基础的过程，直接学习大脑皮层表面数据的分类，完成大脑皮层的分割任务。

Joshi和Sharma(2021)通过CNN自动编码器和GCN对多发性硬化症进行病灶分割。该模型首先使用CNN自动编码器结构对图像进行处理，将图像转换为图结构数据，然后将图结构数据输入至GCN架构，并通过加权归一化矩阵修正模型，在训练过程中添加节点与邻域节点之间的差异性信息和相关性信息，有效提高了多发性硬化病变组织分割的精度。

表 1梳理了GCN在医学图像分割中的部分代表性工作。可以看出，将GCN应用于医学图像分割的普遍构图方法是以ROI区域作为节点，以ROI区域是否存在连接作为边，对于某些成像独特的数据(例如脑部体素数据和心脏冠状动脉表面网格数据)，可利用KNN算法将其转换为图结构。与此同时，医学图像分割中的模型架构从CNN与GCN的简单堆叠，逐渐转变为多种模型的复杂组合。

表 1 GCN在医学图像分割中的应用
Table 1 Application example of GCN in medical image segmentation

下载CSV

文献	模型	构图方法	分割目标
Shin等人(2019)	CNN+GCN	以ROI区域为节点，ROI区域之间是否连接作为边	视网膜
Zhai等人(2019)	CNN+GCN	以ROI区域通过CNN得到的特征图作为节点，ROI区域之间是否连接作为边	肺部动静脉血管
Wolterink等人(2019)	KNN+GCN	以冠状动脉腔表面网格上的顶点作为图节点，顶点是否连接作为边	心脏冠状动脉
Zhang等人(2019)	KNN+GCN	以MRI生成的超体素作为图结构	脑组织
Wu等人(2019)	CNN+GCN	以流形结构为图	大脑皮层
Tian等人(2020)	CNN+GCN	以ROI区域为节点，ROI区域之间是否连接作为边	前列腺
Yang等人(2020b)	ResNet+LSTM+GCN	以ROI区域为节点，ROI区域之间是否连接作为边	心脏冠状动脉

4.2 疾病检测

4.2.1 脑部疾病检测

4.2.2 胸部疾病检测

4.2.3 其他疾病检测

Ou等人(2020)认为结构不变的静态拓扑假设限制了GCN在卷积过程中学习新特征的能力。他们提出在学习过程中自适应更新邻接矩阵的特征编码器，该编码器首先将原始图像特征转换为嵌入空间(embedding space)，然后通过余弦相似度创建邻接矩阵，最后利用图卷积操作使其成为自适应过程，有效地提高了宫颈癌检测性能。

Huang和Chung(2020)提出了一种新型的图卷积模型，其引入了可训练的边适配器，能够将非成像数据(如年龄和性别)并行归一化编码为节点的连边；同时，该适配器在梯度下降优化过程中是一个可微可学习过程，能够提升眼部疾病检测的能力。

表 2梳理了基于GCN的代表性医学图像疾病检测方法和典型应用。可以看出，早期GCN在医学图像疾病检测中的应用主要集中在脑部图像，基于对象之间的各种关系利用GCN完成疾病检测。近期的研究主要分为两大步骤，即首先利用各种CNN模型对原始医学图像进行特征提取，然后使用KNN算法或GAT算法进行特征重构，最后利用GCN挖掘特征之间的潜在关系完成特征分类。

表 2 GCN在医学图像疾病检测中的应用
Table 2 Application example of GCN in medical image classification

下载CSV

文献	模型	数据集	检测目标
Zhang等人(2018b)	CNN+GCN	PPMI	帕金森氏症
Parisot等人(2018)	MLP/Auto Encoder +GCN	ABIDE和ADNI	阿尔茨海默病和自闭症
Song等人(2019)	GCN	ADNI	阿尔茨海默病
Kazi等人(2019)	InceptionNet+GCN	ABIDE和ADNI	阿尔茨海默病和自闭症
Mao等人(2019)	CNN+GraphSAGE+GCN	ChestX-ray14	14种胸腔疾病
Du等人(2019)	CNN+GAT	INbreast	乳腺癌
Ye等人(2019)	U-Net+GCN	BACH 2018	乳腺癌
Yu等人(2021)	CNN+KNN+GCN	胸部X-Ray和胸部CT	新冠肺炎
注：PPMI: Parkinson’s progression Markers initiative; ABIDE: autism brain imaging data exchange; ADNI: Alzheimer’s disease neuroimaging initiative; BACH: grand challenge on breAst cancer histology images。

4.3 图像重建

5 结语

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