Cascade Sparse Convolution and Decision Tree Ensemble Model for Nuclear Segmentation in Pathology Images
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摘要: 数字病理图像分析对于乳腺癌、肾癌等良恶性分级诊断具有重要意义, 其中细胞核的形态测量是病理量化分析的关键. 然而, 由于病理图像背景复杂, 细胞核高密度分布、细胞粘连等, 个体细胞核精准分割是一个挑战性问题. 本文提出一个级联稀疏卷积与决策树集成学习的细胞核分割模型. 该模型由稀疏可分离卷积模块和集成决策树学习的正则化回归模块堆叠级联组成, 其中: 前者采取秩-1张量分解学习机制, 可分层抽取细胞核的多尺度方向分布式抽象特征; 而后者采取随机采样、树剪枝以及正则化回归机制提升逐像素回归分类能力. 相比于现有深度学习模型, 该模型无需非线性激活和后向传播计算, 参数规模较小, 可实现端到端的学习. 通过乳腺、前列腺、肾脏、胃和膀胱等多组病理图像的分割实验表明: 该模型能够实现复杂数字病理图像中的高密度细胞核的快速个体目标检测和分割, 在Jaccard相似性系数、F1分数和平均边缘距离三个指标上均优于目前CNN2、CNN3和U-Net等深度学习方法, 具有较好应用前景.Abstract: The quantitative analysis of digital pathology images plays a significant role in the diagnosis of benign and malignant diseases such as breast and prostate cancer, in which nuclear morphology measurement serve as a basis of quantitative analyses. However, due to the complex background of pathology images, dense distributions of nuclei, and nucleus adhesions, accurate segmentation of individual nuclei remains a challenging problem. In this paper, we propose a new method to automatically segment nuclei from digital pathology images with cascade sparse convolution and decision tree ensemble (CscDTE) model. In particular, the sparse separable convolution learning module and the decision tree ensemble learning module are stacked in a cascaded manner to form the CscDTE model. The former adopts rank-one tensor decomposition learning mechanism that can extract multiscale and multi-directional distributed abstract features; while the latter employs random sampling, pruning, and regularized regression mechanism to boost per-pixel regression and/or classification performance. Compared with the popular deep neural networks, the proposed CscDTE model does not require nonlinear activation and backpropagation computation, and depends on fewer parameters. Our CscDTE model is trained in a layer-wise manner that can achieve an end-to-end pixelwise learning and fast nuclear detection and segmentation in high-throughput imagery. We demonstrated the superiority of our method in terms of Jaccard index, F1 score, and average boundary distance by evaluating it on the multi-disease state and multi-organ dataset where consistently higher performance was obtained as compared to convolutional neural networks and fully convolutional networks.
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图 1 病理细胞核图像分割的挑战与人工分割结果
Fig. 1 Challenges in nuclear segmentation and associated ground truth
图 2 用于病理图像分割的CNN体系结构
Fig. 2 The CNN-style architecture for pathology image segmentation
图 3 用于病理图像分割的U-Net体系结构
Fig. 3 The U-Net-style architecture for pathology image segmentation
图 5 基于张量分解技术学习一组秩-1可分离核
Fig. 5 Tensor decomposition for learning rank-1 separable kernels
图 6 CscDTE框架中的集成决策树学习模块的训练过程
Fig. 6 Flowchart of the training procedure for the decision tree ensemble learning module of CscDTE framework
图 8 Kumar病理细胞核相同器官图像的分割比较
Fig. 8 Comparative segmentation results on the Kumar same-organs testing pathology images
图 9 Kumar病理细胞核不同器官图像的分割比较
Fig. 9 Comparative segmentation results on the Kumar different-organs testing pathology images
图 10 不同算法在具有重叠、形状及大小不规则的病理图像上的轮廓可视化分割结果图
Fig. 10 Visualizing segmented contours of different algorithms on the pathology image with shape and color variations and overlapping regions
图 11 本文方法与U-Net方法在KIRC数据集上的分割比较
Fig. 11 Comparative segmentation using ours and U-Net on the KIRC dataset
表 1 提出的CscDTE模型的最优参数值. 像素位置样本总数为800 000
Table 1 The optimal hyper-parameter values of our CscDTE model. The total number of pixel samples is 800 000
数据集 $N$ $L$ ${d^2(R)}$( ${1^{\rm{st}}}$layer; ${2^{\rm{nd}}\sim L^{\rm{th}}}$layers) $M$ TCGA WSIs 200 000 5 $11^2$(25), $17^2$(8), $21^2$(72), $29^2$(8), $43^2$(44); $11^2$(25), $21^2$(36), $43^2$(36) 50 
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表 2 用于病理图像分割的CNN2体系结构
Table 2 The CNN2 architecture for pathology image segmentation
网络层 滤波器尺寸 激活 输出尺寸 随机丢弃率 输入 – – $ {\rm{55}} \times {\rm{55}} \times {\rm{3}} $ – 卷积 1 $ {\rm{6}} \times {\rm{6}} $ ReLU $ {\rm{50}} \times {\rm{50}} \times {\rm{48}} $ 0.1 池化 1 $ {\rm{2}} \times {\rm{2}} $ Max $ {\rm{25}} \times {\rm{25}} \times {\rm{48}} $ – 卷积 2 $ {\rm{4}} \times {\rm{4}} $ ReLU $ {\rm{22}} \times {\rm{22}} \times {\rm{48}} $ 0.2 池化 2 $ {\rm{2}} \times {\rm{2}} $ Max $ {\rm{11}} \times {\rm{11}} \times {\rm{48}} $ – 全连接 1 – ReLU $ {\rm{1\,024}} \times {\rm{1}} $ 0.5 全连接 2 – ReLU ${\rm{1\,024} } \times {\rm{1} }$ 0.5 输出 – SoftMax $ 2 \times 1 $ –
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表 3 用于病理图像分割的CNN3体系结构
Table 3 The CNN3 architecture for pathology image segmentation
网络层 滤波器尺寸 激活 输出尺寸 随机丢弃率 输入 – – $ {\rm{51}} \times {\rm{51}} \times {\rm{3}} $ – 卷积 1 $ {\rm{4}} \times {\rm{4}} $ ReLU $ {\rm{48}} \times {\rm{48}} \times {\rm{25}} $ 0.1 池化 1 $ {\rm{2}} \times {\rm{2}} $ Max $ {\rm{24}} \times {\rm{24}} \times {\rm{25}} $ – 卷积 2 $ {\rm{5}} \times {\rm{5}} $ ReLU $ {\rm{20}} \times {\rm{20}} \times {\rm{50}} $ 0.2 池化 2 $ {\rm{2}} \times {\rm{2}} $ Max $ {\rm{10}} \times {\rm{10}} \times {\rm{50}} $ – 卷积 3 $ {\rm{6}} \times {\rm{6}} $ ReLU $ {\rm{5}} \times {\rm{5}} \times {\rm{80}} $ 0.25 池化 3 $ {\rm{2}} \times {\rm{2}} $ Max $ {\rm{3}} \times {\rm{3}} \times {\rm{80}} $ – 全连接 1 – ReLU ${\rm{1\,024} } \times {\rm{1} }$ 0.5 全连接 2 – ReLU ${\rm{1\,024} } \times {\rm{1} }$ 0.5 输出 – SoftMax $ 3 \times 1 $ –
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表 4 本文方法与其他方法在Kumar病理数据集上的分割性能(均值)比较
Table 4 Performance comparison of other methods with our CscDTE (For each metric, the mean are listed)
器官 图像 Jaccard相似性系数 精确率 F1分数 平均边缘距离 本文 U-Net CNN3 CNN2 分水岭 本文 U-Net CNN3 CNN2 分水岭 本文 U-Net CNN3 CNN2 分水岭 本文 U-Net CNN3 CNN2 分水岭 乳腺 1 0.594 0.539 0.570 0.569 0.545 0.810 0.832 0.756 0.764 0.591 0.745 0.700 0.726 0.725 0.706 14.90 42.78 29.68 64.46 42.36 2 0.675 0.613 0.603 0.448 0.592 0.832 0.803 0.844 0.853 0.625 0.806 0.760 0.752 0.619 0.744 12.99 13.12 14.34 62.27 18.49 前列腺 1 0.646 0.634 0.656 0.625 0.585 0.867 0.858 0.858 0.871 0.679 0.785 0.776 0.792 0.769 0.739 12.56 15.87 11.41 10.22 24.40 2 0.342 0.485 0.459 0.387 0.409 0.834 0.827 0.906 0.832 0.603 0.510 0.653 0.629 0.558 0.581 88.69 34.51 40.34 56.01 37.81 肾脏 1 0.692 0.673 0.641 0.691 0.570 0.752 0.782 0.848 0.755 0.606 0.818 0.804 0.781 0.817 0.726 12.14 15.25 19.47 12.24 30.03 2 0.513 0.539 0.524 0.463 0.512 0.765 0.789 0.763 0.681 0.570 0.678 0.701 0.687 0.633 0.677 16.35 21.48 12.73 21.38 9.48 膀胱 1 0.603 0.551 0.581 0.550 0.325 0.846 0.756 0.720 0.795 0.330 0.752 0.711 0.735 0.709 0.490 41.97 86.13 22.91 52.33 79.61 2 0.759 0.629 0.580 0.656 0.508 0.867 0.898 0.926 0.909 0.516 0.863 0.772 0.734 0.792 0.674 6.58 14.32 17.09 19.03 22.04 胃 1 0.781 0.645 0.622 0.577 0.647 0.881 0.920 0.824 0.913 0.692 0.877 0.784 0.767 0.732 0.785 1.99 7.44 8.49 9.16 3.67 2 0.785 0.641 0.714 0.623 0.679 0.891 0.931 0.948 0.910 0.736 0.880 0.781 0.833 0.767 0.809 1.09 6.82 5.41 6.75 1.76 相同器官 0.577 0.581 0.576 0.531 0.536 0.810 0.815 0.829 0.793 0.612 0.724 0.732 0.728 0.687 0.696 26.27 23.84 21.33 37.76 27.10 不同器官 0.732 0.617 0.624 0.602 0.540 0.871 0.876 0.855 0.882 0.569 0.843 0.762 0.767 0.750 0.690 12.91 28.68 13.48 21.82 26.77 整体 0.639 0.595 0.595 0.559 0.537 0.835 0.840 0.839 0.828 0.595 0.771 0.744 0.744 0.712 0.693 20.93 25.77 18.19 31.39 26.97
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表 5 本文方法与其他方法在Kumar病理数据集上的分割性能(标准差)比较
Table 5 Performance comparison of other methods with our CscDTE (For each metric, the standard deviation are listed)
器官 Jaccard相似性系数 精确率 F1分数 平均边缘距离 本文 U-Net CNN3 CNN2 分水岭 本文 U-Net CNN3 CNN2 分水岭 本文 U-Net CNN3 CNN2 分水岭 本文 U-Net CNN3 CNN2 分水岭 乳腺 0.057 0.052 0.023 0.086 0.033 0.016 0.021 0.062 0.063 0.024 0.043 0.042 0.018 0.075 0.027 1.35 20.97 10.85 1.55 16.88 前列腺 0.215 0.105 0.139 0.168 0.125 0.023 0.022 0.034 0.028 0.054 0.195 0.087 0.115 0.149 0.112 53.83 13.18 20.46 32.38 9.48 肾脏 0.127 0.095 0.083 0.161 0.041 0.009 0.005 0.060 0.052 0.026 0.099 0.073 0.067 0.130 0.035 2.98 4.41 4.77 6.46 14.53 膀胱 0.110 0.055 0.001 0.075 0.129 0.015 0.100 0.146 0.081 0.132 0.079 0.043 0.001 0.059 0.130 25.02 50.78 4.12 23.55 40.71 胃 0.003 0.003 0.065 0.033 0.023 0.007 0.008 0.088 0.002 0.031 0.002 0.002 0.047 0.025 0.017 0.64 0.44 2.18 1.70 1.35 相同器官 0.132 0.071 0.075 0.117 0.069 0.044 0.029 0.058 0.072 0.037 0.116 0.057 0.062 0.099 0.061 30.62 12.09 11.45 25.79 12.23 不同器官 0.087 0.044 0.063 0.047 0.161 0.020 0.081 0.105 0.058 0.185 0.061 0.034 0.046 0.037 0.145 19.52 38.45 8.00 21.02 36.39 整体 0.136 0.062 0.071 0.098 0.106 0.047 0.061 0.076 0.078 0.113 0.112 0.049 0.057 0.084 0.096 26.37 24.09 10.52 24.18 22.91
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表 6 本文方法与U-Net在KIRC数据集上的分割性能(均值, 标准差)比较
Table 6 Performance comparison of U-Net with our CscDTE (For each metric, the mean and standard deviation are listed)
KIRC Jaccard系数 精确率 F1分数 平均边缘距离 均值 标准差 均值 标准差 均值 标准差 均值 标准差 本文方法 0.735 0.054 0.832 0.050 0.846 0.037 22.66 9.51 U-Net 0.642 0.064 0.742 0.093 0.780 0.049 57.78 23.11
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表 7 不同算法在病理数据集上的参数规模
Table 7 Number of parameters of different algorithms on the pathology dataset
方法 本文算法 U-Net CNN3 CNN2 参数规模 184KB 1.75MB 1.97MB 7.04MB
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