doi: 10.3934/ipi.2020049

Automatic extraction of cell nuclei using dilated convolutional network

1. 

Department of Mathematical Sciences, The University of Texas at Dallas, Richardson, TX 75080, USA

2. 

Department of Mathematical Sciences, The University of Texas at Dallas, Richardson TX 75080, USA

3. 

Quantitative Biomedical Research Center, Department of Population and Data Sciences, University of Texas Southwestern Medical Center, Dallas TX 75390, USA

* Corresponding author: Yan Cao

Received  December 2019 Revised  April 2020 Published  August 2020

Fund Project: This work was supported in part by the National Science Foundations Enriched Doctoral Training Program, DMS grant #1514808.

Pathological examination has been done manually by visual inspection of hematoxylin and eosin (H&E)-stained images. However, this process is labor intensive, prone to large variations, and lacking reproducibility in the diagnosis of a tumor. We aim to develop an automatic workflow to extract different cell nuclei found in cancerous tumors portrayed in digital renderings of the H&E-stained images. For a given image, we propose a semantic pixel-wise segmentation technique using dilated convolutions. The architecture of our dilated convolutional network (DCN) is based on SegNet, a deep convolutional encoder-decoder architecture. For the encoder, all the max pooling layers in the SegNet are removed and the convolutional layers are replaced by dilated convolution layers with increased dilation factors to preserve image resolution. For the decoder, all max unpooling layers are removed and the convolutional layers are replaced by dilated convolution layers with decreased dilation factors to remove gridding artifacts. We show that dilated convolutions are superior in extracting information from textured images. We test our DCN network on both synthetic data sets and a public available data set of H&E-stained images and achieve better results than the state of the art.

Citation: Rajendra K C Khatri, Brendan J Caseria, Yifei Lou, Guanghua Xiao, Yan Cao. Automatic extraction of cell nuclei using dilated convolutional network. Inverse Problems & Imaging, doi: 10.3934/ipi.2020049
References:
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K. Simonyan and A. Zisserman, Very deep convolutional networks for large-scale image recognition, in 3rd International Conference on Learning Representations, ICLR 2015, San Diego, CA, USA, May 7-9, 2015, Conference Track Proceedings, 2015, URL http://arxiv.org/abs/1409.1556. Google Scholar

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show all references

References:
[1]

V. Badrinarayanan, A. Kendall and R. Cipolla, Segnet: A deep convolutional encoder-decoder architecture for image segmentation, IEEE Trans. Pattern Anal. Mach. Intell., 39 (2017), 2481–2495. doi: 10.1109/TPAMI.2016.2644615.  Google Scholar

[2]

L. Chen, G. Papandreou, I. Kokkinos, K. Murphy and A. L. Yuille, Deeplab: Semantic image segmentation with deep convolutional nets, atrous convolution, and fully connected crfs,, IEEE Trans. Pattern Anal. Mach. Intell., 40 (2018), 834–848. doi: 10.1109/TPAMI.2017.2699184.  Google Scholar

[3]

R. Hamaguchi, A. Fujita, K. Nemoto, T. Imaizumi and S. Hikosaka, Effective use of dilated convolutions for segmenting small object instances in remote sensing imagery, 2018 IEEE Winter Conference on Applications of Computer Vision (WACV), 2018, URL http://arxiv.org/abs/1709.00179. doi: 10.1109/WACV.2018.00162.  Google Scholar

[4]

N. Japkowicz and S. Stephen, The class imbalance problem: A systematic study, Intelligent Data Analysis, 6 (2002), 429-449.  doi: 10.3233/IDA-2002-6504.  Google Scholar

[5]

M. Jung and M. Kang, Efficient nonsmooth nonconvex optimization for image restoration and segmentation, Journal of Scientific Computing, 62 (2015), 336-370.  doi: 10.1007/s10915-014-9860-y.  Google Scholar

[6]

A. KhanN. RajpootD. Treanor and D. Magee, A non-linear mapping approach to stain normalisation in digital histopathology images using image-specific colour deconvolution, IEEE Trans. Biomedical Engineering, 61 (2014), 1729-1738.   Google Scholar

[7]

D. P. Kingma and J. L. Ba, Adam: A method for stochastic optimization, in 3rd International Conference on Learning Representations, ICLR 2015, San Diego, CA, USA, May 7-9, 2015, Conference Track Proceedings, 2015, URL http://arxiv.org/abs/1412.6980. Google Scholar

[8]

A. Krizhevsky, I. Sutskever and G. E. Hinton, Imagenet classification with deep convolutional neural networks,, in Communications of the ACM, 2017, 1–9, URL http://papers.nips.cc/paper/4824-imagenet-classification-with-deep-convolutional-neural-networks.pdf. doi: 10.1145/3065386.  Google Scholar

[9]

N. KumarR. VermaS. SharmaS. BhargavaA. Vahadane and A. Sethi, A dataset and technique for generalized nuclear segmentation for computational pathology, IEEE Trans. Med. Imag., 36 (2017), 1550-1560.  doi: 10.1109/TMI.2017.2677499.  Google Scholar

[10]

Y. LecunL. BottouY. Bengio and P. Haffner, Gradient-based learning applied to document recognition, Proceedings of the IEEE, 86 (1998), 2278-2324.  doi: 10.1109/5.726791.  Google Scholar

[11]

C. LiuM. Ng and T. Zeng, Weighted variational model for selective image segmentation with application to medical images, Pattern Recognition, 76 (2018), 367-379.  doi: 10.1016/j.patcog.2017.11.019.  Google Scholar

[12]

MATLAB, version 9.5 (R2018b), The MathWorks Inc., Natick, Massachusetts, 2018. Google Scholar

[13]

H. Noh, S. Hong and B. Han, Learning deconvolution network for semantic segmentation,, in Proceedings of the 2015 IEEE International Conference on Computer Vision (ICCV), ICCV '15, IEEE Computer Society, Washington, DC, USA, 2015, 1520–1528. doi: 10.1109/ICCV.2015.178.  Google Scholar

[14]

N. Qian, On the momentum term in gradient descent learning algorithms, Neural Networks: The Official Journal of the International Neural Network Society, 12 (1999), 145-151.  doi: 10.1016/S0893-6080(98)00116-6.  Google Scholar

[15]

E. ReinhardM. AdhikhminB. Gooch and P. Shirley, Color transfer between images, IEEE Comput. Graph. Appl., 21 (2001), 34-41.   Google Scholar

[16]

O. Ronneberger, P. Fischer and T. Brox, U-net: Convolutional networks for biomedical image segmentation,, in Medical Image Computing and Computer-Assisted Intervention (MICCAI), vol. 9351 of LNCS, Springer, 2015,234–241, URL http://lmb.informatik.uni-freiburg.de/Publications/2015/RFB15a, (available on arXiv: 1505.04597 [cs.CV]). doi: 10.1007/978-3-319-24574-4_28.  Google Scholar

[17]

E. Shelhamer, J. Long and T. Darrell, Fully convolutional networks for semantic segmentation, IEEE Trans. Pattern Anal. Mach. Intell., 39 (2017), 640–651. doi: 10.1109/TPAMI.2016.2572683.  Google Scholar

[18]

K. Simonyan and A. Zisserman, Very deep convolutional networks for large-scale image recognition, in 3rd International Conference on Learning Representations, ICLR 2015, San Diego, CA, USA, May 7-9, 2015, Conference Track Proceedings, 2015, URL http://arxiv.org/abs/1409.1556. Google Scholar

[19]

F. Yu and V. Koltun, Multi-scale context aggregation by dilated convolutions, CoRR, abs/1511.07122. Google Scholar

Figure 1.  $ 3 \times 3 $ convolution kernels with different dilation factors 1, 2 and 3 respectively. Red dots indicate nonzero values
Figure 2.  A matrix $ A $ and its reordering $ B $. It also shows a dilated convolution on $ A $ and its corresponding convolution on $ B $
Figure 3.  Source image (left), Target image (middle) and Normalized image by Reinhard method (Right)
Figure 4.  Sample training images in the triangle data set with a uniform foreground and a uniform background
Figure 5.  Sample training images in the triangle data set with a textured foreground and a textured background
Figure 6.  Test images (1st row) with corresponding segmentations using SegNet (2nd row), U-Net3 (3rd row), U-Net4 (4th row) and our dilated convolutional network (5th row)
Figure 7.  Test images (1st row) with corresponding segmentations using SegNet (2nd row), U-Net3 (3rd row), U-Net4 (4th row) and our dilated convolutional network (5th row)
Figure 8.  Sample normalized image patches and corresponding manual segmentations from the dataset
Figure 9.  Test images (1st column) with corresponding segmentations using SegNet (2nd column), U-Net3 (3rd column) and our dilated convolutional network (4th column). Ground truth contours are plotted in red
Table 1.  Comparison of the network architectures of the SegNet and our Dilated Convolutional network, where "Conv" means "Convolutions" and D is the dilation factor. Third column shows how to use matrix splitting and merging procedures to implement dilated convolutions through efficient conventional convolutions
SegNet Our DCN Our DCN
(for efficient training)
128x128x3 Input 128x128x3 Input 128x128x3 Input
(or 64x64 Input) (or 64x64 Input) (or 64x64) Input
64 3x3 Conv 64 3x3 Conv, D=1 64 3x3 Conv
Normalization & RELU Normalization & RELU Normalization & RELU
ReLU ReLU ReLU
64 3x3 Conv 64 3x3 Conv, D=1 64 3x3 Conv
Normalization & RELU Normalization & RELU Normalization & RELU
Max Pooling Matrix Splitting
64 3x3 Conv 64 3x3 Conv, D=2 64 3x3 Conv
Encoder Normalization & RELU Normalization & RELU Normalization & RELU
64 3x3 Conv 64 3x3 Conv, D=2 64 3x3 Conv
Normalization & RELU Normalization & RELU Normalization & RELU
Max Pooling Matrix Splitting
64 3x3 Conv 64 3x3 Conv, D=4 64 3x3 Conv
Batch Normalization Batch Normalization Batch Normalization
ReLU ReLU ReLU
64 3x3 Conv 64 3x3 Conv, D=4 64 3x3 Conv
Batch Normalization Batch Normalization Batch Normalization
ReLU ReLU ReLU
Max Pooling
Max Unpooling
64 3x3 Conv 64 3x3 Conv, D=4 64 3x3 Conv
Normalization & RELU Normalization & RELU Normalization & RELU
Matrix Merging
64 3x3 Conv 64 3x3 Conv, D=2 64 3x3 Conv
Normalization & RELU Normalization & RELU Normalization & RELU
Max Unpooling Matrix Merging
64 3x3 Conv 64 3x3 Conv, D=1 64 3x3 Conv
Decoder Normalization & RELU Normalization & RELU Normalization & RELU
64 3x3 Conv 64 3x3 Conv, D=1 64 3x3 Conv
Normalization & RELU Normalization & RELU Normalization & RELU
Max Unpooling
64 3x3 Conv
Normalization & RELU
2 3x3 Conv 2 1x1 Conv 2 1x1 Conv
Normalization & RELU
Softmax Softmax Softmax
Pixel Classification Pixel Classification Pixel Classification
SegNet Our DCN Our DCN
(for efficient training)
128x128x3 Input 128x128x3 Input 128x128x3 Input
(or 64x64 Input) (or 64x64 Input) (or 64x64) Input
64 3x3 Conv 64 3x3 Conv, D=1 64 3x3 Conv
Normalization & RELU Normalization & RELU Normalization & RELU
ReLU ReLU ReLU
64 3x3 Conv 64 3x3 Conv, D=1 64 3x3 Conv
Normalization & RELU Normalization & RELU Normalization & RELU
Max Pooling Matrix Splitting
64 3x3 Conv 64 3x3 Conv, D=2 64 3x3 Conv
Encoder Normalization & RELU Normalization & RELU Normalization & RELU
64 3x3 Conv 64 3x3 Conv, D=2 64 3x3 Conv
Normalization & RELU Normalization & RELU Normalization & RELU
Max Pooling Matrix Splitting
64 3x3 Conv 64 3x3 Conv, D=4 64 3x3 Conv
Batch Normalization Batch Normalization Batch Normalization
ReLU ReLU ReLU
64 3x3 Conv 64 3x3 Conv, D=4 64 3x3 Conv
Batch Normalization Batch Normalization Batch Normalization
ReLU ReLU ReLU
Max Pooling
Max Unpooling
64 3x3 Conv 64 3x3 Conv, D=4 64 3x3 Conv
Normalization & RELU Normalization & RELU Normalization & RELU
Matrix Merging
64 3x3 Conv 64 3x3 Conv, D=2 64 3x3 Conv
Normalization & RELU Normalization & RELU Normalization & RELU
Max Unpooling Matrix Merging
64 3x3 Conv 64 3x3 Conv, D=1 64 3x3 Conv
Decoder Normalization & RELU Normalization & RELU Normalization & RELU
64 3x3 Conv 64 3x3 Conv, D=1 64 3x3 Conv
Normalization & RELU Normalization & RELU Normalization & RELU
Max Unpooling
64 3x3 Conv
Normalization & RELU
2 3x3 Conv 2 1x1 Conv 2 1x1 Conv
Normalization & RELU
Softmax Softmax Softmax
Pixel Classification Pixel Classification Pixel Classification
Table 2.  Quantitative metrics of the segmentation results on triangle data sets. Best values are displayed in bold
Triangle Global Mean Mean Weighted Mean
Dataset Accuracy Accuracy IoU IoU BFScore
SegNet Uniform 0.9325 0.9508 0.7829 0.8882 0.4172
U-Net3 Uniform 0.9694 0.9531 0.8784 0.9438 0.6572
U-Net4 Uniform 0.9974 0.9953 0.9884 0.9949 0.9488
Our DCN Uniform 0.9952 0.9941 0.9786 0.9906 0.8946
SegNet Textured 0.8764 0.9280 0.6818 0.8139 0.3605
U-Net3 Textured 0.8119 0.8614 0.5855 0.7359 0.2157
U-Net4 Textured 0.7250 0.8148 0.4945 0.6391 0.2000
Our DCN Textured 0.9658 0.9741 0.8728 0.9386 0.4638
Triangle Global Mean Mean Weighted Mean
Dataset Accuracy Accuracy IoU IoU BFScore
SegNet Uniform 0.9325 0.9508 0.7829 0.8882 0.4172
U-Net3 Uniform 0.9694 0.9531 0.8784 0.9438 0.6572
U-Net4 Uniform 0.9974 0.9953 0.9884 0.9949 0.9488
Our DCN Uniform 0.9952 0.9941 0.9786 0.9906 0.8946
SegNet Textured 0.8764 0.9280 0.6818 0.8139 0.3605
U-Net3 Textured 0.8119 0.8614 0.5855 0.7359 0.2157
U-Net4 Textured 0.7250 0.8148 0.4945 0.6391 0.2000
Our DCN Textured 0.9658 0.9741 0.8728 0.9386 0.4638
Table 3.  Quantitative metrics of the segmentation results on the H&E-stained image data set. Best values are displayed in bold
Image Global Mean Mean Weighted Mean
Set Accuracy Accuracy IoU IoU BFScore
SegNet Lung 0.8819 0.8975 0.7324 0.8074 0.9204
U-Net3 Lung 0.8917 0.9013 0.7475 0.8190 0.9266
U-Net4 Lung 0.8929 0.8966 0.7484 0.8193 0.9343
Our DCN Lung 0.9045 0.9033 0.7690 0.8355 0.9448
SegNet Breast 0.8691 0.8990 0.7002 0.7917 0.8900
U-Net3 Breast 0.8829 0.9051 0.7183 0.8124 0.8743
U-Net4 Breast 0.8775 0.8977 0.7086 0.8057 0.8700
Our DCN Breast 0.9047 0.9123 0.7538 0.8415 0.9210
SegNet Kidney 0.9122 0.9249 0.7290 0.8634 0.9425
U-Net3 Kidney 0.9133 0.9281 0.7259 0.8639 0.9218
U-Net4 Kidney 0.8993 0.9145 0.7013 0.8462 0.9306
Our DCN Kidney 0.9329 0.9277 0.7725 0.8911 0.9634
SegNet Prostate 0.8956 0.9142 0.7533 0.8271 0.9105
U-Net3 Prostate 0.8949 0.9041 0.7496 0.8255 0.9047
U-Net4 Prostate 0.8961 0.9032 0.7510 0.8271 0.9090
Our DCN Prostate 0.9211 0.9163 0.7962 0.8632 0.9336
SegNet Overall 0.8897 0.9000 0.7383 0.8184 0.9159
U-Net3 Overall 0.8957 0.8976 0.7467 0.8264 0.9069
U-Net4 Overall 0.8914 0.8905 0.7380 0.8201 0.9110
Our DCN Overall 0.9158 0.9039 0.7815 0.8548 0.9407
Image Global Mean Mean Weighted Mean
Set Accuracy Accuracy IoU IoU BFScore
SegNet Lung 0.8819 0.8975 0.7324 0.8074 0.9204
U-Net3 Lung 0.8917 0.9013 0.7475 0.8190 0.9266
U-Net4 Lung 0.8929 0.8966 0.7484 0.8193 0.9343
Our DCN Lung 0.9045 0.9033 0.7690 0.8355 0.9448
SegNet Breast 0.8691 0.8990 0.7002 0.7917 0.8900
U-Net3 Breast 0.8829 0.9051 0.7183 0.8124 0.8743
U-Net4 Breast 0.8775 0.8977 0.7086 0.8057 0.8700
Our DCN Breast 0.9047 0.9123 0.7538 0.8415 0.9210
SegNet Kidney 0.9122 0.9249 0.7290 0.8634 0.9425
U-Net3 Kidney 0.9133 0.9281 0.7259 0.8639 0.9218
U-Net4 Kidney 0.8993 0.9145 0.7013 0.8462 0.9306
Our DCN Kidney 0.9329 0.9277 0.7725 0.8911 0.9634
SegNet Prostate 0.8956 0.9142 0.7533 0.8271 0.9105
U-Net3 Prostate 0.8949 0.9041 0.7496 0.8255 0.9047
U-Net4 Prostate 0.8961 0.9032 0.7510 0.8271 0.9090
Our DCN Prostate 0.9211 0.9163 0.7962 0.8632 0.9336
SegNet Overall 0.8897 0.9000 0.7383 0.8184 0.9159
U-Net3 Overall 0.8957 0.8976 0.7467 0.8264 0.9069
U-Net4 Overall 0.8914 0.8905 0.7380 0.8201 0.9110
Our DCN Overall 0.9158 0.9039 0.7815 0.8548 0.9407
Table 4.  Comparison of the training and testing time of SegNet, U-Net3 and our DCN
SegNet U-Net3 Our DCN Our DCN (efficient)
Training Time 15 min 14 sec 18 min 36 sec 26 min 47 sec 19 min 45 sec
Testing Time 7.6 sec 37.7 sec 10.1 sec 19.9 sec
SegNet U-Net3 Our DCN Our DCN (efficient)
Training Time 15 min 14 sec 18 min 36 sec 26 min 47 sec 19 min 45 sec
Testing Time 7.6 sec 37.7 sec 10.1 sec 19.9 sec
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