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Reproducible kernel Hilbert space based global and local image segmentation
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. | Quantitative Biomedical Research Center, Department of Population and Data Sciences, University of Texas Southwestern Medical Center, Dallas TX 75390, USA |
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.
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. |
[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. |
[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. |
[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. |
[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. |
[6] |
A. Khan, N. Rajpoot, D. 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 |
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doi: 10.1145/3065386. |
[9] |
N. Kumar, R. Verma, S. Sharma, S. Bhargava, A. 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. |
[10] |
Y. Lecun, L. Bottou, Y. Bengio and P. Haffner,
Gradient-based learning applied to document recognition, Proceedings of the IEEE, 86 (1998), 2278-2324.
doi: 10.1109/5.726791. |
[11] |
C. Liu, M. 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. |
[12] |
MATLAB, version 9.5 (R2018b), The MathWorks Inc., Natick, Massachusetts, 2018. Google Scholar |
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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. |
[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. |
[15] |
E. Reinhard, M. Adhikhmin, B. 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. |
[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. |
[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 |
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. |
[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. |
[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. |
[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. |
[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. |
[6] |
A. Khan, N. Rajpoot, D. 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. |
[9] |
N. Kumar, R. Verma, S. Sharma, S. Bhargava, A. 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. |
[10] |
Y. Lecun, L. Bottou, Y. Bengio and P. Haffner,
Gradient-based learning applied to document recognition, Proceedings of the IEEE, 86 (1998), 2278-2324.
doi: 10.1109/5.726791. |
[11] |
C. Liu, M. 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. |
[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. |
[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. |
[15] |
E. Reinhard, M. Adhikhmin, B. 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. |
[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. |
[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 |









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 |
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 |
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 |
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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