Figure 1.
The Architecture of PDR U-Net. f represents the number of filters.d represents the dilated rate.The keep rate of dropout is 0.7
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Automatic segmentation of the femur and tibia bones from X-ray images based on pure dilated residual U-Net
| 1. | School of Artificial Intelligence, Hebei University of Technology, Tianjin 300401, China |
| 2. | Tianjin Institute of Orthopaedics, Tianjin Hospital, Tianjin University, Tianjin 300211, China |
| 3. | Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen 518055, China |
| 4. | School of Artificial Intelligence, Hebei Key Laboratory of Robot Perception and Human-Robot Interaction, Hebei University of Technology, Tianjin 300401, China |
X-ray images of the lower limb bone are the most commonly used imaging modality for clinical studies, and segmentation of the femur and tibia in an X-ray image is helpful for many medical studies such as diagnosis, surgery and treatment. In this paper, we propose a new approach based on pure dilated residual U-Net for the segmentation of the femur and tibia bones. The proposed approach employs dilated convolution completely to increase the receptive field, in this way, we can make full use of the advantages of dilated convolution. We conducted experiments and evaluations on datasets provided by Tianjin hospital. Comparison with the classical U-net and FusionNet, our method has fewer parameters, higher accuracy, and converges more rapidly, which means the high performance of the proposed method.
Mathematics Subject Classification:
Primary: 68T07; Secondary: 68T20.
Citation:
Weihao Shen, Wenbo Xu, Hongyang Zhang, Zexin Sun, Jianxiong Ma, Xinlong Ma, Shoujun Zhou, Shijie Guo, Yuanquan Wang.
Automatic segmentation of the femur and tibia bones from X-ray images based on pure dilated residual U-Net. Inverse Problems & Imaging, doi: 10.3934/ipi.2020057
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O. Bandyopadhyay, A. Biswas and B. B. Bhattacharya,
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J. Carballido-Gamio, et al., Automatic multi-parametric quantification of the proximal femur with quantitative computed tomography, Quantitative Imaging in Medicine and Surgery, 5 (2015), 552-568. Google Scholar |
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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. |
| [6] |
Ö. Çiçek, A. Abdulkadir, S. S. Lienkamp, T. Brox and O. Ronneberger, 3d u-net: Learning dense volumetric segmentation from sparse annotation, in Medical Image Computing and Computer-Assisted Intervention - MICCAI 2016 - 19th International Conference, Athens, Greece, October 17-21, 2016, Proceedings, Part II, Lecture Notes in Computer Science, 9901, 2016,424–432.
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F. Ding, W. K. Leow and T. S. Howe, Automatic segmentation of femur bones in anterior-posterior pelvis x-ray images, in Computer Analysis of Images and Patterns, 12th International Conference, CAIP 2007, Vienna, Austria, August 27-29, 2007, Proceedings (eds. W. G. Kropatsch, M. Kampel and A. Hanbury), Lecture Notes in Computer Science, 4673, Springer, 2007,205–212.
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L.-H. Fan, J.-G. Han, Y. Jia, C. Zhao and B. Yang, Segmentation of femurs in x-ray image with generative adversarial networks, DEStech Transactions on Engineering and Technology Research, 289–295.
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C. N. Öztürk and S. Albayrak,
Automatic segmentation of cartilage in high-field magnetic resonance images of the knee joint with an improved voxel-classification-driven region-growing algorithm using vicinity-correlated subsampling, Comp. Bio. Med., 72 (2016), 90-107.
doi: 10.1016/j.compbiomed.2016.03.011. |
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T. T. Peng, et al., Detection of femur fractures in x-ray images, Master of Science Thesis, National University of Singapore. Google Scholar |
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A. Pries, P. J. Schreier, A. Lamm, S. Pede and J. Schmidt, Deep morphing: Detecting bone structures in fluoroscopic x-ray images with prior knowledge, preprint, arXiv: 1808.04441. Google Scholar |
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O. Ronneberger, P. Fischer and T. Brox, U-net: Convolutional networks for biomedical image segmentation, in Medical Image Computing and Computer-Assisted Intervention - MICCAI 2015-18th International Conference Munich, Germany, October 5-9, 2015, Proceedings, Part III (eds. N. Navab, J. Hornegger, W. M. W. III and A. F. Frangi), Lecture Notes in Computer Science, 9351, Springer, 2015,234–241.
doi: 10.1007/978-3-319-24574-4_28. |
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T. Salimans, I. J. Goodfellow, W. Zaremba, V. Cheung, A. Radford and X. Chen, Improved techniques for training gans, in Advances in Neural Information Processing Systems 29: Annual Conference on Neural Information Processing Systems 2016, December 5-10, 2016, Barcelona, Spain (eds. D. D. Lee, M. Sugiyama, U. von Luxburg, I. Guyon and R. Garnett), 2016, 2226–2234 Google Scholar |
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doi: 10.7763/LNSE.2013.V1.44. |
| [32] |
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 (eds. Y. Bengio and Y. LeCun), preprint Google Scholar |
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R. Smith, Segmentation and fracture detection in x-ray images for traumatic pelvic injury., Google Scholar |
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C. Stolojescu-Crisan and S. Holban, An interactive x-ray image segmentation technique for bone extraction, in International Work-Conference on Bioinformatics and Biomedical Engineering, IWBBIO 2014, Granada, Spain, April 7-9, 2014 (eds. I. Rojas and F. M. O. Guzman), Copicentro Editorial, 2014, 1164–1171 Google Scholar |
| [35] |
H. Sun, et al., Aunet: Attention-guided dense-upsampling networks for breast mass segmentation in whole mammograms, Phys. Med. Biol., 65 (2020), 055005.
doi: 10.1088/1361-6560/ab5745. |
| [36] |
C. Szegedy, et al., Going deeper with convolutions, in IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2015, Boston, MA, USA, June 7-12, 2015
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| [37] |
A. Tack, A. Mukhopadhyay and S. Zachow,
Knee menisci segmentation using convolutional neural networks: Data from the osteoarthritis initiative, Osteoarthritis and Cartilage, 26 (2018), 680-688.
doi: 10.1016/j.joca.2018.02.907. |
| [38] |
W. Wang, Y. Wang, Y. Wu, T. Lin, S. Li and B. Chen,
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Figure 2.
The details of the standard block and residual block. f represents the number of filters. d represents the dilated rate
Figure 3.
the illustration on the left is an unfilled femur label and on the right is a filled tibia label
Figure 4.
The whole process of data augmentation
Figure 5.
The caption on the left is the loss of PDRU-Net on the training set, and that on the right is the loss of PDRU-Net on the validation set
Figure 6.
Segmentation results of the first three training epochs
Figure 7.
The first three columns show the segmentation results of U-Net, FusionNet and PDR U-Net respectively.The third and fourth columns show the corresponding ground truth images and input images respectively
Table 1.
The receptive field of each block in the encoding path of PDRU-Net
| Block Type | Convolutional Layer | Receptive Field |
| standard block 1 | conv1_1 | 1-1+1 |
| dilated rate = 1 | conv1_2 | 3-1+1 |
| residual block 2 | conv2_1 | 5-1+2 |
| dilated rate = 2 | conv2_2 | 9-1+2 |
| residual block 3 | conv3_1 | 13-1+4 |
| dilated rate = 4 | conv3_2 | 21-1+4 |
| residual block 4 | conv4_1 | 29-1+8 |
| dilated rate = 8 | conv4_2 | 45-1+8 |
| residual block 5 | conv5_1 | 61-1+16 |
| dilated rate = 16 | conv5_2 | 93-1+16 |
| residual block 6 | conv6_1 | 125-1+32 |
| dilated rate = 32 | conv6_2 | 189-1+32 |
| residual block 7 | conv7_1 | 253-1+32 |
| dilated rate = 32 | conv7_2 | 317-1+32 |
| residual block 8 | conv8_1 | 381-1+32 |
| dilated rate = 32 | conv8_2 | 445-1+32 |
| Block Type | Convolutional Layer | Receptive Field |
| standard block 1 | conv1_1 | 1-1+1 |
| dilated rate = 1 | conv1_2 | 3-1+1 |
| residual block 2 | conv2_1 | 5-1+2 |
| dilated rate = 2 | conv2_2 | 9-1+2 |
| residual block 3 | conv3_1 | 13-1+4 |
| dilated rate = 4 | conv3_2 | 21-1+4 |
| residual block 4 | conv4_1 | 29-1+8 |
| dilated rate = 8 | conv4_2 | 45-1+8 |
| residual block 5 | conv5_1 | 61-1+16 |
| dilated rate = 16 | conv5_2 | 93-1+16 |
| residual block 6 | conv6_1 | 125-1+32 |
| dilated rate = 32 | conv6_2 | 189-1+32 |
| residual block 7 | conv7_1 | 253-1+32 |
| dilated rate = 32 | conv7_2 | 317-1+32 |
| residual block 8 | conv8_1 | 381-1+32 |
| dilated rate = 32 | conv8_2 | 445-1+32 |
Table 2.
Comparison of the PDRU-Net, U-Net and FusionNet
| model | parameters | Dice Coefficient | Pixel Accuracy | Recall | Precision | F1 score |
| U-Net | ~33M | 0.918 | 0.943 | 0.839 | 0.987 | 0.907 |
| FusionNet | ~78M | 0.944 | 0.969 | 0.877 | 0.997 | 0.933 |
| PDRU-Net | ~0.36M | 0.973 | 0.987 | 0.953 | 0.976 | 0.964 |
| model | parameters | Dice Coefficient | Pixel Accuracy | Recall | Precision | F1 score |
| U-Net | ~33M | 0.918 | 0.943 | 0.839 | 0.987 | 0.907 |
| FusionNet | ~78M | 0.944 | 0.969 | 0.877 | 0.997 | 0.933 |
| PDRU-Net | ~0.36M | 0.973 | 0.987 | 0.953 | 0.976 | 0.964 |
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