# American Institute of Mathematical Sciences

doi: 10.3934/ipi.2020057

## 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

* Co-Corresponding author: Shoujun Zhou and Yuanquan Wang

These authors contribute equally to this paper

Received  December 2019 Revised  May 2020 Published  August 2020

Fund Project: The first author is supported by NSFC grant 61976241

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.

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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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
The details of the standard block and residual block. f represents the number of filters. d represents the dilated rate
the illustration on the left is an unfilled femur label and on the right is a filled tibia label
The whole process of data augmentation
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
Segmentation results of the first three training epochs
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
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$\times$2+1=3 dilated rate = 1 conv1_2 3-1+1$\times$2+1=5 residual block 2 conv2_1 5-1+2$\times$2+1=9 dilated rate = 2 conv2_2 9-1+2$\times$2+1=13 residual block 3 conv3_1 13-1+4$\times$2+1=21 dilated rate = 4 conv3_2 21-1+4$\times$2+1=29 residual block 4 conv4_1 29-1+8$\times$2+1=45 dilated rate = 8 conv4_2 45-1+8$\times$2+1=61 residual block 5 conv5_1 61-1+16$\times$2+1=93 dilated rate = 16 conv5_2 93-1+16$\times$2+1=125 residual block 6 conv6_1 125-1+32$\times$2+1=189 dilated rate = 32 conv6_2 189-1+32$\times$2+1=253 residual block 7 conv7_1 253-1+32$\times$2+1=317 dilated rate = 32 conv7_2 317-1+32$\times$2+1=381 residual block 8 conv8_1 381-1+32$\times$2+1=445 dilated rate = 32 conv8_2 445-1+32$\times$2+1=509
 Block Type Convolutional Layer Receptive Field standard block 1 conv1_1 1-1+1$\times$2+1=3 dilated rate = 1 conv1_2 3-1+1$\times$2+1=5 residual block 2 conv2_1 5-1+2$\times$2+1=9 dilated rate = 2 conv2_2 9-1+2$\times$2+1=13 residual block 3 conv3_1 13-1+4$\times$2+1=21 dilated rate = 4 conv3_2 21-1+4$\times$2+1=29 residual block 4 conv4_1 29-1+8$\times$2+1=45 dilated rate = 8 conv4_2 45-1+8$\times$2+1=61 residual block 5 conv5_1 61-1+16$\times$2+1=93 dilated rate = 16 conv5_2 93-1+16$\times$2+1=125 residual block 6 conv6_1 125-1+32$\times$2+1=189 dilated rate = 32 conv6_2 189-1+32$\times$2+1=253 residual block 7 conv7_1 253-1+32$\times$2+1=317 dilated rate = 32 conv7_2 317-1+32$\times$2+1=381 residual block 8 conv8_1 381-1+32$\times$2+1=445 dilated rate = 32 conv8_2 445-1+32$\times$2+1=509
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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