《计算机应用》唯一官方网站 ›› 2022, Vol. 42 ›› Issue (9): 2800-2806.DOI: 10.11772/j.issn.1001-9081.2021071216
• 先进计算 • 上一篇
收稿日期:
2021-07-13
修回日期:
2021-09-21
接受日期:
2021-09-24
发布日期:
2021-10-18
出版日期:
2022-09-10
通讯作者:
王宇航
作者简介:
周永霞(1975—),男,浙江诸暨人,副教授,博士,主要研究方向:计算机图像视频处理、机器视觉、人工智能;基金资助:
Yuhang WANG(), Yongxia ZHOU, Liangwu WU
Received:
2021-07-13
Revised:
2021-09-21
Accepted:
2021-09-24
Online:
2021-10-18
Published:
2022-09-10
Contact:
Yuhang WANG
About author:
ZHOU Yongxia, born in 1975, Ph. D., associate professor. His research interests include computer image and video processing, machine vision, artificial intelligence.Supported by:
摘要:
针对卷积神经网络(CNN)中的传统池化算法不能很好地考虑到池化域内每个元素与该池化域所含特征之间关联性的问题,提出一种基于高斯函数的池化算法。首先根据池化域内各元素的值和所有元素的最大值计算高斯函数的三个参数值,然后运用高斯函数计算池化域内所有元素的权重,最后根据这些权重对池化域内所有元素值计算加权平均值,并以此作为池化结果。选择LeNet5、VGG16、ResNet18和MobileNet v3作为实验模型,在公开数据集CIFAR-10、Fer2013和德国交通标志识别基准(GTSRB)上进行实验,并与最大池化、平均池化、随机池化、混合池化、模糊池化、融合随机池化和soft池化这七种池化算法进行对比。实验结果表明,所提算法在三个数据集上相较其他算法在精度方面均有0.5个百分点到6个百分点的提升,且在运行效率方面优于上述除最大池化和平均池化两种池化算法外的其他池化算法,从而验证所提算法有效且具适合应用于对运算时间要求不高但对精度要求较高的情况。
中图分类号:
王宇航, 周永霞, 吴良武. 基于高斯函数的池化算法[J]. 计算机应用, 2022, 42(9): 2800-2806.
Yuhang WANG, Yongxia ZHOU, Liangwu WU. Pooling algorithm based on Gaussian function[J]. Journal of Computer Applications, 2022, 42(9): 2800-2806.
输入尺寸 | 操作 | 激活函数 | 步长 |
---|---|---|---|
224×224×3 | Conv2d,3×3 | h-swish | 2 |
112×112×16 | Bneck,3×3 | ReLU | 2 |
56×56×16 | Bneck,3×3 | ReLU | 2 |
28×28×24 | Bneck,3×3 | ReLU | 1 |
28×28×24 | Bneck,5×5 | h-swish | 2 |
14×14×40 | Bneck,5×5 | h-swish | 1 |
14×14×40 | Bneck,5×5 | h-swish | 1 |
14×14×40 | Bneck,5×5 | h-swish | 1 |
14×14×48 | Bneck,5×5 | h-swish | 1 |
14×14×48 | Bneck,5×5 | h-swish | 2 |
7×7×96 | Bneck,5×5 | h-swish | 1 |
7×7×96 | Conv2d,1×1 | h-swish | 1 |
7×7×576 | Pool,7×7 | — | 1 |
1×1×576 | Conv2d 1×1 | h-swish | 1 |
1×1×1 024 | Conv2d 1×1 | — | 1 |
表1 MobileNet v3 Small模型结构
Tab.1 Structure of MobileNet v3 Small model
输入尺寸 | 操作 | 激活函数 | 步长 |
---|---|---|---|
224×224×3 | Conv2d,3×3 | h-swish | 2 |
112×112×16 | Bneck,3×3 | ReLU | 2 |
56×56×16 | Bneck,3×3 | ReLU | 2 |
28×28×24 | Bneck,3×3 | ReLU | 1 |
28×28×24 | Bneck,5×5 | h-swish | 2 |
14×14×40 | Bneck,5×5 | h-swish | 1 |
14×14×40 | Bneck,5×5 | h-swish | 1 |
14×14×40 | Bneck,5×5 | h-swish | 1 |
14×14×48 | Bneck,5×5 | h-swish | 1 |
14×14×48 | Bneck,5×5 | h-swish | 2 |
7×7×96 | Bneck,5×5 | h-swish | 1 |
7×7×96 | Conv2d,1×1 | h-swish | 1 |
7×7×576 | Pool,7×7 | — | 1 |
1×1×576 | Conv2d 1×1 | h-swish | 1 |
1×1×1 024 | Conv2d 1×1 | — | 1 |
实验模型 | Epoch | ||
---|---|---|---|
20 | 40 | 60 | |
LeNet5-最大池化 | 55.030 | 56.160 | 57.020 |
LeNet5-平均池化 | 50.160 | 53.010 | 54.790 |
LeNet5-随机池化 | 53.030 | 57.280 | 58.910 |
LeNet5-混合池化 | 54.860 | 57.900 | 61.810 |
LeNet5-模糊池化 | 55.790 | 59.010 | 62.390 |
LeNet5-融合随机池化 | 56.420 | 60.720 | 63.750 |
LeNet5-soft池化 | 57.920 | 61.750 | 64.960 |
LeNet5-本文算法 | 59.370 | 62.780 | 65.480 |
VGG16-最大池化 | 79.090 | 82.840 | 83.810 |
VGG16-平均池化 | 75.730 | 81.080 | 82.630 |
VGG16-随机池化 | 77.720 | 84.390 | 84.610 |
VGG16-混合池化 | 78.620 | 82.970 | 83.880 |
VGG16-模糊池化 | 79.860 | 83.910 | 84.860 |
VGG16-融合随机池化 | 80.040 | 84.100 | 84.570 |
VGG16-soft池化 | 81.850 | 84.160 | 84.850 |
VGG16-本文算法 | 82.760 | 84.650 | 85.610 |
ResNet18-最大池化 | 81.820 | 85.740 | 86.830 |
ResNet18-平均池化 | 82.540 | 86.400 | 87.420 |
ResNet18-随机池化 | 83.040 | 86.900 | 88.110 |
ResNet18-混合池化 | 82.940 | 86.630 | 87.870 |
ResNet18-模糊池化 | 82.180 | 85.970 | 88.170 |
ResNet18-融合随机池化 | 82.970 | 86.540 | 88.350 |
ResNet18-soft池化 | 83.090 | 87.650 | 89.200 |
ResNet18-本文算法 | 83.930 | 87.940 | 89.930 |
MobileNet-最大池化 | 77.040 | 80.890 | 82.750 |
MobileNet-平均池化 | 76.880 | 80.670 | 82.890 |
MobileNet-随机池化 | 78.940 | 82.270 | 84.000 |
MobileNet-混合池化 | 78.210 | 82.390 | 83.680 |
MobileNet-模糊池化 | 77.990 | 81.530 | 83.520 |
MobileNet-融合随机池化 | 79.010 | 82.470 | 84.140 |
MobileNet-soft池化 | 78.980 | 82.330 | 84.170 |
MobileNet-本文算法 | 79.100 | 82.990 | 84.720 |
表2 各模型在CIFAR-10数据集上的top-1指标 (%)
Tab.2 Top-1 index of each model on CIFAR-10 dataset
实验模型 | Epoch | ||
---|---|---|---|
20 | 40 | 60 | |
LeNet5-最大池化 | 55.030 | 56.160 | 57.020 |
LeNet5-平均池化 | 50.160 | 53.010 | 54.790 |
LeNet5-随机池化 | 53.030 | 57.280 | 58.910 |
LeNet5-混合池化 | 54.860 | 57.900 | 61.810 |
LeNet5-模糊池化 | 55.790 | 59.010 | 62.390 |
LeNet5-融合随机池化 | 56.420 | 60.720 | 63.750 |
LeNet5-soft池化 | 57.920 | 61.750 | 64.960 |
LeNet5-本文算法 | 59.370 | 62.780 | 65.480 |
VGG16-最大池化 | 79.090 | 82.840 | 83.810 |
VGG16-平均池化 | 75.730 | 81.080 | 82.630 |
VGG16-随机池化 | 77.720 | 84.390 | 84.610 |
VGG16-混合池化 | 78.620 | 82.970 | 83.880 |
VGG16-模糊池化 | 79.860 | 83.910 | 84.860 |
VGG16-融合随机池化 | 80.040 | 84.100 | 84.570 |
VGG16-soft池化 | 81.850 | 84.160 | 84.850 |
VGG16-本文算法 | 82.760 | 84.650 | 85.610 |
ResNet18-最大池化 | 81.820 | 85.740 | 86.830 |
ResNet18-平均池化 | 82.540 | 86.400 | 87.420 |
ResNet18-随机池化 | 83.040 | 86.900 | 88.110 |
ResNet18-混合池化 | 82.940 | 86.630 | 87.870 |
ResNet18-模糊池化 | 82.180 | 85.970 | 88.170 |
ResNet18-融合随机池化 | 82.970 | 86.540 | 88.350 |
ResNet18-soft池化 | 83.090 | 87.650 | 89.200 |
ResNet18-本文算法 | 83.930 | 87.940 | 89.930 |
MobileNet-最大池化 | 77.040 | 80.890 | 82.750 |
MobileNet-平均池化 | 76.880 | 80.670 | 82.890 |
MobileNet-随机池化 | 78.940 | 82.270 | 84.000 |
MobileNet-混合池化 | 78.210 | 82.390 | 83.680 |
MobileNet-模糊池化 | 77.990 | 81.530 | 83.520 |
MobileNet-融合随机池化 | 79.010 | 82.470 | 84.140 |
MobileNet-soft池化 | 78.980 | 82.330 | 84.170 |
MobileNet-本文算法 | 79.100 | 82.990 | 84.720 |
实验模型 | Epoch | ||
---|---|---|---|
10 | 20 | 30 | |
LeNet5-最大池化 | 44.581 | 46.893 | 48.119 |
LeNet5-平均池化 | 43.299 | 44.887 | 47.033 |
LeNet5-随机池化 | 43.689 | 46.308 | 49.206 |
LeNet5-混合池化 | 45.302 | 48.590 | 48.760 |
LeNet5-模糊池化 | 47.181 | 48.760 | 51.156 |
LeNet5-融合随机池化 | 47.334 | 49.955 | 52.082 |
LeNet5-soft池化 | 48.878 | 50.165 | 52.674 |
LeNet5-本文算法 | 49.596 | 50.961 | 53.385 |
VGG16-最大池化 | 49.847 | 55.503 | 57.816 |
VGG16-平均池化 | 50.822 | 57.453 | 58.596 |
VGG16-随机池化 | 46.197 | 55.113 | 61.048 |
VGG16-混合池化 | 48.531 | 56.450 | 59.571 |
VGG16-模糊池化 | 51.420 | 57.156 | 60.960 |
VGG16-融合随机池化 | 52.147 | 57.098 | 61.082 |
VGG16-soft池化 | 53.461 | 57.385 | 61.904 |
VGG16-本文算法 | 53.803 | 58.011 | 62.435 |
ResNet18-最大池化 | 50.334 | 55.974 | 60.978 |
ResNet18-平均池化 | 50.348 | 56.293 | 60.841 |
ResNet18-随机池化 | 50.485 | 56.590 | 61.624 |
ResNet18-混合池化 | 51.240 | 56.961 | 62.544 |
ResNet18-模糊池化 | 51.026 | 57.476 | 63.098 |
ResNet18-融合随机池化 | 50.702 | 57.998 | 63.345 |
ResNet18-soft池化 | 51.395 | 58.132 | 64.333 |
ResNet18-本文算法 | 52.187 | 59.457 | 65.676 |
MobileNet-最大池化 | 50.485 | 54.755 | 58.080 |
MobileNet-平均池化 | 50.181 | 54.659 | 57.863 |
MobileNet-随机池化 | 51.006 | 54.802 | 58.240 |
MobileNet-混合池化 | 50.702 | 55.076 | 58.302 |
MobileNet-模糊池化 | 50.847 | 55.916 | 58.647 |
MobileNet-融合随机池化 | 51.017 | 55.715 | 58.461 |
MobileNet-soft池化 | 51.096 | 55.637 | 58.996 |
MobileNet-本文算法 | 51.028 | 56.450 | 59.739 |
表3 各模型在Fer2013数据集上的top-1指标 (%)
Tab.3 Top-1 index of each model on Fer2013 dataset
实验模型 | Epoch | ||
---|---|---|---|
10 | 20 | 30 | |
LeNet5-最大池化 | 44.581 | 46.893 | 48.119 |
LeNet5-平均池化 | 43.299 | 44.887 | 47.033 |
LeNet5-随机池化 | 43.689 | 46.308 | 49.206 |
LeNet5-混合池化 | 45.302 | 48.590 | 48.760 |
LeNet5-模糊池化 | 47.181 | 48.760 | 51.156 |
LeNet5-融合随机池化 | 47.334 | 49.955 | 52.082 |
LeNet5-soft池化 | 48.878 | 50.165 | 52.674 |
LeNet5-本文算法 | 49.596 | 50.961 | 53.385 |
VGG16-最大池化 | 49.847 | 55.503 | 57.816 |
VGG16-平均池化 | 50.822 | 57.453 | 58.596 |
VGG16-随机池化 | 46.197 | 55.113 | 61.048 |
VGG16-混合池化 | 48.531 | 56.450 | 59.571 |
VGG16-模糊池化 | 51.420 | 57.156 | 60.960 |
VGG16-融合随机池化 | 52.147 | 57.098 | 61.082 |
VGG16-soft池化 | 53.461 | 57.385 | 61.904 |
VGG16-本文算法 | 53.803 | 58.011 | 62.435 |
ResNet18-最大池化 | 50.334 | 55.974 | 60.978 |
ResNet18-平均池化 | 50.348 | 56.293 | 60.841 |
ResNet18-随机池化 | 50.485 | 56.590 | 61.624 |
ResNet18-混合池化 | 51.240 | 56.961 | 62.544 |
ResNet18-模糊池化 | 51.026 | 57.476 | 63.098 |
ResNet18-融合随机池化 | 50.702 | 57.998 | 63.345 |
ResNet18-soft池化 | 51.395 | 58.132 | 64.333 |
ResNet18-本文算法 | 52.187 | 59.457 | 65.676 |
MobileNet-最大池化 | 50.485 | 54.755 | 58.080 |
MobileNet-平均池化 | 50.181 | 54.659 | 57.863 |
MobileNet-随机池化 | 51.006 | 54.802 | 58.240 |
MobileNet-混合池化 | 50.702 | 55.076 | 58.302 |
MobileNet-模糊池化 | 50.847 | 55.916 | 58.647 |
MobileNet-融合随机池化 | 51.017 | 55.715 | 58.461 |
MobileNet-soft池化 | 51.096 | 55.637 | 58.996 |
MobileNet-本文算法 | 51.028 | 56.450 | 59.739 |
实验模型 | Epoch | ||
---|---|---|---|
5 | 10 | 15 | |
LeNet5-最大池化 | 45.891 | 67.675 | 82.668 |
LeNet5-平均池化 | 45.142 | 68.324 | 82.443 |
LeNet5-随机池化 | 46.151 | 68.890 | 83.905 |
LeNet5-混合池化 | 45.801 | 67.712 | 83.494 |
LeNet5-模糊池化 | 46.246 | 68.567 | 84.099 |
LeNet5-融合随机池化 | 45.980 | 68.759 | 84.560 |
LeNet5-soft池化 | 46.721 | 69.000 | 84.318 |
LeNet5-本文算法 | 47.130 | 69.450 | 85.074 |
VGG16-最大池化 | 53.692 | 70.246 | 89.397 |
VGG16-平均池化 | 54.026 | 70.856 | 88.180 |
VGG16-随机池化 | 53.280 | 69.960 | 90.269 |
VGG16-混合池化 | 54.678 | 70.210 | 89.517 |
VGG16-模糊池化 | 54.024 | 71.538 | 90.837 |
VGG16-融合随机池化 | 55.099 | 72.986 | 90.920 |
VGG16-soft池化 | 54.689 | 73.223 | 91.205 |
VGG16-本文算法 | 55.568 | 74.642 | 92.167 |
ResNet18-最大池化 | 70.801 | 87.769 | 96.837 |
ResNet18-平均池化 | 71.220 | 87.387 | 97.100 |
ResNet18-随机池化 | 72.413 | 89.657 | 97.375 |
ResNet18-混合池化 | 71.070 | 88.165 | 96.998 |
ResNet18-模糊池化 | 72.142 | 90.120 | 97.554 |
ResNet18-融合随机池化 | 72.814 | 90.105 | 97.445 |
ResNet18-soft池化 | 72.909 | 91.025 | 97.869 |
ResNet18-本文算法 | 74.678 | 91.920 | 98.708 |
MobileNet-最大池化 | 64.142 | 84.249 | 94.070 |
MobileNet-平均池化 | 64.494 | 84.129 | 93.756 |
MobileNet-随机池化 | 65.046 | 85.078 | 94.801 |
MobileNet-混合池化 | 64.000 | 84.935 | 94.130 |
MobileNet-模糊池化 | 63.958 | 85.140 | 94.814 |
MobileNet-融合随机池化 | 65.176 | 85.394 | 94.732 |
MobileNet-soft池化 | 65.169 | 85.373 | 94.810 |
MobileNet-本文算法 | 65.373 | 85.589 | 95.336 |
表4 各模型在GTSRB数据集上的top-1指标
Tab.4 Top-1 index of each model on GTSRB dataset
实验模型 | Epoch | ||
---|---|---|---|
5 | 10 | 15 | |
LeNet5-最大池化 | 45.891 | 67.675 | 82.668 |
LeNet5-平均池化 | 45.142 | 68.324 | 82.443 |
LeNet5-随机池化 | 46.151 | 68.890 | 83.905 |
LeNet5-混合池化 | 45.801 | 67.712 | 83.494 |
LeNet5-模糊池化 | 46.246 | 68.567 | 84.099 |
LeNet5-融合随机池化 | 45.980 | 68.759 | 84.560 |
LeNet5-soft池化 | 46.721 | 69.000 | 84.318 |
LeNet5-本文算法 | 47.130 | 69.450 | 85.074 |
VGG16-最大池化 | 53.692 | 70.246 | 89.397 |
VGG16-平均池化 | 54.026 | 70.856 | 88.180 |
VGG16-随机池化 | 53.280 | 69.960 | 90.269 |
VGG16-混合池化 | 54.678 | 70.210 | 89.517 |
VGG16-模糊池化 | 54.024 | 71.538 | 90.837 |
VGG16-融合随机池化 | 55.099 | 72.986 | 90.920 |
VGG16-soft池化 | 54.689 | 73.223 | 91.205 |
VGG16-本文算法 | 55.568 | 74.642 | 92.167 |
ResNet18-最大池化 | 70.801 | 87.769 | 96.837 |
ResNet18-平均池化 | 71.220 | 87.387 | 97.100 |
ResNet18-随机池化 | 72.413 | 89.657 | 97.375 |
ResNet18-混合池化 | 71.070 | 88.165 | 96.998 |
ResNet18-模糊池化 | 72.142 | 90.120 | 97.554 |
ResNet18-融合随机池化 | 72.814 | 90.105 | 97.445 |
ResNet18-soft池化 | 72.909 | 91.025 | 97.869 |
ResNet18-本文算法 | 74.678 | 91.920 | 98.708 |
MobileNet-最大池化 | 64.142 | 84.249 | 94.070 |
MobileNet-平均池化 | 64.494 | 84.129 | 93.756 |
MobileNet-随机池化 | 65.046 | 85.078 | 94.801 |
MobileNet-混合池化 | 64.000 | 84.935 | 94.130 |
MobileNet-模糊池化 | 63.958 | 85.140 | 94.814 |
MobileNet-融合随机池化 | 65.176 | 85.394 | 94.732 |
MobileNet-soft池化 | 65.169 | 85.373 | 94.810 |
MobileNet-本文算法 | 65.373 | 85.589 | 95.336 |
池化算法 | 分辨率 | ||
---|---|---|---|
100×100 | 1 000×1 000 | 10 000×10 000 | |
最大池化 | 0.093 | 4.675 | 307.083 |
平均池化 | 0.252 | 9.025 | 867.590 |
随机池化 | 0.444 | 12.446 | 1 268.931 |
混合池化 | 0.196 | 8.988 | 831.617 |
模糊池化 | 0.689 | 16.031 | 1 812.159 |
融合随机池化 | 0.631 | 15.296 | 1 604.357 |
soft池化 | 0.454 | 13.155 | 1 239.741 |
本文算法 | 0.372 | 11.387 | 1036.137 |
表5 各算法在不同图片分辨率下的运行时间 (ms)
Tab.5 Running time of each algorithm under different image resolution
池化算法 | 分辨率 | ||
---|---|---|---|
100×100 | 1 000×1 000 | 10 000×10 000 | |
最大池化 | 0.093 | 4.675 | 307.083 |
平均池化 | 0.252 | 9.025 | 867.590 |
随机池化 | 0.444 | 12.446 | 1 268.931 |
混合池化 | 0.196 | 8.988 | 831.617 |
模糊池化 | 0.689 | 16.031 | 1 812.159 |
融合随机池化 | 0.631 | 15.296 | 1 604.357 |
soft池化 | 0.454 | 13.155 | 1 239.741 |
本文算法 | 0.372 | 11.387 | 1036.137 |
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