U-Net architectures have been instrumental in advancing biomedical image segmentation (BIS) but often struggle with capturing long-range information. One reason is the conventional down-sampling techniques that prioritize computational efficiency at the expense of information retention. This paper introduces a simple but effective strategy, we call it Stair Pooling, which moderates the pace of down-sampling and reduces information loss by leveraging a sequence of concatenated small and narrow pooling operations in varied orientations. Specifically, our method modifies the reduction in dimensionality within each 2D pooling step from 41 to 21. This approach can also be adapted for 3D pooling to preserve even more information. Such preservation aids the U-Net in more effectively reconstructing spatial details during the up-sampling phase, thereby enhancing its ability to capture long-range information and improving segmentation accuracy. Extensive experiments on three BIS benchmarks demonstrate that the proposed Stair Pooling can increase both 2D and 3D U-Net performance by an average of 3.8% in Dice scores. Moreover, we leverage the transfer entropy to select the optimal down-sampling paths and quantitatively show how the proposed Stair Pooling reduces the information loss.
Figures & tables
Figure 1: The overview of our proposed Stair Pooling. It splits the original max pooling layer into a series of concatenated small and narrow pooling kernels. To break the linear relationship, each pooling operation is followed by a convolutional layer and a ReLU activation.
Methods
DSC↑
HD↓
Aorta
Gallbladder
Kidney(L)
Kidney(R)
Liver
Pancreas
Spleen
Stomach
R50 U-Net
74.68
36.87
87.74
63.66
80.6
78.19
93.74
56.9
85.87
74.16
U-Net
76.85
39.7
89.07
69.72
77.77
68.6
93.43
53.98
86.67
75.58
R50 Att-UNet
75.57
37.66
55.92
63.91
79.2
72.71
93.56
49.37
87.19
74.95
Att-UNet
77.77
36.87
89.55
68.88
77.98
71.11
93.57
58.04
87.3
75.75
R50 ViT
71.29
32.27
73.73
55.13
73.52
72.2
91.51
45.99
81.99
73.95
TransUnet
77.48
31.69
87.23
63.13
81.87
77.02
94.08
55.86
85.08
75.62
Table 1: Segmentation accuracy of different methods on the Synapse multi-organ CT dataset. The highest value in each column is highlighted in bold. Gray rows refer to methods whose sizes are significantly larger than others.
Methods
DSC
RV
Myo
LV
R50 U-Net
87.55
87.1
80.63
94.92
U-Net
86.63
85.46
81.08
93.35
R50 ViT
87.57
86.07
81.88
94.75
TransUnet
89.71
88.86
84.53
95.73
SwinUnet
90.00
88.55
85.62
95.83
Pyramid UNet
89.17
88.14
83.85
95.52
Table 2: Segmentation accuracy of different methods on the ACDC dataset in DSC( % ).
Figure 2: Qualitative comparison of different approaches on the Synapse dataset. From left to right: Ground Truth, U-Net, SwinUnet, UNet with HWT pooling, our SP UNet and the TE selected variant.
Methods
DSC
Kidney
Masses
Tumor
UNETER
73.4
95.54
69.07
60.56
UNETER+SENet
74.9
95.70
69.73
60.50
UNETERt+CBAM
75.2
95.33
70.05
62.46
U-Net++
75.9
95.65
70.94
62.64
Attention UNETER
76.6
95.47
70.65
62.73
SP UNETER
77.1
95.71
71.77
63.85
Table 3: Segmentation accuracy of different methods on the KiT23 dataset in DSC( % ).
Figure 3: Segmentation results and sizes of different models on the Synapse dataset.
Dataset
Step1
Step2
Step3
Synpase
P21′ , P12′
P21′ , P12′
P12′ , P21′
ACDC
P21′ , P12′
P21′ , P12′
P21′ , P12′
KiT23
P122′ , P212′ , P221′
P122′ , P221′ , P212′
P122′ , P212′ , P221′
Table 4: Optimal paths selected by calculating TE on three datasets, where Pvhw′ refers to a v×h×w pooling kernel.
Figure 4: Correlations between DSC and TE on the KiT23 dataset.
Figure 5: Violin plots for visualizing distributions of transfer entropy across different paths on three datasets.