# Gaze Estimation via Strip Pooling and Multi-Criss-Cross Attention Networks
## 3 Proposed SPMCCA-Net Models
### Feature-Enhanced Bottleneck Blocks SPbottleneck  
The strip pooling attention mechanism has been applied to many domains and demonstrated its powerful applications, such as the medical domain [30]. In addition, in the field of gaze estimation, since both eyes are asymmetric, the feature extraction process must take into account not only the individual changes of the eyes but also their joint feature information associated with binocular changes, requiring the model to capture the long-distance dependencies between the eyes. We thus incorporated a strip pooling module into the bottleneck block to design a novel feature-enhanced bottleneck block called SPbottleneck (bottleneck with strip pooling module), which addresses the aforementioned issue.  
The green grid in Figure 3a depicts the effect of traditional global pooling, and the red grid in Figure 3b depicts the effect of the strip pooling module. The two modules are applied to the face image at the same time. As demonstrated by Figure 3, traditional global pooling uses a square window, which will inevitably contain interference information from regions not related to gaze, while the strip pooling module can better capture long-distance dependencies across eye regions (indicated by yellow border regions). The latter approach prevents information unrelated to gaze from interfering with gaze prediction.  
Figure 3: The effects of traditional global pooling and strip pooling for gaze estimation. (**a**) the effects of traditional global pooling images; (**b**) the effects of strip pooling.  
Figure 2: The structure of ResNet-SMC.  
We implemented the strip pooling module in three steps: a feature map of dimensions \(H\) and \(W\) is initially provided as input; the feature map is pooled into \(H\times 1\) and \(1\times W\) by horizontal pooling and vertical pooling, respectively; the values of elements \(x_{i,j}\) (\(ij\) indicate the position of specific elements within the feature map) in the pooling are averaged and returned as pooled output values. Following horizontal pooling, the output \(y_{i}^{h}\) can be expressed as:  
\[y_{i}^{h}=\frac{1}{W}\underset{0\leq j<W}{\sum}x_{i,j}. \tag{1}\]  
Following vertical pooling, the output \(y_{i}^{h}\) can be expressed as:  
\[y_{j}^{v}=\frac{1}{H}\underset{0\leq i<H}{\sum}x_{i,j}. \tag{2}\]  
The size of both feature maps is then expanded to \(H\times W\) via 1D convolutions. The expanded feature maps are summed:  
\[y_{c,i,j}=y_{c,i}^{h}+y_{c,j}^{v}. \tag{3}\]  
In the above expression, \(c\) is the number of channels. The final output \(Z\) is expressed as follows:  
\[Z=Scale(x,\sigma(f(y))), \tag{4}\]  
where \(Scale(\cdot,\cdot)\) denotes element-wise multiplication, \(\sigma\) denotes the sigmoid function, and \(f\) denotes a \(1\times 1\) convolution.  
After the above process, each position in the output tensor is built using data from each position in the vertical and horizontal directions of the corresponding position in the input tensor, which represent all the elements in the crossover position.  
By repeating the above aggregation process, long-distance spatial dependencies can be constructed from the whole-face image. Figure 4 provides details on the strip pooling module.  
As shown in Figure 5, the feature-enhanced bottleneck block SPbottleneck is based on the bottleneck block with an added strip pooling module after 3 \(\times\) 3 convolution. Thus, SPbottleneck can encode global horizontal and vertical information about the feature map to balance its weights for feature optimization. This approach avoids unnecessary connections between distant positions so that, when the gaze changes, the weight values associated with the eye regions can be balanced under the control of joint features reflecting changes in both eyes. At the same time, fewer weight values will be assigned to regions unrelated to gaze to prevent their interference with gaze prediction. We demonstrate the success of the proposed method quite well in the experimental section thro  
Figure 4: The details of the Strip Pooling module.