# Small-Scale Face Detection Based on Improved R-FCN
## 5 Receptive Field Adaptation Block (RFAB)  
Traditional CNN uses fixed-size convolutional kernels for feature extraction. The size of the receptive field of each layer of neurons is fixed, which may damage the discrimination of features. In the human visual cortex, the size of the receptive field is affected by many factors. For example, the size of population receptive field (pRF) is a function of the eccentricity of retinal imaging. As the eccentricity increases, the receptive field also increases [27]. It can be understood that the brain gets more information from the area closer to the visual center, but less from the area farther away from the visual center. RFB is proposed according to [27], which highlights the importance of the sampling center area. The insensitivity of CNN to small spatial changes is improved, and it achieves good results in object detection.  
However, in the human visual system, the size of the receptive field is related not only to the eccentricity of retinal imaging but also the stimulation of the visual nerves. That is, the stimulation of the same neuron is different, and the corresponding receptive field size of the neuron is not fixed. In RFB, inception structure and dilated convolution are used to simulate the receptive field mechanism in human retina imaging, and linear superposition is used to integrate the features with different receptive fields in the spatial dimension. Although dilated convolution increases the weight of features  
Figure 3: Structure of feature fusion branch in R-FCN with a feature fusion branch (f-R-FCN).  
closer to the sampling center to achieve the purpose of enhancing the discrimination of features, the effect of neuron stimulation on the receptive field is ignored. Therefore, we add a RFAB based on f-R-FCN to enhance the feature of small-scale faces by combining RFB and selective kernel (SK) [28] module. In this way, the influence of eccentricity and the neuronal stimulation on the receptive field are considered. The structure of RFAB is shown in Figure 4.  
The former part of RFAB is the same as that of RFB. The input is divided into three branches by convolution operation of different sizes. The corresponding receptive field of each branch is different. Two \(3\times 3\) convolutions are used to replace the \(5\times 5\) convolution for reducing the calculation. \"rate\" in Figure 4 represents the dilation rate of dilated convolution. Then, the features of the three branches are fused, after global average pooling, \(1\times 1\) convolution and softmax operation, and the corresponding probability value is obtained for each channel. The CNN selects the size of the receptive field for each channel through element product. RFAB also uses a shortcut to retain the original features and adds the processed features to obtain the final features. RFAB is used in the last layer of feature fusion branch to improve the discrimination of the shared feature map.  
We add a RFAB based on f-R-FCN to enhance the feature of small-scale faces by combining RFB and SK module. The structure of RFAB-f-R-FCN is shown in Figure 5. Compared with those in Figure 3, \(C_{5}\) is removed, and the feature fusion branch is constructed based on \(C_{2}\), \(C_{3}\), \(C_{4}\) The reason is that we find that average precision (AP) of detection on \(F_{4}\) is higher than that on \(F_{5}\). See Section 6.2.1 for details.