Self-Calibrated Convolutions

Liu et al. presented self-calibrated convolution as a means to enlarge the receptive field at each spatial location.

Self-calibrated convolution is used together with a standard convolution. It first divides the input feature $X$ into $X_{1}$ and $X_{2}$ in the channel domain. The self-calibrated convolution first uses average pooling to reduce the input size and enlarge the receptive field: \begin{align} T_{1} = AvgPool_{r}(X_{1}) \end{align} where $r$ is the filter size and stride. Then a convolution is used to model the channel relationship and a bilinear interpolation operator $Up$ is used to upsample the feature map:

\begin{align} X'_{1} = \text{Up}(Conv_2(T_1)) \end{align}

Next, element-wise multiplication finishes the self-calibrated process:

\begin{align} Y'_{1} = Conv_3(X_1) \sigma(X_1 + X'_1) \end{align}

Finally, the output feature map of is formed: \begin{align} Y_{1} &= Conv_4(Y'_{1}) \end{align} \begin{align} Y_2 &= Conv_1(X_2) \end{align} \begin{align} Y &= [Y_1; Y_2] \end{align} Such self-calibrated convolution can enlarge the receptive field of a network and improve its adaptability. It achieves excellent results in image classification and certain downstream tasks such as instance segmentation, object detection and keypoint detection.