# Self-Improved Learning for Salient Object Detection
## 3 Method
### Self-Improvement Training Strategy
#### 3.1.1 PUM: Progressively Updated Module  
Formally, we design a progressively updated module (PUM), denoted by \(\mathcal{F}_{\text{PUM}}\), to generate smooth labels. \(\mathcal{F}_{\text{PUM}}\) shares the same network structure with the SOD network \(\mathcal{F}_{\text{SOD}}\). Specifically, let the parameters of \(\mathcal{F}_{\text{SOD}}\) be \(\theta_{\text{SOD}}\), and the parameters of \(\mathcal{F}_{\text{PUM}}\) be \(\theta_{\text{PUM}}\). First, we randomly initialize \(\theta_{\text{SOD}}\). Then, we initialize \(\theta_{\text{PUM}}\) by  
\[t=0:\qquad\theta_{\text{PUM}}^{(0)}=\theta_{\text{SOD}}^{(0)}, \tag{1}\]  
where \(t\) is the iteration of the training (Iteration \(t\) refers to a mini-batch training iteration instead of an epoch). At this point, \(F_{\text{PUM}}\) is identical to \(F_{\text{SOD}}\). They can only generate a  
Figure 2: The overview of our proposed framework. Our framework consists of two components, the Self-Improvement Training strategy (SIT) and Augmentation-based Consistent Learning scheme (ACL). The PUM Module of SIT generates smooth labels at training time, progressively improving the SOD model in a momentum-updating manner. SIT relaxes the binary annotations with smooth labels, reducing the learning difficulty. ACL enforces the consistency between raw images and augmented images, regularizing the model at both feature level and prediction level.  
random salient output before training. To progressively improve the quality of the smooth labels, we update \(\theta_{\text{PUM}}\) at a momentum coefficient \(\eta\) from \(\theta_{\text{SOD}}\) as follows  
\[t=1: \theta_{\text{PUM}}^{(1)}=\eta\cdot\theta_{\text{PUM}}^{(0)}+(1- \eta)\cdot\theta_{\text{SOD}}^{(1)}, \tag{2}\] \[t=2: \theta_{\text{PUM}}^{(2)}=\eta\cdot\theta_{\text{PUM}}^{(1)}+(1- \eta)\cdot\theta_{\text{SOD}}^{(2)},\] \[\vdots \vdots\] \[t=T: \theta_{\text{PUM}}^{(T)}=\eta\cdot\theta_{\text{PUM}}^{(T-1)}+( 1-\eta)\cdot\theta_{\text{SOD}}^{(T)}.\]  
It is worth noting that only parameters \(\theta_{\text{SOD}}\) are updated via backpropagation, whereas parameters \(\theta_{\text{PUM}}\) are updated progressively by \(\theta_{\text{SOD}}\) at the training time of \(\mathcal{F}_{\text{SOD}}\). The momentum update in Equation (2) makes \(\theta_{\text{PUM}}\) evolve more smoothly than \(\theta_{\text{SOD}}\). As a result, the generated smooth labels are improved smoothly with the training of \(\mathcal{F}_{\text{SOD}}\). In this way, the PUM progressively integrates the parameter from the SOD network and generates more informative supervisions for the output of the SOD network during training, as illustrated in Figure 2b.  
With PUM, we can obtain smooth labels \(z\) by feeding an input image \(x\) into \(\mathcal{F}_{\text{PUM}}\) as  
\[z^{(t)}=\mathcal{F}_{\text{PUM}}(x;\theta_{\text{PUM}}^{(t)}), \tag{3}\]  
where predictions \(z\) are of the same size as ground truth \(y\). While \(y\) is \(\in\{0,1\}^{H\times W}\), \(z\) is \(\in(0,1]^{H\times W}\)  
With smooth labels \(z\), we regularize \(\mathcal{F}_{\text{SOD}}\) by  
\[\mathcal{L}_{\text{PUM}}=\sum_{i=1}^{H}\sum_{j=1}^{W}(p_{i,j}^{(t)}-z_{i,j}^{( t)})^{2}, \tag{4}\]  
where \(p\in(0,1]^{H\times W}\) are the predictions of \(\mathcal{F}_{\text{SOD}}\), and \(z\in(0,1]^{H\times W}\) are the obtained smooth labels by \(\mathcal{F}_{\text{PUM}}\).