## 3 Method
### Self-Training-Based Pseudo-Proposal Generation Network  
To excavate potential foreground instances from the unannotated background, we introduce STPPGN. In the fine-tuning phase, for each image \(i\in I\), our method uses the multiscale features extracted from \(i\) to generate two sets of proposals. One set is the original proposals \(P_{O}\) generated by the original RPN from Branch 1, as shown in Figure 1a; the other set is the pseudo-proposals generated by the STPPGN where the structure is shown in Figure 1b. Both sets of proposals have the same structure \(P=\{B,O\}\) where \(B=\{x,y,h,w\}\) denotes the bounding box coordinates of each proposal, and \(O\) is the confidence of the proposal, indicating the probability that the bounding box contains an object. As shown in Figure 1b, STPPGN consists of two submodules:teacher RPN and student RPN, which are structurally consistent with the original RPN. The teacher RPN is updated using the exponential moving average of the student RPN weights [48]. The original proposals output by the original RPN may belong to either novel or base classes, and the pseudo-proposals output by STPPGN represent potential foregrounds in the background rather than being specifically novel class proposals.  
The teacher RPN generates and produces a set of high-quality teacher proposals \(P_{th}\), which have an intersection over union (IoU) of less than a threshold \(\tau_{bg}\) with all ground truth objects. The student RPN, under the guidance of the teacher RPN, produces a set of student proposals, denoted by \(P_{stu}\).  
During the fine-tuning phase, since the teacher and student RPN are initialized with the weights of the original RPN, they may not produce high-quality outputs at the beginning of training. Therefore, we add the novel class instances \(X_{novel}\) in the corresponding images to the outputs of the teacher and student RPN. We only consider the classification loss of a proposal when it matches and has a high overlap with \(X_{novel}\). The advantage of this approach is that it enables the student RPN to fully learn the class-specific features of novel instances without being distracted by their positional information. This enhances its ability to uncover potential unlabeled novel class instances. Let \(P_{match}=\{p_{i}\in P_{stu}\mid p_{i}\text{ is match with }P_{th}\}\), \(P_{match}\) signify the proposals in \(P_{stu}\) that are matched with \(P_{th}\). If student proposals \(p_{i}\in P_{match}\) match a certain proposal \(p_{i}^{*}\) in teacher proposal \(P_{th}\), and conversely, it matches any novel instances \(\bar{p}_{i}\) in \(X_{novel}\). The loss function of the student RPN \(\mathcal{L}_{stu}^{rpn}\) can be expressed as follows:  
\[\mathcal{L}_{stu}^{rpn}(P_{stu},P_{th},X_{novel})=\mathcal{L}_{stu}^{rpn-cls}+ \mathcal{L}_{stu}^{rpn-reg} \tag{3}\]  
\[\mathcal{L}_{stu}^{rpn-cls}=\sum_{p_{i}\in P_{match}}\mathcal{L}_{stu}^{cls}( p_{i},p_{i}^{*})+\sum_{p_{i}\in P_{stu}/P_{match}}w_{i}\mathcal{L}_{stu}^{cls}( p_{i},\bar{p}_{i}) \tag{4}\]  
\[\mathcal{L}_{stu}^{rpn-reg}=\sum_{p_{i}\in P_{match}}\mathcal{L}_{stu}^{reg}( p_{i},p_{i}^{*}) \tag{5}\]  
Here, \(\mathcal{L}_{stu}^{rpn-cls}\) represents the classification loss of the student RPN, while \(\mathcal{L}_{stu}^{rpn-reg}\) denotes the regression loss of the student RPN. \(w_{i}\) is a coefficient that indicates whether to include the classification loss for \(p_{i}\).  
\[w_{i}=\begin{cases}1,&\text{if }p_{i}\in P_{stu}/P_{match}\text{ and } IoU(p_{i},\overline{p_{i}})>\tau_{IoU},\\ 0,&\text{otherwise}.\end{cases} \tag{6}\]  
where \(IoU(.,.)\) denotes the IoU.  
Finally, \(P_{stu}\) is filtered and subjected to non-maximum suppression (NMS) to generate a high-quality set of pseudo-proposals \(P_{P}\). This set of pseudo-proposals will be further processed in Section 3.4 to generate pseudo-samples.