# SemABC: Semantic-Guided Adaptive Bias Calibration for Generative Zero-Shot Point Cloud Segmentation
## 3 Methods
### Visual-Semantic Fusion Branch  
The proposed visual-semantic fusion branch aims to integrate the visual features \(F_{s+u}\) with the category semantic embeddings \(T\) for a more accurate classification between the seen and unseen classes. The network architecture of the branch is illustrated in Figure 3. We utilize a contrastive learning strategy to train it. \(F_{s+u}\) is the visual features produced by the primary segmentation branch, which consists of the seen features from the encoder \(E\) and unseen features synthesized by the generator \(G\). \(T\) denotes the semantic embeddings  
Figure 2: The framework of the semantic-guided dual-branch bias calibration network contains three components: a primary segmentation branch (main branch), a visual–semantic fusion branch (auxiliary branch), and an adaptive bias calibration module. The encoder, generator, segmentor, and visual–semantic fusion branch undergo sequential optimization during the training process. Only the encoder is used to process the point cloud for features without using the generator during inference. of all the category labels \(C\). We first separately project the visual features \(F_{s+u}\) and semantic embeddings \(T\) to obtain the same dimensions along the feature channels, denoted as \(\hat{F}\) and \(\hat{T}\). Then, we perform channel and spatial attention to fuse the visual features \(\hat{F}\) and semantic embeddings \(\hat{T}\). Specifically, channel attention calculates the importance of each channel of one modality, allowing the features of the other modality to concentrate on the relevant key channels. Meanwhile, spatial attention enhances significant regions and depresses irrelevant regions by analyzing the spatial correlation of the two modalities. The channel attention is formulated as follows:  
\[ \begin{split} Q_{tc}=\hat{T}W_{qt,c},K_{tc}=\hat{T}W_{kt,c},V_{fc} =\hat{F}W_{vf,},\\ F_{c}=\hat{F}+\mathcal{Softmax}(\frac{Q_{tc}^{T}K_{tc}}{\sqrt{D_{K} }})V_{fc},\end{split}  \tag{1}\]  
\[ \begin{split} Q_{fc}=\hat{F}W_{qf,c},K_{fc}=\hat{F}W_{lf,c},V_{tc} =\hat{T}W_{vt,c},\\ T_{c}=\hat{T}+\mathcal{Softmax}(\frac{Q_{fc}^{T}K_{fc}}{\sqrt{D_{K} }})V_{tc},\end{split}  \tag{2}\]  
where \(W_{qt,c}\), \(W_{kt,c}\), and \(W_{vf,c}\) are the learnable projection weights that map \(\hat{T}\) to the query (\(Q_{tc}\)) and key (\(K_{tc}\)) vectors and map \(\hat{F}\) to the value (\(V_{fc}\)) vectors. Similarly, \(W_{qf,c}\), \(W_{kf,c}\), and \(W_{vt,c}\) project \(\hat{F}\) to the corresponding query (\(Q_{fc}\)) and key (\(K_{fc}\)) and project \(\hat{T}\) to the value (\(V_{tc}\)). \(D_{K}\) is the dimension size of the projected vectors. In this way, we obtain the fused visual features \(F_{c}\) and semantic features \(T_{c}\) encoded with channel attention. The spatial attention is computed as follows:  
\[ \begin{split} Q_{fs}=F_{c}W_{qf,s},K_{ts}=T_{c}W_{kt,s},V_{ts}=T_{ c}W_{vt,s},\\ F_{s}=F_{c}+\mathcal{Softmax}(\frac{Q_{fs}K_{ts}^{T}}{\sqrt{D_{K} }})V_{ts},\end{split}  \tag{3}\]  
\[ \begin{split} Q_{ts}=T_{c}W_{qt,s},K_{fs}=F_{c}W_{lf,c},V_{fs}=F_ {c}W_{vf,},\\ T_{s}=T_{c}+\mathcal{Softmax}(\frac{Q_{ts}K_{ts}^{T}}{\sqrt{D_{K} }})V_{fs},\end{split}  \tag{4}\]  
where \(W_{qf,s}\), \(W_{kt,s}\), and \(W_{vt,s}\) denote the learnable weights that map \(F_{c}\) to its corresponding query (\(Q_{fs}\)) and map \(T_{c}\) to the key (\(K_{ts}\)) and value (\(V_{ts}\)) vectors, whereas \(W_{qt,s}\), \(W_{kf,s}\), and \(W_{vf,s}\)  
Figure 3: The computational process of the visual–semantic fusion module. \(\oplus\) denotes element-wise addition. \(\otimes\) denotes the dot product. similarly project \(T_{c}\) and \(F_{c}\) to the query (\(Q_{ts}\)), key (\(K_{fs}\)), and value (\(V_{fs}\)). \(D_{K}\) is the dimension of the output vectors. After the spatial attention, we obtain the fused visual features \(F_{s}\) and semantic features \(T_{s}\).