# ConceptVAE: Self-Supervised Fine-Grained Concept Disentanglement from 2D Echocardiographies
## 5 Quantitative Model Analysis
### Style-Based Synthetic Data Generation  
We further explore how style information can be used to generate synthetic data. Such data can be valuable for creating inputs conditioned by patient attributes, such as generating images with more textured walls. To achieve this, we leverage the known range of \(x_{style}\) (since the constraint \(\mathcal{L}_{style}\) is enforced during training), and investigate style-based image generation. This involves adding Gaussian noise at various levels \(\beta\) as described in Equation (7):  
\[n \sim\mathcal{N}(\mathbf{0},I) \tag{7}\] \[x_{style}^{*} =\frac{x_{style}+\beta n}{\sqrt{1+\beta^{2}}}\]  
where \(\beta\) controls the amount of noise injected into \(x_{style}^{*}\).  
We then reconstruct the image using these style attributes. Randomly sampled reconstructions w.r.t. multiple \(\beta\) (reusing the same sampled \(n\)) are illustrated in Figure 7, while  
\begin{table}
\begin{tabular}{c c c} \hline \hline  & \multicolumn{2}{c}{**Model**} \\ \cline{2-3}
**Metric** & **ConceptVAE** & **Baseline** \\ \hline “open-AV” class AP & 0.337 & 0.297 \\ “closed-AV” class AP & 0.386 & 0.459 \\ mean AP & 0.362 & 0.378 \\ \hline objectness AP & 0.786 & 0.665 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Mean average precision scores for object detection on PLAX views.  
Figure 8 illustrates reconstructions with multiple noise samplings \(n_{k}\sim\mathcal{N}(\mathbf{0},I)\) and fixed \(\beta=0.3\). We observe that even with relatively high \(\beta\) values, the reconstructions closely resemble the unaltered concepts, while the image textures are modified (with minimal changes to anatomical structures in terms of their shape or placement). This leads to the following observations:  
* The model uses \(x_{concept}\) to decode semantic content, such as anatomical structures like chamber walls, blood pools, and valves, while \(x_{style}\) is used to particularize local textures, shadows and speckles.
* With ConceptVAE, synthetic data can be generated by modifying only textures and speckles while retaining anatomical structures. This allows for the generation of novel samples that can serve as style augmentations without modifying the content, potentially enhancing the training performance of dense downstream models, such as those used for segmentation.  
The samples generated with ConceptVAE remain within the original data distribution, and thus can serve as a more calibrated augmentation method. In contrast, classical transformations such as rotations and blurring may generate data points with appearances not observed in the initial distribution (e.g., 'unnatural rotations or texture changes'). Ultrasound medical imaging inherently introduces noise in video acquisitions in the form of pixel speckles. ConceptVAE simulates the effect of different realizations of echocardiography-specific noise, producing images that reflect this variability. Given the large variability between acquisitions and patients in ultrasound imaging [49], the proposed method can potentially improve the robustness of the models on downstream tasks.  
Figure 8: Reconstructed images with unaltered \(x_{style}\) (**left**) alongside three reconstructions with constant noise level \(\beta=0.3\). Each noisy reconstruction uses different noise, \(n\sim\mathcal{N}(\mathbf{0},I)\), as described in Equation (7).  
Figure 7: Original images (**left**) displayed alongside reconstructions using \(x_{style}^{*}\) with increasing levels of injected noise, \(\beta\). From the second column to the **right**, \(\beta\) values are 0 (unaltered reconstruction), 0.2, 0.4 and 0.6, respectively.