# High-Fold 3D Gaussian Splitting Model Pruning Method Assisted by Opacity
## 3 Methods
### Gaussian Point Spherical Harmonic Coefficient Compression  
The previous sections have addressed the compression of the number of Gaussians, but there remains significant potential for further reduction in the model's parameter size. The 3D Gaussian Splatting model is primarily composed of the attribute parameters associated with each Gaussian point. In the traditional uncompressed model, the degree of spherical harmonic function is usually 3. Each Gaussian point contains a total of 59 parameters. Among these, 48 are spherical harmonic coefficients, which take up most of the storage space. The expressive capability of spherical harmonic functions increases with higher spherical harmonic function degrees, but this also significantly elevates the number of parameters that need to be stored. Experiments [21] have demonstrated that a spherical harmonic degree of 2, when combined with knowledge distillation aided by novel views, can effectively represent scenes while reducing the number of spherical harmonic coefficients. Furthermore, it has been observed that a lot of points within a scene exhibit similar color characteristics. Storing colors independently for each Gaussian point incurs substantial storage overhead. To mitigate this, we apply vector quantization to the spherical harmonic coefficients representing color, allowing multiple Gaussian points with similar colors to share a single color feature vector.  
Firstly, the model compressed through the Gaussian Point Quantity Compression module is used as the teacher model to guide the student model, in which the spherical harmonic degree is set to 2. Given that the teacher model is capable of high-quality scene reconstruction, we introduce a random uniform perturbation to the poses of the old views to generate new view renderings. These are added to the training dataset for the student model. Compared to the limited dataset of old views, the enriched dataset with new perspective renderings enables the student model to learn more beneficial information.  
\(\delta\) as a perturbation threshold, the formula for generating new views is:  
\[v_{new}=v_{old}+U(0,\delta) \tag{12}\]  
The loss function shown in Equation (11) is calculated on a pixel-by-pixel basis, taking the sum of the Euclidean distances rendered by the teacher model and the student model as the loss.  
\[L=\frac{1}{HW}\sum_{i=1}^{HW}\lVert C_{teacher}(p_{i})-C_{student}(p_{i}) \rVert_{2}^{2} \tag{13}\]  
After obtaining the student model through distillation, vector quantization is applied to the spherical harmonic coefficients. The process is shown as Figure 3. The process begins with the initialization using the K-means algorithm [44], clustering the spherical harmonic coefficient vectors into K clusters, where K is the size of the codebook. Within each cluster, the most representative SH coefficient vector is determined to serve as a codebook key \(c_{k}\). Since the number of Gaussian points far exceeds K, this method can achieve a very high compression ratio.  
This approach reduces the model's overall storage requirements for color parameters. Although knowledge distillation and vector quantization lead to a slight decline in reconstruction quality, they result in a more compact color representation within the 3 DGS model, significantly aiding model compression by reducing the number of parameters.