# Neural Radiance Fields with Hash-Low-Rank Decomposition
## 5 Experiments
### Comparison on Public Datasets
#### 5.2.2 Quantitative Comparison  
In this section, we show a qualitative comparison of our methods. We compared the current mainstream grid-based NeRF method [4; 5; 6; 21], the method based on multi-hash coding [14], and the method based on low-rank decomposition [13]. Finally, we also compared it with the currently very popular 3 DGS [12] technology. Our results can be seen in Table 1. It is worth noting that we emphasize the compactness of our model, and this compactness is achieved through the characteristics of the basic method. Our model has not been subjected to any existing quantification or distillation techniques.  
Looking at the rendering-related metrics, we can see that, in the Synthetic-NeRF dataset, our model was comparable to the current best scene characterization, 3 DGS, in terms of rendering metrics, and PSNR also exceeded 3 DGS. At the same time, our model only used 7% of the model size and 30% of the number of training steps to achieve this performance, which is enough to prove the efficiency of our model. Compared to the hash-based encoding method I-NGP, our results demonstrate a significant improvement of 0.9 dB on this dataset. Additionally, our method also achieved a notable performance  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & & \multicolumn{3}{c}{**Synthetic-NeRF**} & \multicolumn{3}{c}{**NSVF**} \\ \hline
**Method** & **Batch Size** & **Steps\(\downarrow\)** & **Param (MB)\(\downarrow\)** & **PSNR\(\uparrow\)** & **SSIM\(\uparrow\)** & \(LPIPS_{\text{\tiny{sltx}}}\)** & **PSNR\(\uparrow\)** & **SSIM\(\uparrow\)** & \(LPIPS_{\text{\tiny{seg}}}\)** \\ \hline NeRF & 4096 & 300k & 5 & 31.01 & 0.947 & - & 30.81 & 0.952 & 0.043 \\ NSVF & 300 & 150k & - & 31.75 & 0.953 & 0.047 & 35.18 & 0.979 & 0.015 \\ TensoRF & 4096 & 30k & 71.8 & 33.14 & 0.963 & 0.027 & 36.52 & 0.982 & 0.012 \\ I-NGP & 10k-85k & 30k & 46.56 & 32.59 & 0.960 & 0.031 & - & - & - \\ DVGO & 5000 & 30k & 612.1 & 31.95 & 0.957 & 0.035 & 35.08 & 0.975 & 0.019 \\ Plenoxels & 5000 & 128k & 778.1 & 31.71 & 0.958 & - & - & - & - \\
3 DGS & - & 100k & 676 & 33.32 & 0.959 & 0.023 & - & - & - \\ \hline Ours & 4096 & 30k & 71.9 & 33.49 & 0.964 & 0.025 & 37.10 & 0.984 & 0.009 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Performance comparison on the Synthetic-nerf and NSVF datasets. Red means the best, and yellow means the second best.  
gain of 0.35 dB compared to the pure tensor decomposition method TensoRF. This result also demonstrates that these two different encoding approaches have distinct ways of understanding the scene, each with its own advantages. Our method successfully combines the strengths of both approaches, achieving superior performance. In the NSVF dataset, our model is significantly improved compared to previous pure low-rank decomposition algorithms, which proves that our method effectively fuses and utilizes the encoding information of hash encoding. Our method achieved a state-of-the-art performance in this dataset.  
In the Tanks and Temples dataset, we utilized the specialized data provided by NSVF for comparison with the grid-based methods. The results, presented in Table 2, demonstrate that our approach maintains a performance advantage over existing grid-based methods. This further proves that our method is not only effective on synthetic datasets, but also performs well on real-world datasets. Our method achieves a significant PSNR improvement compared to the pure tensor decomposition method TensoRF on the syntheticNeRF and NSVF datasets. However, the improvement is relatively smaller on the real dataset. This is primarily because the dataset requires rendering ultra-high-resolution images, while our model relies on hash encoding to compress information. For high-resolution images, the integrity of the information is crucial, which leads to our method performing better in some underfitting scenarios, but showing no significant improvement in overfitting scenarios.