# Latitude-Adaptive Integer Bit Allocation for Quantization of Omnidirectional Images
## 6 Experiments
### Results and Analysis for NNI-Based Methods  
Given the absence of specifically designed integer bit allocation methods for omnidirectional images, we compare our method with those proposed by [PERSON] et al. [25] and [PERSON] et al. [31] whose bit allocation methods were designed for planar images. All methods are given the same bit budget and their quality is evaluated using WS-PSNR. In contrast to the method described in Section 6.3, we utilize non-negative scalar quantization based on the Lloyd algorithm following the greedy algorithms. To compare the effects of uniform quantization and non-uniform quantization, we have also designed uniform quantizers  
Figure 5: Rate distortion curves for JPEG-based methods over 100 images with a resolution of \(512\times 1024\) pixels [10; 20; 23]. \begin{table}
\begin{tabular}{c c} \hline \hline
**Method** & \(\Delta_{BD}\)** **Rate** \\ \hline [PERSON] et al. [20] & 2.06 \\ [PERSON] et al. [10] & \(-4.41\) \\ Proposed Method & \(-7.90\) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: \(\Delta_{BD}\) of the average percentage of rate difference between JPEG-based omnidirectional methods and JPEG for WS-PSNR. after bit allocation. This comparative analysis is conducted both on images with dimensions of \(256\times 512\) pixels and \(512\times 1024\) pixels. The results are shown in Figures 6 and 7, respectively. The black line and blue line represent the results obtained by generating non-uniform quantizers and uniform quantizers after NNIBA, respectively. Combining the rate-distortion curves in Figures 6 and 7, our method achieves an average WS-PSNR improvement of 0.35 dB compared to the method proposed by [PERSON] et al. [31],and an average improvement of 2.66 dB compared to the method proposed by [PERSON] et al. [25] at the same bit budget. The approach delineated by [PERSON] et al. [31] demonstrates performance comparable to our method at relatively low rates. This can be attributed to its bit allocation not being in integer bits, but rather based on an integer resolution \(r\), where \(r=2^{b}\) and \(b\) is the allocated bit. However, integer resolution allocation consumes more time and computational resources in the greedy algorithm compared to our integer bit allocation method, introducing additional complexity. Compared to non-uniform quantizers, the performance of uniform quantizers is not satisfactory, which may be due to our method being designed for non-uniform quantizers. This also demonstrates the effectiveness of using non-uniform quantization in our method. In contrast to the aforementioned methods, our non-uniform approach incorporates a more sophisticated bit allocation strategy across tiles, complemented by the use of non-uniform scalar quantization techniques. Through  
Figure 6: Rate distortion curves for non-negative integer bit allocation (NNIBA) methods over 100 images with a resolution of \(256\times 512\) pixels [25; 31]. Figure 7: Rate distortion curves for non-negative integer bit allocation (NNIBA) methods over 100 images with a resolution of \(512\times 1024\) pixels [25; 31]. bit allocation across latitudes, we allocated bits to the more crucial parts of the image, considering both the impact of coefficient distribution and the influence of different latitudes. Additionally, as described in Section 6.2, we have integrated empirical distributions into our framework to further optimize the bit distribution and quantization process, enhancing its overall effectiveness. Then, we present a visual comparison among the three methods at the same rate, which is evaluated by the bit budget. Figure 8 shows the test images from the Pano3D dataset [34]. All the four test images are converted to 8-bit greyscale images. Figures 9 and 10 show the zoomed version of test image A and test image B at 0.4 bpp. Figures 11 and 12 present the detailed views of test image C and test image D at 0.75 bpp, respectively.