# Latitude-Adaptive Integer Bit Allocation for Quantization of Omnidirectional Images
## 7 Conclusions  
In this paper, we introduce a novel NNIBA technique, specifically designed to enhance omnidirectional compression quality via efficient quantization of transform coefficients. Initially, we derive the ORBA using the WMSE measure. This is followed by the implementation of a two-step consecutive greedy algorithm for the allocation of NNI bits to each  
Figure 11: Zoomedversion of test image C at 0.75 bpp [25; 31].  
Figure 10: Zoomed version of test image B at 0.4 bpp [25; 31].  
scalar quantizer. Furthermore, with the help of experiments, it has been validated that the proposed NNIBA technique outperforms the existing sampling density and integer bit allocation methods on omnidirectional images.  
Our method still has some limitations. The proposed method relies on coefficients to model empirical distribution and generate non-uniform quantizers, so its performance is influenced by the input omnidirectional images. Furthermore, our method necessitates the Lloyd algorithm to iterate to convergence, thereby entailing higher computational complexity compared to uniform quantization. Additionally, our greedy algorithm cannot guarantee to find the optimal solution to this combinatorial optimization problem (5).  
In our future work, we plan to continue our research in three main directions. Firstly, we aim to explore the application of our bit allocation method to neural networks or adapt it to existing image/video compression frameworks for improvement. Secondly, our method is independent of the transform. We may consider utilizing other transforms such as the graph Fourier transform (GFT) to effectively exploit spherical characteristics and further enhance performance. Lastly, we will consider other methods such as simulated annealing or genetic algorithms to obtain approximate optimal solutions for bit allocation.  
Conceptualization, Q.S., H.F. and B.H.; methodology, Q.S. and H.F.; software, Q.S.; validation, Q.S. and H.F.; formal analysis, Q.S.; investigation, Q.S.; resources, Q.S.; data curation, Q.S.; writing--original draft preparation, Q.S.; writing--review and editing, H.F. and B.H.; visualization, Q.S.; supervision, H.F. and B.H. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
Data Availability Statement: Data are contained within the article.  
The authors declare no conflicts of interest.  
The following abbreviations are used in this manuscript:  
\begin{tabular}{l l} ERP & \multicolumn{1}{c}{Equirectangular projection} \\ NNIBA & Non-negative integer bit allocation \\ PSNR & Peak signal-to-noise ratio \\ NNI & Non-negative integer \\ VR & Virtual reality \\ AR & Augmented reality \\
2D & Two-dimensional \\ QP & Quantization parameter \\ ORBA & Optimal real-valued bit allocation \\ DCT & Discrete cosine transform \\ RDO & Rate-distortion optimization \\ pdf & Probability density function \\ MSE & Mean squared error \\ FOE & First-order entropy \\ DC & Direct current \\ AC & Alternating current \\ GFT & Graph Fourier transform \\ \end{tabular}