# Latitude-Adaptive Integer Bit Allocation for Quantization of Omnidirectional Images
###### Abstract
In addition, adaptive quantization methods partly rely on conventional techniques that were not originally designed for omnidirectional images. Our paper falls within the category of sampling density correction methods and focuses on omnidirectional images under ERP, where the design of quantizers plays a pivotal role. Methods already proposed predominantly employ uniform quantization and rely on conventional quantization techniques such as JPEG [23] and quantization parameter (QP) in HEVC [24]. However, these conventional methods, designed for 2D  
Figure 1: Overview of omnidirectional image compression methods. images and videos, may not be well-suited for omnidirectional images, whereas our method can produce non-uniform scalar quantizers with assigned bits. In this paper, we introduce a novel NNIBA technique to achieve high-quality image quantization through a combination of greedy bit allocation and non-uniform quantization of the transform coefficients. It is crucial to emphasize that our method is compatible with any block-based transformation, like discrete cosine transform (DCT). The process begins by performing the transform block by block, obtaining statistical parameters of a batch of images, followed by deriving the optimal real-valued bit allocation (ORBA). Due to the characteristics of spherical image projection, we posit that coefficients at different latitudes exhibit distinct distributions. To capture this, we utilize empirical distribution instead of the Gaussian distribution assumed in [25]. The subsequent step involves a two-step greedy algorithm to allocate the non-negative integer (NNI) bits. Further, we design non-uniform quantizers using the Lloyd algorithm instead of conventional quantization techniques, which has demonstrated superior performance than uniform quantizers employed by [20,21]. Because of certain spherical properties inherent in panoramic images, conventional 2D image quality metrics such as peak signal-to-noise ratio (PSNR) are no longer suitable for evaluating panoramic images. Consequently, for practicality and simplicity, we have adopted the WS-PSNR metric and WMSE distortion [26]. With the help of experiments, we have validated that the proposed NNIBA technique outperforms previously proposed sampling correction and bit allocation methods under WS-PSNR. Our proposed method effectively reduces redundancy in omnidirectional image compression and enhances the quantization of transform coefficients, thereby improving overall compression quality. This improvement enhances the storage and transmission performance of omnidirectional images. In applications such as AR and VR, where real-time requirements are critical, it can reduce image latency and provide superior image quality. Our main contributions can be summarized in the following aspects:  
1. To quantize transform coefficients with non-uniform scalar quantizers, we derive the theoretical ORBA and provide a detailed analysis under WMSE distortion. 2. Two consecutive low-complexity greedy algorithms are employed to obtain the integer bit allocation. 3. We empirically verify the effectiveness of our method through simulation. The rest of the paper is organized as follows. In Section 2, we provide an overview of related work on sampling-related methods and integer bit allocation. In Section 3, we introduce the system model and formulate the optimization problem. The theoretical analysis for ORBA and proposed greedy algorithms are presented in Sections 4 and Section 5, respectively. Section 6 shows the validation experiment. Finally, Section 7 concludes the whole paper. Additionally, we first list the notations used in the paper in Table 1 below.