# Latitude-Adaptive Integer Bit Allocation for Quantization of Omnidirectional Images
###### Abstract  
Omnidirectional images have gained significant popularity and drawn great attention nowadays, which poses challenges to omnidirectional image processing in solving the bottleneck of storage and transmission. Projecting onto a two-dimensional image plane is generally used to compress an omnidirectional image. However, the most commonly used projection format, the equirectangular projection (ERP), results in a significant amount of redundant samples in the polar areas, thus incurring extra bitrate and geometric distortion. We derive the optimal latitude-adaptive bit allocation for each image tile. Subsequently, we propose a greedy algorithm for non-negative integer bit allocation (NNBA) for non-uniform quantization under an omnidirectional image quality metric WMSE. In our experiment, we design quantization tables based on JPEG and compare our approach with other sampling-related methods. Our method achieves an average bit saving of 7.9% compared with JPEG while outperforming other sampling-related methods. Besides, we compare our non-uniform quantization approach with two proposed bit allocation methods, achieving an average improvement of 0.35 dB and 2.66 dB under WS-PSNR, respectively. The visual quality assessment also confirms the superiority of our method. omnidirectional image; transform coding; quantization; bit allocation +
Footnote †: journal: Applied  
0000-0001-9993-3227][PERSON] 0000-0001-9993-3227][PERSON] 0000-0001-9993-3227][PERSON] 0000-0002-3227-3273][PERSON] 0000-0002-3227-3273][PERSON] 0000-0002-3227-3273][PERSON] transform [9]. Methods in the spherical domain can avoid the distortion induced by projection, while they may not outperform well-established 2D image compression techniques, which require further development [10]. The 360\({}^{\circ}\) images can also be projected to 2D planes to leverage the existing traditional image compression standards [4]. Although 2D image compression techniques have reached a high level of maturity, these methods do not adequately accommodate the spherical nature of omnidirectional images. Therefore, various methods have been proposed to address the issues of redundancy and distortion in projected omnidirectional images, which can be categorized into three main groups: re-projection, perceptual methods, and sampling density correction. Re-projection methods seek to leverage compression-friendly re-projection techniques. Certain approaches involve rotating the panoramic content within the spherical domain [11; 12]. Others develop new projection methods, including HEC [13], HCP [14], OGM [15], etc. Re-projection methods allow regions demanding high visual quality to be situated in less distorted areas on the projected 2D plane before compression. However, it is important to note that these methods are highly content-dependent. Perceptual compression methods aim to improve the perceptual quality of omnidirectional images within the viewport. This category can be divided into viewport-based coding, such as [16; 17], and saliency-based adaptive coding, such as [18; 19]. Perceptual compression methods can yield improved results while necessitating additional data and increased computational resources. Sampling density correction methods aim to mitigate the oversampling induced by the projection, thereby enhancing the compression efficiency of panoramic images. Sampling-related methods primarily include down-sampling [20; 21] and adaptive quantization [10; 22] methods. There are also learned image compression methods leveraging sampling-related approaches [5]. Due to the necessity for complex methodologies and extensive training data, it falls outside the scope of our consideration. Sampling density correction methods, primarily based on conventional 2D methods with enhancements, are relatively straightforward to understand and implement. However, down-sampling methods predominantly hinge on intuitive insights and exhibit a limited foundation in terms of robust theoretical support.