# Texture-Guided Graph Transform Optimization for Point Cloud Attribute Compression
## 1 Introduction  
The advancement of three-dimensional (3D) sensing and acquisition technologies has elevated point clouds as a prevalent media format for representing 3D objects and scenes across various multimedia applications [1, 2, 3, 4]. A point cloud consists of a set of points distributed in 3D space, with each point possessing geometry positions and attribute information, such as color, intensity, reflectance, etc. Concurrently, the escalating market demand for high-resolution 3D representation has led to a significant increase in the data volume of point clouds, characterized by abundant geometry information and rich attributes [5, 6, 7]. Consequently, the imperative to compress point clouds while preserving high fidelity has garnered substantial attention from both industry and academia. The field of point cloud compression has seen fruitful advancements, particularly in geometry compression [8, 9, 10] and attribute compression [11, 12, 13]. In this paper, we focus on point cloud attribute compression. Here, the attributes primarily pertain to point cloud color information, chosen as a representative attribute for evaluating compression performance due to its visually informative nature. However, it is important to note that our approach extends beyond color alone. The essence of our method lies in leveraging the spatial correlation of attributes within point clouds. Therefore, our approach is applicable to various attributes present in point clouds. The objective of point cloud attribute compression is to minimize the required number of bits for representation by eliminating redundancy while ensuring the quality of the decoded point cloud through a rate-distortion (R-D) optimization process. Numerous prediction-based attribute compression methods have been devised for removing attribute redundancy, demonstrating notable performance [14; 15; 16], particularly the attribute predictive coding scheme within the standard G-PCC platform [17]. However, the sparse and uneven geometry distribution inherent in point clouds presents challenges in reducing attribute correlation effectively in 3D space [18]. In G-PCC, a point cloud is represented through levels of detail (LoD), and attribute intra-coding is executed within this structure using a k-nearest neighbor (k-NN)-based attribute linear interpolation scheme. Nevertheless, the LoD structure in G-PCC fails to fully consider the 3D topological structure of point clouds, resulting in an incomplete capture of the underlying attribute correlation within the geometry [15]. Consequently, there is a demand for improved coding tools to effectively address frequency-domain signal redundancy in point cloud attribute compression. Graphs have emerged as popular representations of point clouds, providing a flexible framework for capturing the intricate spatial relationships inherent in such data [19; 20; 21]. Given that point clouds comprise irregularly distributed points in 3D space, graph structures dependly encapsulate these complex geometries and topologies. Concurrently, graph transform tools have become effective components in point cloud attribute compression [16; 18; 22]. The work in [22] is a pioneer that leverages graph transform tools to address the challenges of attribute redundancy within point clouds. Based on this, [PERSON] et al. [16] propose a sparsity-optimized graph transform to improve the coding performance. Recently, [PERSON] et al. [18] proposed an optimized graph transform scheme based on region-aware geometry analysis, which is the state-of-the-art graph transform scheme for point cloud attribute compression. Current graph transform-based attribute coding schemes encounter several limitations. Firstly, many of these schemes rely solely on k-NN methods for graph construction, which restricts their ability to capture inherent attribute correlations, consequently limiting transform performance. To address this issue, our approach incorporates graph optimization techniques, improving graph construction through tailored energy functions.