# Texture-Guided Graph Transform Optimization for Point Cloud Attribute Compression
## 2 Related Work on Point Cloud Attribute Compression  
The efficient compression of point cloud attributes necessitates the removal of two main types of signal redundancy: spatial-domain redundancy and frequency-domain redundancy. Current approaches to point cloud attribute compression can be categorized into three groups based on the methods employed for redundancy removal: prediction based, transform based, and hybrid schemes. Prediction-based schemes aim to remove redundancy by predicting attribute values from neighboring points, while transform-based schemes focus on representing attributes in transformed domains to exploit signal decorrelation. Hybrid schemes integrate a combination of attribute prediction and transform coding tools within a comprehensive framework. In the realm of prediction-based attribute codecs, [PERSON] et al. in [23] first propose a prediction-based attribute coding scheme by creating the color octree to enable neighboring-based prediction. Based on this, [PERSON] et al. in [24] propose an octree-based progressive attribute coding scheme to remove attribute redundancy in octree nodes. Instead of using octree for point cloud representation, [PERSON] et al. [25] adopt the Hilbert space-filling curve to reorganize the point cloud and design a prediction scheme based on the reorganized scan order for point cloud attribute compression. Moreover, [PERSON] et al. [15] introduce the partial differential equation to tackle the attribute prediction task and devise a PDE-based attribute coding scheme to perform attribute prediction by optimizing attribute gradients of adjacent point cloud areas. Those prediction-based attribute codecs achieve notable progress in attribute spatial redundancy removal, while attribute frequency-domain redundancy needs to be further reduced. Regarding transform-based attribute codecs, [PERSON] et al. in [22] pioneer a transform-based approach by decomposing point clouds into graphs and employing graph Fourier transform (GFT) for attribute compression. Building upon this, [PERSON] et al. in [26] extend the work with an enhanced graph construction scheme for improved point cloud attribute compression. Then, [PERSON] et al. in [27] propose to integrate block partitioning with \(k\)-dimensional trees for graph construction. Further, [PERSON] et al. in [16] provide a Lagrangian-optimized GFT in a block-based attribute coding scheme. [PERSON] et al. in [28] introduce a spatio-temporal GFT for dynamic point cloud attribute compression. In response to the time-consuming nature of GFT-based codecs, [PERSON] et al. in [29] devise a more efficient transform-based attribute coding scheme named RAHT, and this work is adopted as a part of the solution in MPEG G-PCC. Moreover, [PERSON] et al. in [18] design a block-adaptive graph transform method to improve attribute coding performance. However, the approach solely relies on geometry information for constructing the graph transform basis, which could potentially limit its coding performance. We propose to enhance it through a texture-guided graph optimization scheme, leveraging texture information alongside geometry to improve graph construction and coding performance. Graph optimization is crucial in the design of graph transform coding tools for point cloud attribute compression. The challenge lies in deriving an appropriate graph kernel that accurately reflects attribute similarities within local regions of the point cloud. Many existing graph optimization approaches utilize the graph Laplacian operator to capture the irregular structure of the point cloud data by representing it as a graph. This operator is essential for graph spectral decomposition to derive the associated GFT basis. [PERSON] et al. in [30] formulate the attributes in a point cloud as signals following a Gaussian Markov Random Field (GMRF) model and construct graphs in the point cloud. Then, the redundancy among point cloud attribute signals can be optimally decorrelated by the eigenvector-based transform matrix derived from the graph Laplacian. [PERSON] et al.