# TransPGC: Point Cloud Geometry Compression Based on Transformers
## 2 Related Work
### Deep Learning Methods  
With the development of deep learning architectures, networks have recently been created for the autoencoder-based reconstruction [29; 30], completion [31], or production of point clouds [32]. Learning-based geometric compression techniques have been developed to enhance compression performance by acquiring efficient representations from point clouds, leveraging point cloud autoencoder techniques. Some of these methods involve converting raw point clouds into voxels and subsequently employing a 3D CNN to encode the geometry into a binary form. [PERSON] et al. [5] introduced a geometric information compression algorithm based on convolutional operations and uniform quantization. This approach utilizes a tradeoff parameter for joint optimization of rate and distortion, transforming the decoding process into a binary classification problem of point cloud occupancy. Subsequently, an improved version was proposed, incorporating entropy coding with hyperprior modeling, optimal threshold decoding, and sequential model training [6]. [PERSON] et al. [7] presented an end-to-end learning-based algorithm for efficient compression of point cloud geometric information using a stacked convolutional neural network-based variational autoencoder. They also leveraged the sparsity of point clouds to perform progressive resampling for hierarchical point cloud reconstruction [8] and further proposed voxel compression using inter-scale and intra-scale correlations [9]. Researchers like [PERSON] [14] and others [10] enhanced compression performance by adding modules to the multi-scale point cloud geometry compression network. [PERSON] et al. [33] proposed a multi-layer residual module designed on sparse convolution-based autoencoders which progressively down-samples the input point clouds and hierarchically reconstructs them. [PERSON] et al. [34] introduced a rate expansion method based on contrastive learning to expand the bit rate range of the model.  
[PERSON] et al. [10] introduced a lossless compression method for point cloud geometry information, leveraging neural networks and context-adaptive arithmetic coding. To address the slow inference caused by predicting occupancy probability in voxel order in prior designs, a multi-scale architecture was proposed, optimizing voxel occupancy modeling from coarse to fine order [11]. They subsequently suggested using neural network estimation of voxel occupancy probability distribution [12]. [PERSON] and [PERSON] later delved into attribute compression of point clouds [13; 15]. [PERSON] et al. [35] proposed a patch-based point cloud compression algorithm, followed by enhancements in patch-based point cloud compression [36]. On another front, the authors of [24] attempted to process coordinates directly based on PointNet++ [37]. While this method performed well on small and sparse models, its limited robustness became apparent, as global features used for reconstruction struggled to generate accurate contours on unseen shapes. [PERSON] [16] developed an autoencoder compression framework for sparse point cloud graphs, utilizing features extracted from the encoder and associated points as compression data. [PERSON] et al. [17] introduced a novel network model called TransPCC, employing a Transformer autoencoder architecture for point cloud geometry compression. Despite its high robustness, its application remained confined to sparse points within blocks segmented from original dense point clouds. These point-based compression methods avoid the accuracy loss seen in voxel networks, but their complex network structures limit their ability to effectively utilize dense points. Octsqueeze [18] and VoxelcontextNet [38] are part of a series of works dedicated to outdoor scene compression, introducing network improvements in entropy coding performance. [PERSON] [39] took a step further by incorporating spatiotemporal relationships between multiple scans of outdoor scenes, thereby reducing the bitrate of both geometric and intensity values.