# SCGFormer: Semantic Chebyshev Graph Convolution Transformer for 3D Human Pose Estimation
## 1 Introduction  
Traditional deep learning models, such as LSTM [1] and CNN [2], have demonstrated notable performance in Euclidean space data (language, images, videos, etc.). However, they exhibit certain limitations when processing non-Euclidean space data, such as social networks and information networks. Graph convolutional networks (GCNs) [3, 4], as a recently emerged class of generalized neural network structures based on graph structures, have garnered significant attention and research due to their unique computational capabilities. Scholars have introduced the abstract concept of graphs from graph theory to represent non-Euclidean structured data and leveraged graph convolutional networks to process graph data, delving deeper into its features and patterns. The human skeleton, representing joints as nodes and bones as edges, can be conceptualized as a graph structure, providing a new direction for advancements in human pose estimation tasks. In recent years, 3D human pose estimation has gained significant attention in computer vision, with applications spanning virtual reality [5, 6], motion recognition [7, 8, 9, 10], motion tracking [11], and more. This field has been advancements in both single-stage [12, 13, 14, 15, 16, 17, 18] and multi-stage regression approaches [19, 20, 21, 22, 23, 24]. Single-stage regression directly extracts features from images to reconstruct 3D skeleton coordinates but is sensitive to external factors such as background and lighting. In contrast, multi-stage regression initially predicts the planar coordinates of the skeleton and subsequently estimates 3D features using 2 Djoint information. The latter approach has reached maturity, benefiting from a plethora of methods for detecting 2D skeletons in RGB images. Nonetheless, 3D pose estimation encounters challenges including depth ambiguity, self-obscuration, and a scarcity of outdoor datasets. Graph structures, which represent skeletal connections among 2D joints, have been harnessed by graph convolutional neural networks (GCNs) to acquire effective 3D human body representations [25, 26, 27, 28]. However, prior GCN-based approaches [29] exhibited certain limitations. They often relied on first-order neighborhood matrices, constraining their ability to capture information from distant joints, and employed the same kernel matrix for all edges, resulting in underutilization of relationships between adjacent nodes. SemConv [27] improved the operation of graph convolution. Its key idea is to learn channel-wise weights for edges as priors implied in the graph and then combine them with kernel matrices. This significantly improves the power of graph convolutions. The work [28] introduces a graph-oriented Transformer structure that incorporates a self-attention mechanism to better capture the relationships between joint points and a graph convolutional structure to infer pose information in the graph structure. In order to improve the utilization of joint features, we propose SCGFormer, a semantic Chebyshev graph convolutional Transformer. SCGFormer harnesses the strengths of Transformer and graph convolutions, comprising two pivotal components: semantic graph--attention (SGraAttention) and Chebyshev graph convolution with combined adjacency matrix information (AcChebGconv). SGraAttention amalgamates Transformer and semantic graph convolution, facilitating the extraction of global information through self-attention while preserving human kinematic constraints. Concurrently, AcChebGconv improves Chebyshev graph convolution by fully exploiting 2D joint features and reinforcing local connections. We assess the performance of SCGFormer on the Human3.6M [30, 31] and MPI-INF-3 HP [12] datasets, achieving outstanding results across various action categories. The task achieved the best results on 9 actions (from a total of 15 actions), with an overall average error decrease of approximately 1.5 points compared to the baseline.