Understanding human behavior fundamentally relies on accurate 3D human pose estimation. Graph Convolutional Networks (GCNs) have recently shown promising advancements, delivering state-of-the-art performance with rather lightweight architectures. In the context of graph-structured data, leveraging the eigenvectors of the graph Laplacian matrix for positional encoding is effective. Yet, the approach does not specify how to handle scenarios where edges in the input graph are missing. To this end, we propose a novel positional encoding technique, PerturbPE, that extracts consistent and regular components from the eigenbasis. Our method involves applying multiple perturbations and taking their average to extract the consistent and regular component from the eigenbasis. PerturbPE leverages the Rayleigh-Schrodinger Perturbation Theorem (RSPT) for calculating the perturbed eigenvectors. Employing this labeling technique enhances the robustness and generalizability of the model. Our results support our theoretical findings, e.g. our experimental analysis observed a performance enhancement of up to $12\%$ on the Human3.6M dataset in instances where occlusion resulted in the absence of one edge. Furthermore, our novel approach significantly enhances performance in scenarios where two edges are missing, setting a new benchmark for state-of-the-art.

翻译：理解人类行为从根本上依赖于精确的三维人体姿态估计。图卷积网络（GCNs）近期展现出有前景的进展，以相当轻量级的架构实现了最先进的性能。在图结构数据的背景下，利用图拉普拉斯矩阵的特征向量进行位置编码是有效的。然而，该方法并未明确说明如何处理输入图中边缺失的场景。为此，我们提出了一种新颖的位置编码技术——PerturbPE，它从特征基中提取一致且规则的成分。我们的方法涉及施加多重扰动并取其平均值，以从特征基中提取一致且规则的成分。PerturbPE 利用瑞利-薛定谔微扰定理（RSPT）来计算受扰动的特征向量。采用这种标记技术增强了模型的鲁棒性和泛化能力。我们的结果支持了理论发现，例如，实验分析观察到在遮挡导致一条边缺失的情况下，在 Human3.6M 数据集上的性能提升高达 $12\%$。此外，我们的新方法在两条边缺失的场景中显著提升了性能，为最先进水平树立了新的标杆。