用2D信息生成可控制的手部抓握，提升精度与评估效率

Controllable affordance Hand-Object Interaction (HOI) generation has become an increasingly important area of research in computer vision. In HOI generation, the hand grasp generation is a crucial step for effectively controlling the geometry of the hand. Current hand grasp generation methods rely on 3D information for both the hand and the object. In addition, these methods lack controllability concerning the hand's location and orientation. We treat the hand pose as the discrete graph structure and exploit the geometric priors. It is well established that higher order contextual dependency among the points improves the quality of the results in general. We propose a framework of higher order geometric representations (HOR's) inspired by spectral graph theory and vector algebra to improve the quality of generated hand poses. We demonstrate the effectiveness of our proposed HOR's in devising a controllable novel diffusion method (based on 2D information) for hand grasp generation that outperforms the state of the art (SOTA). Overcoming the limitations of existing methods: like lacking of controllability and dependency on 3D information. Once we have the generated pose, it is very natural to evaluate them using a metric. Popular metrics like FID and MMD are biased and inefficient for evaluating the generated hand poses. Using our proposed HOR's, we introduce an efficient and stable framework of evaluation metrics for grasp generation methods, addressing inefficiencies and biases in FID and MMD.