Pose Estimation in Conformal Geometric Algebra Part I: The Stratification of Mathematical Spaces

2D-3D pose estimation means to estimate the relative position and orientation of a 3D object with respect to a reference camera system. This work has its main focus on the theoretical foundations of the 2D-3D pose estimation problem: We discuss the involved mathematical spaces and their interaction within higher order entities. To cope with the pose problem (how to compare 2D projective image features with 3D Euclidean object features), the principle we propose is to reconstruct image features (e.g. points or lines) to one dimensional higher entities (e.g. 3D projection rays or 3D reconstructed planes) and express constraints in the 3D space. It turns out that the stratification hierarchy [11] introduced by Faugeras is involved in the scenario. But since the stratification hierarchy is based on pure point concepts a new algebraic embedding is required when dealing with higher order entities. The conformal geometric algebra (CGA) [24] is well suited to solve this problem, since it subsumes the involved mathematical spaces. Operators are defined to switch entities between the algebras of the conformal space and its Euclidean and projective subspaces. This leads to another interpretation of the stratification hierarchy, which is not restricted to be based solely on point concepts. This work summarizes the theoretical foundations needed to deal with the pose problem. Therefore it contains mainly basics of Euclidean, projective and conformal geometry. Since especially conformal geometry is not well known in computer science, we recapitulate the mathematical concepts in some detail. We believe that this geometric model is useful also for many other computer vision tasks and has been ignored so far. Applications of these foundations are presented in Part II [36].Bodo Rosenhahn gained his diploma degree in Computer Science in 1999. Since then he has been pursuing his Ph.D. at the Cognitive Systems Group, Institute of Computer Science, Christian-Albrechts University Kiel, Germany. He is working on geometric applications of Clifford algebras in computer vision.Prof. Dr. Gerald Sommer received a diploma degree in physics from the Friedrich-Schiller-Universität Jena, Germany, in 1969, a Ph.D. degree in physics from the same university in 1975, and a habilitation degree in engineering from the Technical University Ilmenau, Germany, in 1988. Since 1993 he is leading the research group Cognitive Systems at the Christian-Albrechts-Universität Kiel, Germany. Currently he is also the scientific coordinator of the VISATEC project.     

基于人体和场景上下文的多人3D姿态估计

深度歧义是单帧图像多人3D姿态估计面临的重要挑战,提取图像上下文对缓解深度歧义极具潜力.自顶向下方法大多基于人体检测建模关键点关系,人体包围框粒度粗背景噪声占比较大,极易导致关键点偏移或误匹配,还将影响基于人体尺度因子估计绝对深度的可靠性.自底向上的方法直接检出图像中的人体关键点再逐一恢复3D人体姿态.虽然能够显式获取场景上下文,但在相对深度估计方面处于劣势.提出新的双分支网络,自顶向下分支基于关键点区域提议提取人体上下文,自底向上分支基于三维空间提取场景上下文.提出带噪声抑制的人体上下文提取方法,通过建模“关键点区域提议”描述人体目标,建模姿态关联的动态稀疏关键点关系剔除弱连接减少噪声传播.提出从鸟瞰视角提取场景上下文的方法,通过建模图像深度特征并映射鸟瞰平面获得三维空间人体位置布局;设计人体和场景上下文融合网络预测人体绝对深度.在公开数据集MuPoTS-3D和Human3.6M上的实验结果表明:与同类先进模型相比,所提模型HSC-Pose的相对和绝对3D关键点位置精度至少提高2.2%和0.5%;平均根关键点位置误差至少降低4.2 mm.     

基于多层空间特征融合的三维人体姿态估计

在三维人体姿态估计任务当中, 人体关节之间的连接关系形成了一种复杂的拓扑结构, 利用图卷积网络对该结构进行建模, 可以有效捕捉局部关节间的联系; 尽管不相邻关节之间没有直接的物理连接, 但由于人体的运动和姿态受到生物力学约束以及人体关节之间的协同作用, 利用Transformer编码器建立关节之间的上下文关系, 可以更好地推断出人体姿态; 在大模型的背景下, 如何在保证模型性能的同时, 降低参数量, 也显得尤为重要. 针对上述问题, 设计了一个基于图卷积和Transformer的多层空间特征融合网络模型(MLSFFN), 在使用相对少量的参数基础上, 有效地融合了局部和全局空间特征. 实验结果表明, 本文提出的方法在仅需2.1M参数量的情况下, 在Human3.6M数据集上达到了49.9 mm的平均每关节误差(MPJPE). 此外, 模型在MPI-INF-3DHP数据集上也展示出了较强的泛化能力.