Normalizing flows have proven their efficacy for density estimation in
Euclidean space, but their application to rotational representations, crucial
in various domains such as robotics or human pose modeling, remains
underexplored. Probabilistic models of the human pose can benefit from
approaches that rigorously consider the rotational nature of human joints. For
this purpose, we introduce HuProSO3, a normalizing flow model that operates on
a high-dimensional product space of SO(3) manifolds, modeling the joint
distribution for human joints with three degrees of freedom. HuProSO3's
advantage over state-of-the-art approaches is demonstrated through its superior
modeling accuracy in three different applications and its capability to
evaluate the exact likelihood. This work not only addresses the technical
challenge of learning densities on SO(3) manifolds, but it also has broader
implications for domains where the probabilistic regression of correlated 3D
rotations is of importance.

在旋转表示中，标准化流已经证明了它们在欧几里得空间中密度估计的功效，但其在各个领域如机器人技术或人体姿势建模中的应用仍未充分探索。我们引入了 HuProSO3，一个在 SO (3) 流形的高维乘积空间上运行的标准化流模型，用于对具有三个自由度的人体关节的联合分布进行建模。通过在三个不同应用中表现出的卓越建模准确性和准确似然度量能力，HuProSO3 相比现有方法具有优势。这项工作不仅解决了在 SO (3) 流形上学习密度的技术挑战，也对需要对相关的 3D 旋转进行概率回归的领域具有广泛的影响。