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Objects' rigid motions in 3D space are described by rotations andtranslations of a highly-correlated set of points, each with associated $x,y,z$coordinates that real-valued networks consider as separate entities, losinginformation. Previous works exploit quaternion algebra and their ability tomodel rotations in 3D space. However, these algebras do not properly encodetranslations, leading to sub-optimal performance in 3D learning tasks. Toovercome these limitations, we employ a dual quaternion representation of rigidmotions in the 3D space that jointly describes rotations and translations ofpoint sets, processing each of the points as a single entity. Our approach istranslation and rotation equivariant, so it does not suffer from shifts in thedata and better learns object trajectories, as we validate in the experimentalevaluations. Models endowed with this formulation outperform previousapproaches in a human pose forecasting application, attesting to theeffectiveness of the proposed dual quaternion formulation for rigid motions in3D space.

Dual Quaternion Rotational and Translational Equivariance in 3D Rigid Motion Modelling