Modeling General Linear Local Motion

Develop a representation that extends rigid SE(3) trajectory modeling to general linear local motion, including scaling and shearing.

Background

World Motion Models approximate dynamic 3D scenes using finite sets of rigid SE(3) trajectories, with dense deformation recovered through interpolation, skinning, or binary assignment. This formulation captures rigid and articulated motion but does not represent more general local linear transformations such as scaling or shearing.

The paper explicitly defers this extension, leaving unresolved how the model and its trajectory representation should incorporate these additional forms of local motion.