Hamiltonian latent operators for content and motion disentanglement in image sequences

We introduce textitHALO -- a deep generative model utilising HAmiltonian Latent Operators to reliably disentangle content and motion information in image sequences. The textitcontent represents summary statistics of a sequence, and textitmotion is a dynamic process that determines how information is expressed in any part of the sequence. By modelling the dynamics as a Hamiltonian motion, important desiderata are ensured: (1) the motion is reversible, (2) the symplectic, volume-preserving structure in phase space means paths are continuous and are not divergent in the latent space. Consequently, the nearness of sequence frames is realised by the nearness of their coordinates in the phase space, which proves valuable for disentanglement and long-term sequence generation. The sequence space is generally comprised of different types of dynamical motions. To ensure long-term separability and allow controlled generation, we associate every motion with a unique Hamiltonian that acts in its respective subspace. We demonstrate the utility of textitHALO by swapping the motion of a pair of sequences, controlled generation, and image rotations.