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Dynamic patterns are characterized by complex spatial and motion patterns.Understanding dynamic patterns requires a disentangled representational modelthat separates the factorial components. A commonly used model for dynamicpatterns is the state space model, where the state evolves over time accordingto a transition model and the state generates the observed image framesaccording to an emission model. To model the motions explicitly, it is naturalfor the model to be based on the motions or the displacement fields of thepixels. Thus in the emission model, we let the hidden state generate thedisplacement field, which warps the trackable component in the previous imageframe to generate the next frame while adding a simultaneously emitted residualimage to account for the change that cannot be explained by the deformation.The warping of the previous image is about the trackable part of the change ofimage frame, while the residual image is about the intrackable part of theimage. We use a maximum likelihood algorithm to learn the model that iteratesbetween inferring latent noise vectors that drive the transition model andupdating the parameters given the inferred latent vectors. Meanwhile we adopt aregularization term to penalize the norms of the residual images to encouragethe model to explain the change of image frames by trackable motion. Unlikeexisting methods on dynamic patterns, we learn our model in unsupervisedsetting without ground truth displacement fields. In addition, our modeldefines a notion of intrackability by the separation of warped component andresidual component in each image frame. We show that our method can synthesizerealistic dynamic pattern, and disentangling appearance, trackable andintrackable motions. The learned models are useful for motion transfer, and itis natural to adopt it to define and measure intrackability of a dynamicpattern.

Motion-Based Generator Model: Unsupervised Disentanglement of Appearance, Trackable and Intrackable Motions in Dynamic Patterns