Polar Prediction of Natural Videos

Observer motion and continuous deformations of objects and surfaces imbue natural videos with distinct temporal structures, enabling partial prediction of future frames from past ones. Conventional methods first estimate local motion, or optic flow, and then use it to predict future frames by warping or copying content. Here, we explore a more direct methodology, in which each frame is mapped into a learned representation space where the structure of temporal evolution is more readily accessible. Motivated by the geometry of the Fourier shift theorem and its group-theoretic generalization, we formulate a simple architecture that represents video frames in learned local polar coordinates. Specifically, we construct networks in which pairs of convolutional channel coefficients are treated as complex-valued, and are optimized to evolve with slowly varying amplitudes and linearly advancing phases. We train these models on next-frame prediction in natural videos, and compare their performance with that of conventional methods using optic flow as well as predictive neural networks. We find that the polar predictor achieves better performance while remaining interpretable and fast, thereby demonstrating the potential of a flow-free video processing methodology that is trained end-to-end to predict natural video content.