Composite Dynamic Texture Synthesis Using Hierarchical Linear Dynamical System

We demonstrate that a systematic inclusion of prior structural constraints on the states of a linear dynamical system significantly improves its ability to model complex multidimensional sequences. This constrained LDS, typically termed as the hierarchical linear dynamical system (HLDS), is a Kalman filter based topology that extracts relevant self-segmenting information from the input signal in an unsupervised manner by hierarchically constraining its information representing state subspaces thereby slowing down the signal dynamics. We highlight some of its practical advantages over the existing methods in real-world video applications. As a concrete application, we show that the HLDS, despite being a linear model trained in an unsupervised setting, is able to capture the dynamics of complex texture sequences consisting of multiple co-occurring textures. We compare its performance with a similarly trained LDS model in the reconstruction and synthesis of such signals.