Kernel Learning for Dynamic Texture Synthesis
Dynamic textures (DTs) that represent moving scenes such as flames, smoke, and waves, exhibit fixed dynamics within a period of time and have been successfully modeled using linear dynamic systems (LDS). In this paper, we show that the widely used LDS model can be approximated using a principal component regression (PCR) model with the main advantage of simplicity. Furthermore, to capture the nonlinearity of training frames, we extend traditional PCR to its kernelized version and introduce kernel principal component regression (KPCR) to model and synthesize DTs. To ensure algorithm stability, we remove the standard state model and directly apply the quantized kernel least mean squares algorithm from signal processing domain to approximate the performance achieved with KPCR. We term this improvement kernel adaptive dynamic texture synthesis (KADTS), which also has the benefits of computational and memory efficiency. These advantages make KADTS ideally suited for real-world applications, since the majority of electronic devices, including cell phones and laptops, suffer from limited memory and real-time constraints. We demonstrate, via both theoretical and experimental analyses, the connections between DT synthesis using KPCR and KADTS with a regularization network theory. We also show the superiority of our proposed algorithms for DT synthesis compared with other dynamic system-based benchmarks. MATLAB code is available from our project homepage http://bmal.hust.edu.cn/project/dts.html.