On the usage of the 2D-AR-model in texture completion scenarios with causal boundary conditions: A tutorial

In recent years, significant progress has been witnessed in several image and video completion scenarios. Given a specific application, these methods can produce, reproduce or extend a given texture sample. While there are many promising algorithms available, there is still a lack of theoretical understanding on how some of them are designed and under which conditions they perform. For that, we analyze and describe the technique behind one of the most popular parametric completion algorithms: the autoregressive (AR) model. Furthermore, we address important implementation details, complexity issues and restrictions of the model. Beyond that, we explain how the performance of the AR model can be significantly improved. In summary, this paper aims to achieve three major goals: 1) To provide a comprehensive tutorial for experienced and nonexperienced readers, 2) to propose novel methods that improve the performance of the 2D-AR completion, and 3) to motivate and guide researchers that are interested in the usage of the AR model for texture completion tasks.