A two-dimensional (2D) adaptive filter is very much like an 1-dimensional adaptive filter in the sense that it is a linear system whose parameters are adaptively updated throughout the process, according to some optimization approach. The main difference between 1D and 2D adaptive filters is that the former usually takes as inputs signals with respect to time, what implies in causality constraints, while the latter handles signals with 2 dimensions, like x-y coordinates in the space domain, which are usually non-causal. Moreover, just like 1D filters, most 2D adaptive filters are digital filters, because of the complex and iterative nature of the algorithms.