Non Separable 2D Sampling (Generalization):

Rectangular sampling is a separable sampling. However sampling positions in one dimension can be shifted depending on the location in other dimension in the 2D case. Constraints may further be imposed by the acquisition devices e.g. for signals generated by video cameras, sampling grids are restricted to a constant line spacing S. Different regular grids of 2D sampling are shown below. By regularity of grids we mean a certain periodicity of a basic structure. These can be expressed by systems of basic vectors and such that linear combinations of these vectors when multiplied by point to effective sampling positions where is an integer indexing vector.

The basis vectors can be interpreted as columns of sampling matrix , which maps the index values to the actual sampling positions of the spatially continuous signal.

i.e.

For rectangular case where

For shear sampling case:

Figure(3.2.20)

Shear Sampling