The generalization of the 1D convolution we've introduced in terms of the 2D case is natural. Images, in particular, can be seen as 2D discrete signals. In the 2D case, the counterpart of the Dirac Delta function is the Kronecker Delta function, and it can be expressed independently from the dimensionality of the space it is used in. It's seen as a tensor, δ, with components:
Images can be thought as 2D versions of LTI systems. In this case, we are talking about Linear Space-Invariant (LSI) systems.
In the bi-dimensional discrete case, the convolution operation is defined as follows:
Images are finite dimension signals with ...
