Convolution involving one-dimensional signals is referred to as 1D convolution or just convolution. Otherwise, if the convolution is performed between two signals spanning along two mutually perpendicular dimensions (i.e., if signals are two-dimensional in nature), then it will be referred to as 2D convolution. This concept can be extended to involve multi-dimensional signals due to which we can have multi-dimensional convolution.
In the digital domain, convolution is performed by multiplying and accumulating the instantaneous values of the overlapping samples corresponding to two input signals, one of which is flipped. This definition of 1D convolution is applicable even for 2D convolution except that, in the latter case, one of the inputs is flipped twice.
This kind of operation is extensively used in the field of digital image processing wherein the 2D matrix representing the image will be convolved with a comparatively smaller matrix called 2D kernel.
