Convolution
The convolution of two picture functions g and f , denoted g * f , is defined as:
g * f (x, y) = &int &int- &infin&infin g(u, v) · f(x - u, y - v) du dv
For example, the image recorded by a camera is the convolution of the original image with the point spread function of the camera optics.
If the function decays rapidly to zero outside a local area, convolution can be approximated by applying a grid-like operator to the image:
| 1 | 1 | 1 |
| 0 | 0 | 0 |
| -1 | -1 | -1 |
Such an operator can rapidly be applied to a whole image by special hardware, either operating on a stored image or on a raster scan.