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.

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