Normally, the picture is not continuous and converting full ria is not continuous function is to convert signals from space-domain, frequency domain has become.
Images are usually discontinuous functions. And the Fourier transform of the discrete function converts the signal from the spatial domain into the frequency domain. So we use the Fourier transform of discontinuous functions used in image processing.
Usually image function is not continuous. And conversion of discrete Fourier transform function to convert signals from spatial domain to a frequency domain.