Frequency domain
For
simplicity, assume that the image I being considered is formed by
projection from scene S (which might be a two- or three-dimensional
scene, etc.).
The frequency domain is a space in which each image
value at image position F represents the amount that the intensity
values in image I vary over a specific distance related to F.
In the frequency domain, changes in image position
correspond to changes in the spatial frequency, (or the rate at which
image intensity values) are changing in the [[spatial domain]] image
I.
For example, suppose that there is the value
20 at the point that represents the frequency 0.1 (or 1 period every 10
pixels). This means that in the corresponding spatial domain image I
the intensity values vary from dark to light and back to dark over a
distance of 10 pixels, and that the contrast between the lightest and
darkest is 40 gray levels (2 times 20).
The [[spatial frequency]]
domain is interesting because:
1) it may make
explicit periodic relationships in the spatial domain, and
2) some image processing operators are more efficient or indeed
only practical when applied in the frequency domain.
In most cases, the Fourier Transform is used to convert images
from the spatial domain into the frequency domain and vice-versa.
A
related term used in this context is [[spatial frequency]], which
refers to the (inverse of the) periodicity with which the image
intensity values change. Image features with high spatial frequency
(such as edges) are those that change greatly in intensity over short
image distances.
If an image has large values at high frequency components then the data is changing rapidly on a short distance scale. e.g. a page of text
If the image has large low frequency components then the large scale features of the picture are more important. e.g. a single fairly simple object which occupies most of the image.
