Biomedical Engineering Reference
In-Depth Information
Fig. 5.12. Examples of use and abuse of Fourier analysis and filtering. Top: the noisy image of an
atomic lattice on the left shows clear spots in the FFT image (inset). Measuring these spots allows the
user to determine the lattice parameters. Filtering is achieved by selecting the six intense spots, as
shown above the arrow, and removing the rest of the image in Fourier space. Carrying out an inverse
FFT gives the image on the right - the selected features are preserved and the noise is removed.
Unfortunately, as shown below, carrying out the same operation on an image of pure noise (left, note
the inset FFT image shows no spots) can also give a wholly artificial image (right). (A colour version
of this illustration can be found in the plate section.)
used to analyse atomic lattice parameters [372, 373]. Images showing the atomic lattice,
even if very noisy, will tend to show intense spots in the Fourier space image, indicating
the unit cells of the atomic lattice. An example of this is given in Figure 5.12.
In order to determine the spatial wavelength of the features seen in the Fourier-space
image, they can be measured directly with the analysis software, or an alternative is to use
Fourier filtering to isolate the components of interest. The way this is done is by editing the
image in Fourier space directly. Typically, the user draws boxes (or ellipses) in the Fourier
image around the features of interest. The software keeps these marked areas, and clears
the rest of the image. Then an inverse Fourier transform is applied to the modified image.
This has the effect of converting the image back into the spatial domain, i.e. into real
space, but with only the selected components remaining. This removes all other features
from the images, leaving only the features the user selected, allowing clear visualization or
measurement of the pattern of repeating features. As may be imagined, this technique is
