between individual structural elements found in the image
itself. These can originate from both contrast and
shape-based features contained in the image, as well as
an analysis of features that are mathematically condensed
into a representative set.
Sliding Fourier transform
As an example of image domain analysis, we demonstrate
a sliding fast Fourier transform (FFT) filter [77]
for analysis of surface reconstructions on epitaxially
grown films of La5/8Ca3/8MnO3 (LCMO). The image analyzed
in Figure 10a, is a 50 × 50 nm2 STM topography
image (captured at a resolution of 512 × 512 pixels). We
analyze a small window of the surface (outlined as a
white square in the figure, of size 128 × 128 pixels) and
generate a FFT image of that area. The window is then
slid across the image by a preset number of pixels (in
this case, 8), and the FFT image is captured once again;
this process is repeated until the window has covered
the entire real-space image in the horizontal direction.
The window is then stepped in the y-direction and the