Open the bird cage… 
Now the question one is asking is:
How free this bird from its cage ??? (je
sais, je dessine assez mal… ;))
First, one have to study the Fourier transform of this image:
If one looks closely, one can see that this FT (here it is its moduli
that are displayed) consists in a set of equidistant peaks on the
horizontal direction going through the origin (image centre) and of a
more complex variation without any particular favoured direction.
According to what we have seen concerning the lattices, the set of
peaks in the FT should come from a lattice in the image, then from the
cage in front of the bird; the more complex moduli variation then comes
from the bird itself which has a more complex shape than the grid.
To check this, one can eliminate these peaks in the horizontal axis using an adequate masking tool and then calculate the inverse Fourier transform of this modified FT:
The bird is now free!!!
To conclude this example one
can notice that the FT of the original image (bird in cage) is the
convolution of the FT of the free bird with the empty cage (not the
sum):
To see that, one can have a close look around the peaks sitting on the
horizontal line of the FT of the bird in cage image: one can notice
that these peaks are broader than the peaks of the FT of the empty
cage and even display an asymmetry that also exists around the origin
of the FT of the free bird.
