(Assignment)
(Part A) Read the paper (the
'Materials and Methods' and 'Discussion' sections are particularly
important) and note principles covered in the image processing course.
This work is dealing with 3D matching but many concepts can be readily
transferred from the 2D image processing case. Then write a summary
adressing the following:
(Part B) In what contexts
are the following concepts from the course used here: Fourier transform, convolution,
FFT-acceleration, template convolution, Laplacian filter.
(Part C) What is different about 3D matching (more complex
compared to the 2D matching of images)? Hint: Meant is not the added dimension of the
translational search, rather additional novel complexities in the paper
that were not discussed in class.
(Part D) In the above paper the
edge-detection properties of the Laplacian
filter are used. What is the effect of the Laplacian on the performance
of template
convolution for matching of low-resolution 3D electron microscopy data
(D1)? Application of the Laplacian operator in direct space is
identical to multiplying in Fourier space with what function (D2)? Hint: Read the
'Discussion' thoroughly and read section 2.1.4 of this
very nice filtering overview (if the link is broken a local copy is
stored here). Based on this
insight, is the
Laplacian filter
high-pass, low-pass, or band-pass (D3)? Finally, a frequently
used noise-reduction technique in electron microscopy is thresholding: density levels below
the molecular surface threshold are set to zero,.
In (D3) you should have answered what kind of noise frequencies are
amplified by Laplacian filtering. So is thresholding a good idea to
reduce the effect of noise when a Laplacian filter is used, or are
there
any caveats (D4)? Hint: This is not explained in the paper, you need to
think. Consider that the Laplacian computes the second derivative in
direct space. If there are problems can you suggest remedies?