Sometimes there are unwanted things present in our work, and it is of course better to have only the things we need to be there. Noise reduction makes a sample more pure, assumptions that can be made more valid, or just make things more beautiful. In this activity, we will be using the ubiquitous Fourier Transform to tone down unwanted specks and enhance the parts we want, err need.
First, we need to understand convolution. Mathematically, it is defined as below.
If f(x) and g(x) are two functions with Fourier transforms F(u) and G(u), then the Fourier transform of the convolution f(x)*g(x) is simply the product of the Fourier transforms of the two functions, F(u) G(u).
Now, let us understand this through these examples.
Figure 1.
Figure 2.
Figure 3.
Figure 4.
Figure 5.
Finger print
Finger print
FT of finger print in log scale
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convolution
http://www.cs.cf.ac.uk/Dave/Vision_lecture/node19.html
finger print
http://archgraphics.pbworks.com/f/finger%20print_blue%20copy.jpg
http://www.cogs.susx.ac.uk/courses/acv/matlab_demos/fft_image_demo.html
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I'd give myself 7 for this activity because I didn't get to finish it.
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