8. Enhancement in the frequency domain (1 of 2)

Image enhancement can be done in the frequency domain by filtering out unwanted frequencies. Computationally, this is done by convolution of a mask and the image of interest.
Before we proceed to enhancing images in the frequency domain, we look into convolution.
Here are images of pairs of dots and squares with corresponding Fourier Transforms.

Dots (top row) and their FTs (bottom row)

 

Squares (top row) and their FTs (bottom row)

 

Here are 2 circles with Gaussian intensity distribution. Increasing variance decreases the frequency-space dimensions of the FT. Also, the patterns are similar to the central regions of the circle and square.

(insert image)

With randomly spaced dirac deltas, the FT appears to be . Convolved with patterns, the resulting FT repeats the patterns in the di

(insert FT of dirac)

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4 thoughts on “8. Enhancement in the frequency domain (1 of 2)

  1. So ganyan pala siya sa optics… If I had know how beautiful physics could be, I would have liked it more. Great images, what equipment did you use to get these?

    1. Ate Ren! 🙂 Simulation lang siya so everything’s done with my trustee laptop and Scilab. Scilab’s is Free and Open as any FOSSy thing could be at friendly siya for matrix operations (similar to Matlab). In this case, the images are all represented by matrices and we just invoke mathematical operations to produce these images.

      1. kala ko pa naman may state of the art spectrometer (or whatever thingamajig you use) sa lab ninyo… 🙂

  2. I had a certain day na buong hapon akong nag spectro… Nakakabaliw. Nangitim yung mga daliri ko sa kakatanggal at lagay ng cuvette. Nag-panic ako at sabi ko sa nanay ko, “Mama, my fingertips, they’re painful and they’re turning gray!”.

    The chemists always have the prettiest spectrostuff… Chem ka pala ate ren.

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