Stephen GruppettaAny image can be reconstructed from a series of sinusoidal gratings.
A sinusoidal grating looks like this…
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It’s called a sinusoidal grating because the grayscale values vary according to the sine function.
If you plot the values along a horizontal line of the grating, you’ll get a plot of a sine function
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…and different frequencies—these are spatial frequencies, not temporal ones
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There's one more parameter that defines a sinusoidal grating: the phase. Gratings with a different phase are shifted with respect to each other…
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You can create a 2D sinusoidal grating in #Python using #NumPy and display it using #matplotlib
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Or even better, you can use a function of both x and y to make any grating
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You can find the parameters of a sinusoidal grating by using the 2D #FourierTransform.
The dots shown contain the amplitude and phase of the grating. Their position from the centre gives the frequency, and their orientation represents the orientation of the grating.
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Now, if you have lots of gratings superimposed on each other, the #FourierTransform gives you a pair of dots for each of the components
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Now, here’s the “magical” part of #Fourier theory.
Any image is made up of lots of sinusoidal gratings. So, the 2D Fourier Transform of an image gives you thousands of pairs of dots, and each pair represent a sinusoidal grating.
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And therefore, you can reconstruct the image by adding all of those sinusoidal gratings together.
The more gratings you add, the closer the result is to the actual image
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Here's another example
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and another one…
There's a lot more than can fit in a single thread.
If you want to read more detail, and go through the step-by-step writing of the code to decompose & recostruct *any* image, read full article here:
#coding #2dfourierimages #2dfouriertransform #fourier
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So, this thread could serve as my my #introduction
I'm Stephen. I used to be a physicist (as you can guess from the thread above) but now I focus on communicating about Python and programming and teaching coding
You can expect more varied content from me, all related to #programming in #Python, from science-y stuff like this, to fun animations using the `turtle` module (no not those boring ones!) and general Python for those learning to code at beginner and intermediate levels
You'll find me easily on Twitter too if you're on there as well. That's a bigger account and get's a lot of interesting conversations going with others in the #Python world
You can see the sort of things I'm interested it there (until this timeline fills up a bit): https://twitter.com/s_gruppetta_ct
