Any image can be reconstructed from a series of sinusoidal gratings.
A sinusoidal grating looks like this…
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
Sinusoidal gratings can have different orientations…
…and different frequencies—these are spatial frequencies, not temporal ones
There's one more parameter that defines a sinusoidal grating: the phase. Gratings with a different phase are shifted with respect to each other…
You can create a 2D sinusoidal grating in #Python using #NumPy and display it using #matplotlib
Or even better, you can use a function of both x and y to make any grating
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.
Now, if you have lots of gratings superimposed on each other, the #FourierTransform gives you a pair of dots for each of the components
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.
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
Here's another example
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
Not sure whether you’re only meant to get a single shot at an #introduction, but I’ll extend on mine a bit now that I’m starting to find my feet here
My main focus is on communicating about #programming, specifically #Python. That includes teaching!
However, my first career was as a physicist
After studying #Maths and #Physics and then getting my PhD in Physics from Imperial College, London, I went down the normal route of a few postdocs, an academic fellowship, and then a lectureship.
Most of my science work centred around novel retinal imaging technology with the primary aim of early disease diagnosis, plus a bit more about the optics of the eye.
I learnt to code as part of my PhD work and then relied on programming (mostly MATLAB, at the time, before the Python-era) for all of my research work, from simulation and modelling, to running the lab experiments, to analysing the data.
When I left academia, I decided to focus on teaching programming to both children and adults.
I spend a lot of time creating learning content, including The Python Coding Book and regular articles on the blog.
I also run codetoday which runs live lessons for children from age 7 to learn coding in Python (only Python, no kids-platforms. Yes, starting from age 7, you’d be surprised how well they pick the basics up)
I’ll be sharing bits on content regularly here too, typically aimed at intermediate learners (including those aiming to move from beginners to intermediate), including steering towards scientific programming and related fields.
OK, I’ve abused #QOTO’s longer character limit too much, so I’d better stop!
@s_gruppetta In my 35 years as a sotfware engineer I have seen a lot of code that looks like it was written by seven year olds. 😆
QOTO: Question Others to Teach Ourselves
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@s_gruppetta Nice python book.