When the FBI had too many fingerprints in storage | The mathematics of image compression 

they also form naturally when x-ray passes thru a crystal, forming a similar x-y dots that reveal the repeat structure of that crystal. It is called "X-ray crystallography imaging".

Both of you: This is how reality works. What we perceive when we watch something with our own eyes, is in reality, just the interference pattern of individual light waves being overlayed. The rules of optics, are just a description of how this interference creates what we perceive as images. Here's the scary part: The same formulas are used in Quantum field theory, to describe how wave functions interfere to create particles and forces. So most likely, every bit of reality is in essence just different interference patterens, and not really there, in the same way that images are not really there either!

@@Tore_Lund we see images & 3D objects when light passes a Hologram film, but this film didn't record a image, it record interference pattern. Pretty cool!

@@xponen Exactly, but real object creates this interference pattern too, so as a hologram is the snapshot of the wave interference reflected off an object, there is really never, say a red photon, travelling as a particle from a red dot in an image in a straight line into your eye. That red dot scatter the light in a semicircular wavefront in a general direction with no information of its origin. The information of the dot really only emerges when the wavefront is overlaid with all the other wavefronts in the image, it only then becomes information of the placements of pigments in the image. Imagine being in a dark room with a red laser (only one frequency, a single sine wave) shone through a lens to make it spread straight at you, being the only light source. You will not be able to deduct anything about the red dot, other than it is red. It won't even be a dot but a pattern of concentric rings = an Airy disc from the photons interfering with themself. Photons do not carry information of the object it has been reflected from, an image is only created in the interference pattern between photons.

Tore Lund - wait, is a rainbow a slightly spread out, reflected (refracted 180°) high pass filter/edge detection of the sphere of the Sun? Or is that too ‘out there’?

I took this course in university but it's called Computer Vision

It is.

@@HDestroyer787 I'm a computer and my vision is nothing like that.

Excali BirB I wanna like this so bad, but it’s at 420, so i wont

@@purrito3892 DeW iT

Undisclosed Music Are you referring to the blurring portion vs the convolution matrix?

There is nothing to explore. The convolution operator is diagonalised by the Fourier transform. That's all.

Mathematicians are already looking into that. ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-R5hSqeLSQC0.html

Omg yes

i don’t see it

u wot m8

Anon10W1z yes i wot

Yeah yeah definitely

Yea same mine is at 0:18 and 0:19

J Sal hahaha

What was that course

@@thesilentvoice3397 Probably Computer Vision or Digital Image Processing.

@@RahulYadav-hq2yy there are courses specifically for digital image processing? !

@@theanalyst9629 Yes, you should find them in most electrical engineering and computer science departments. Also you can find a ton of courses online as well

Yeah... That was a pretty big omission, especially considering that it actually doesn't! The frequency domain representation of an image is the same size as the spacial domain representation we usually look at. The reason it's used in compression is that it is usually easier to simplify the image in the frequency domain, as most images we care about have the bulk of their energy grouped into a few points in the frequency domain, meaning that we can forget most of the low energy points without changing the image much in the spacial domain.

@@bitbyt3r That makes a lot more sense than what Bob Loblaw said.

@@bobloblaw9690 you're getting a bit muddled. Whenever you send any files, it is always at some point represented as 1s and 0s. Whether you're sending a compressed image, or uncompressed image, it is still made up of 1s and 0s. So saying you're either sending an 'full image' or just 'numbers' isn't true. They will both be transmitted as 1s and 0s. Lossy compression means you are losing some information that you can sacrifice, e.g. reducing the resolution of a photo, whereas lossless is compression is where the exact data can be reproduced with no loss in information. You're piratebay analogy does not apply. What that is, is like you said, an archive of all file directories on the server. However, with just file directories, you can not, regardless of the algorithm, recreate any of the files on piratebay. But, you can use those directories to download the files off the server. However, the analogy is even more confusing as piratebay hosts bit torrents, which is peer-to-peer file sharing, so again a different thing. Compression is possible when you have an agreed algorithm on how to encode and decode data. So you may need to download software to interpret the efficiently encoded data, however all the data is still there, which is different to your archive example where the data is not there, but just an address to access the data you want to download. Mark Murnane posted a great response to the initial question, but I just wanted to give you a better understanding of compression.

@@MrSmoothvideos Thanks for explaining....I was using my intuition. I clearly don't know that much about computers lol.

@@bobloblaw9690 never assume

Lossy compressed*

Yeah. Till they start hunting Humpty Dumpty

try 3blue1brown channel as well.

@@blasttrash yep 3B1B did a great job with that

There's a video about it's application to Jpeg compression on computerphile if you're into that sort of stuff

Never heard of that guy

Good old 2010's

@⸻⸻⸻⸻⸻⸻⸻⸻⸻⸻⸻⸻⸻⸻⸻⸻⸻⸻⸻⸻⸻⸻⸻⸻⸻⸻⸻⸻⸻⸻⸻⸻⸻⸻⸻⸻⸻⸻⸻⸻⸻⸻ nice name

under rated comment

@@aasyjepale5210 wasteful name😄

thnak you

They are not trigonometric functions, the one showed is the Mexican hat wavelet which happens to look like that. Daubechies has good work on this. But do a google image search on wavelets and you'll see some mind boggling examples.

Me too

No joke, it really happens. Also, police they are experimenting with computer matching of pictures of faces, and people get arrested, not because they are guilty, but because their face is on the database. Computers don't understand faces.

@@simonmultiverse6349 To be fair to the computers, humans can often confuse people for other people or not recognize people in photos even if the person is standing right in front of us, we just need to be careful not to think that computers are infallible when it comes to comparing faces and treat it the same as some random person saying they think a person is the same person in a wanted poster. A potentially good lead, but not in and of itself proof.

@@Treviisolion Yes, face recognition is difficult even for humans. I think the REAL problem is a combination of two things: some enthusiastic people who are programmers and builders of databases claim that their computer system can recognise faces, AND the police think that this is an easy way of catching criminals.

@@simonmultiverse6349 exactly. computers aren't infallible.

Has the title changed? What was the original title? Something like: "all images are made from sine waves" ?

the fun part is that this is actually true! 😂 "like crunchy leaves" says the wiki

COINCIDENCE I was learning compressed sensing of mri images, this topic covered so much of basics very clearly.

I’m still looking for who asked

@@bruhdabones I think he changed the title, which was something like "all images are made of sine waves"

All physical phenomena can said to be composed of waves... none of this makes sense anymore! Mwahaha!

When one does a Fourier analysis, all signals can be thought of as a combination of sinusoids. It is built into MATLAB. We can take a random signal, decompose it into a combination of sinusoids and then reconstruct it. I mainly did this technique to determine power of a signal, but this application seems obvious once the narrator pointed out :).

Thank you!

Please elaborate

Currently a 3rd yr physics student and we haven't covered wavelets explicitly. We glossed over how wave packets (not sure if they're the same) are used to describe photons in yr 1, that's all. Also Fourier analysis only covered square and saw waves.

crystal have repetitive structure just like an image as described in the video above. When an x-ray passes thru such structure that have a repeat of an exact multiply of the wavelenght of the x-ray, it reflect constructively on the x-y plane, otherwise if no repeat structure on the crystal it reflect destructively. It's like an a clever fourier transform using constructive & destructive interference of light.

Thanks man! And I guess I wanted to make you really stand out haha, really appreciate the support!