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

[@yorickdewid]

This is not only used in fingerprints, but JPEG and MP3 do the exact same thing, which is why they are so compact and considered lossy compression algorithms

[@xponen]

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".

[@Tore_Lund]

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!

[@xponen]

@@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!

[@Tore_Lund]

@@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.

[@Will-kt5jk]

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’?

[@undisclosedmusic4969]

The overlap with what happens inside a convolutional neural network is unbelievable and would be very interesting to explore in an upcoming episode

[@Krashoan]

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

[@Evan490BC]

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

Mathematicians are already looking into that. kzbin.info/www/bejne/iGbLhKSbgbiEeZI

[@excalibirb9204]

Photoshop lectures in universities be like

[@HDestroyer787]

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

[@nerdboy19]

It is.

[@Kj16V]

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

[@purrito3892]

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

[@excalibirb9204]

@@purrito3892 DeW iT

[@milpy1257]

I think he forgot to mention why being stored with this method occupies less space on the HD

[@bitbyt3r]

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.

[@milpy1257]

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

[@MrSmoothvideos]

@@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.

[@bobloblaw9690]

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

[@default632]

@@bobloblaw9690 never assume

[@XanGious]

You're literally teaching one of my last semester's course... If only this video come out 6 months earlier lol. Great work!

[@thesilentvoice3397]

What was that course

[@RahulYadav-hq2yy]

@@thesilentvoice3397 Probably Computer Vision or Digital Image Processing.

[@theanalyst9629]

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

[@RahulYadav-hq2yy]

@@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

[@ashes2ashes3333]

this is the best explanation of a 2D fourier transform I have seen, well done!

[@blasttrash]

try 3blue1brown channel as well.

[@phanindrasarma7973]

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

[@ireallyhatemakingupnamesfo1758]

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

[@keenanchu3089]

If only my image processing professor taught it like this, I would've paid soooo much more attention in that class :)

[@arthurtapper1092]

This was like an entire semester of digital signal processing back in uni compressed into 14 minutes

[@andrea_lanteri]

Lossy compressed*

[@brendawilliams8062]

Yeah. Till they start hunting Humpty Dumpty

[@rowanvedangi100]

Pause the video at 4:21 and notice that the image is vibrating even when paused

[@dangerousnigga7023]

Omg yes

[@victorvirgili4447]

i don’t see it

[@zachm5136]

Incredible video! The tattoo recognition at 10:58 - very impressive! Also, for those of you wondering, those wavelets (I believe) are just normal sine/cosine waves that are multiplied by a decaying factor, such as e^-x^2, commonly known as a "bell curve"

[@bzibubabbzibubab420]

thnak you

[@lizekamtombe2223]

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.

[@jsal7666]

0:17 omg that's my fingerprint!

[@anon10w1z9]

u wot m8

[@jsal7666]

Anon10W1z yes i wot

[@Driga_]

Yeah yeah definitely

[@Binary_Bloom]

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

[@rensaito9009]

J Sal hahaha

[@benoit__]

Wow, last time I was this early I was watching MajorPrep.

[@archiebrew8184]

Never heard of that guy

[@odeo3550]

Good old 2010's

[@aasyjepale5210]

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

[@hamiltonianpathondodecahed5236]

under rated comment

[@zhengguosun2962]

@@aasyjepale5210 wasteful name😄

[@desierra99]

I'm an MRI Technologist and never fully understood the Fourier transform and k-space, but this helped a lot! Thank you for a great video!

[@Treviisolion]

I was expecting the video to end with the FBI ending up with so many many fingerprints that their initial data compression would make fingerprints become identical.

[@henryg4255]

Me too

[@simonmultiverse6349]

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.

[@Treviisolion]

@@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.

[@simonmultiverse6349]

@@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.

[@LineOfThy]

@@simonmultiverse6349 exactly. computers aren't infallible.

[@JobBouwman]

"are *made of* sine waves" You mean: "can be *decomposed into* sine waves": kzbin.info/www/bejne/moakooaiiKaEgaM In the contrary, an MRI image IS made of sine waves, as it is truly sampled in the Fourier Domain. EDIT: I think you changed the title based on my comment. That's cool. You make great content.

[@streetrossi4966]

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

[@bruhdabones]

I’m still looking for who asked

[@JobBouwman]

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

[@diophantine1598]

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

[@lunatik9696]

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 :).

[@8BitShadow]

This is also incredibly helpful for object recognition in AI trying to 'see' our world, a big part of the problem is telling where an object ends and where another begins - i.e. an edge. Many edge 'detection' algorithms tend to fall short often missing either very large parts or many small parts of an image, like laplace, often causing other objects to 'merge' into one another and *requiring* human intervention to increase or decrease the tolerances - which is what the main problem is with AI, obviously. You can see it for yourself using an 'edge filter' or the "magic wand" in something like GIMP or photoshop, a lot - if not all - digital artists rely on the "magic wand" selector + grow (selection, often under the 'select' tab) tools to properly bucket fill behind the outlines (on a layer lower than the outlines) instead of manually painting the missed edges. Detecting where the edge of a model is for collisions (be it 3D or 2D, but in this case pretty much only 2D) is very processor heavy, hence why multiple hitboxes are almost always used. A quick edge detection algorithm (probably not like this unless the object's shape is unchanging, at which point you can just define a 'malformed' hitbox during development) would make hitboxes in 2D games/applications almost irrelevant, we've yet to find one though. There are *many* uses for this beyond just compression, but probably best used in compression.

[@AMANKUMAR-fc1yp]

I studied image processing last semester and now you you really cleared the doubts about the Fourier transform random dots. Thanks Zach, keep creating more of these!

[@johnsnow5305]

When I read the title I was like "How the - sine waves used to store imaged?". But after watching the video it makes a lot more sense.

[@JobBouwman]

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

[@mingchenzhang3113]

You can actually hide information (watermark) in the 2d Fourier transform diagram. After they undergoes a reverse transformation and return to the original image, it is very hard to tell the existence of such watermark by naked eye. You can do a Fourier transformation and get them back. Its like traveling between two different but connected worlds. Such watermark can tolerate many mundane method of destruction, like cutting image, rotate, and blur.

[@exponentmantissa5598]

I came across this as it popped up in my feed. I am an engineer that worked with Fourier series for years in digital communications so this was very interesting.

[@apoorvvyas52]

please do another 15 minute video on basics of wavelets. By the way, this video was great.

[@manzenshaaegis8783]

I've been using low/high pass filters for photos for years and never once had anyone explain the math and naming behind them... Thank you!

[@hackermub2598]

9:46 That's how creeper texture was made

[@YVZSTUDIOS]

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

[@xd_Corruption]

This video was amazing, it showed the little details necessary to understand the bigger picture without going into every detail required to understand it perfectly.

[@nashs.4206]

Every single video you post is chock-full of intuition. Incredible work, Zach. :)

[@zachstar]

Thank you!

[@georgepaul6240]

This is so cool Next video idea: how to fool the algorithm

[@kapilbusawah7169]

Never have I hoped a person would say "subscribe to this channel" after he pitched more real world applications of maths, instead he said curiosity stream. This is the video to advertise your channel. This was a beautiful video and I love it.

[@angelpico3236]

This is a great video, I did many labs on filters and their importance to sinewaves but no one ever explained me their applications in real life.

[@gunblad3]

Fantastic description of the fourier transformation and JPG compression, etc

[@user-pb4jg2dh4w]

I think there is no perfect channel like this on KZbin , thank you so much from the bottom of my heart brooo

[@Binyamin.Tsadik]

This is an important video. I remember in University this kind of thing would show up constantly in the lectures. The idea of a wavelet vs a full Fourier analysis has applications in physics to describe photons.

[@xw591]

Please elaborate

[@CalSeedy]

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.

[@laurenpearson9886]

I kid you not I'm actually learning about this in my PSY323 class. The low and high contrast pictures of Lenna were part of the lecture. This actually helped me understand the concept of contrast in time for my exam tomorrow. Thanks

[@psgarcha92]

this is amazing content. I loved the explanations! These concepts are being used at a lot of places, it really helps understand things a bit better.

[@joemiller9838]

It’s a whole new world watching videos like these now that I’m about to graduate and can actually understand them!

[@elektron2kim666]

This tech is a bit older than the FBI and was made with electricity which has the cosinus/sinus functions built in, as is. What they did later was to add more electrical circuits and even more via software numbers (where you come in), but still based in electrical hardware circuits. Any filter which you can think of can be made with an electrical circuit... Some extra programming/coding or hardware chips just adds more circuitry.

[@callynbarath4005]

I just really want to thank you for all the videos you've posted, whether it be about the real life applications of what we learn or what to expect in our majors at university, I live in South Africa and there's honestly not alot of information about the kind of work we want to do and the type of things we learn, would you believe I confused chemical engineering with actual applied chemistry until I saw ur channel 😂😂😭, I honestly really want to thank you, please continue to keep up the good work and provide such valuable information to many other students like me who don't really have any idea what we are walking into, I appreciate all the videos you do and look forward to many more, stay awesome 💯💯😎

[@ImTheBoss914]

10:52 this dude was involved in the LA Riots and was caught on camera, like he said they used edge detection to find the tattoo on the dudes arm and arrest him. Crazy huh

[@mariusfacktor3597]

Very good explanation. It's hard to learn this stuff from a chalk board but animations are super helpful. At the end though, you kind of forgot to say the most important part. The way the compression works is by removing the high frequency information. It does this in image patches too and since image patches are very small, 8x8 pixels in JPEG, you can get away with removing lots of (high frequency) coefficients. That's how you can remove 95% of the information in an image and not even notice the difference.

[@steves1015]

The people who came up with this in the first place are truly amazing. Awe inspiring!!

[@deepaks.m.6709]

This is so good! You did a great job at explaining a complex algorithm by starting with the very basics (sine wave) and built ideas one by one on top of it. Can't thank you enough! :)

[@legoshaakti]

This is just the 2D analog to a normal Fourier series. Any line can be reproduced with a combination of sine waves, and this also applies to areas and volumes. I think this is an excellent way of visualizing Fourier series.

[@mathfigure]

long story short: save it as jpeg 2000 (which use wavelets) and send it.

[@antipoti]

I think the whole point was that they developed the method later becoming jpeg. You cant just use what doesnt exist yet...

[@clementella]

@@antipoti Or can you...

[@uropig]

no wonder jpg's look like shit :O

[@brimmed]

i took a dsp class since i'm a EE, wish i would've watched this before our first lab.

[@wescassidy7691]

Definitely one of my favorite videos of yours that I've watched-- and I've watched many. Gratefully!

[@andytwgss]

I like how you describe Sine waves don't handle quick changes very well, now I understand why folks invented DSD for audio.

[@easypeasylemonsqueezy4]

I love your channel so much. Your content leaves my jaw slack, Every! Time!! Thank you so much for literally making life more interesting for me T.T 💛💛💛

[@leduy6623]

"Wait, it's all sine waves?" Fourier cocking a gun in the back: "Always has been."

[@MizoxNG]

Discreet Cosine Transform is a pretty standard compression technique in most image, video, and audio compression. it's really good

[@therealquade]

Okay so apparently, the WSQ format that the FBI Uses (Wavelet scalar quantization), is behind a minimum $19 paywall for software to be able to open the format, because it's a proprietary .dll file which you have to buy a license for to use in your own software, costs 253.00 U.S. dollars for the first license (single developer license) and 19.00 U.S. dollars per every additional license (client computer), which means you will never get a freeware client-sided program that can open or edit .wsq files. The closest we'll ever get to this, is JPG2000, which is weirder still

[@okboing]

Man I wanna see you stack these sine bars until you get a recognizable picture

[@devrimturker]

Interesting. It reminded me, x-ray crystallography and reciprocal space. I wonder if these stripes also related to double slit experiment results.

[@xponen]

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.

[@anees2410]

Hey Zack 🌟,why didn't we used sin instead of cos waves this is |||||+\\\\\+//////+=

[@shawon265]

In higher studies everyone kinda uses cos instead of sin. They're basically same graph but shifted, so not much changes tbh. But the fact that cosθ is the Real part of e^(iθ) is the main reason why cos is more popular.

[@juliusfucik4011]

Cos it's symmertrical around 0.

[@OneShot_cest_mieux]

@@juliusfucik4011 cos is symmetrical around the Y-axis, sin is symmetrical around 0

[@zachstar]

Yeah as stated when it comes to Fourier you can use both but I often like to stick to just cos and incorporate phase if/when needed.

[@gobyg-major2057]

anees a use*

[@str0fix]

So much love to you! Im 1st year grad student and I haven’t suspected until now how transforms are important and useful! Thanks to you! Now I have motivation to study exam which is coming in the week!!

[@CoreyJKelly]

Great intro to the topic. Thought you might like to know that the use of the Lena image is now frowned upon in the field, and prohibited in most respected publications.

[@zachstar]

Didn’t know that! Any specific reason?

[@CoreyJKelly]

@@zachstar Wiki gives a brief rundown. There's a great mini-doc Losing Lena. TL;DR - it's sexist.

[@NotHPotter]

@@zachstar Specifically, it's from a Playboy centerfold. Kinda gauche with the benefit of hindsight.

[@jofx4051]

en.wikipedia.org/wiki/Lenna

[@theodiscusgaming3909]

@@NotHPotter so what?

[@jackbarbey]

This video connects to do much stuff, from Photoshop to my Nonparametric Inference stats class I took in college. Great job!

[@ryanjean]

Almost a decade ago, I had to write a code module to decode WSQ data stored in a database into JPEG for display in a web browser. The space savings I saw were closer to 10:1 rather than the 20:1 mentioned in this video. Anyway, what a nice trip down memory lane.

[@rishmatic]

Respect!!! I would have cleared my engineering 10 years back before dropping out!

[@skipintro9988]

Thank you so much for explaining so hard concepts in simple ways

[@mandelbro777]

cool. I had no idea any image could be composed of a set of sine waves and that filtering these is such a useful mechanism in image forensics which also reduces data transfer/storage requirements in the finger print domain. You learn something new everyday. Nice vid. Thanks

[@Br3ttM]

That explains the weird ring around sharp edges which really bug me watching certain styles of animated shows on Netflix. That general type of compression is not made for blocks of solid colors with sharp edges.

[@BitcoinMotorist]

There was a 1980s freakout about how computers (computers not the Internet) are a threat to privacy. They were right. Before, your fingerprints could be analyzed only if you were a suspect, it couldn't be used to come up with a suspect. And there are countless stories of "matches" who were exonerated

[@sk8sbest]

@@Jessica-to8um here we go again

[@uvaishassan]

Thank god for making this channel exist.

[@shanugaur8218]

Brother how do you even come up with things like this amazing

[@mdrsz7649]

11:39 Arctic Monkeys! Great video by the way, I would hear more about the fourier transfrormation's real world useage. For example sound correcting, autotune etc.

[@patrickjdarrow]

The new content is awesome. Glad you're able to evolve the channel with more generalized topics

[@prashantnook]

(havent watched the video fully 5:00) i am sure its like a 2D plot of Fourier transform? edit : nvm he said it LMAO

[@PedroVencore]

I always wondered what really happen while doing a High Pass Filter in Photoshop, I guess it have to be this or something like this, I love the mathematical explanation behind a technique I use so much

[@tonym5857]

Wsq is a complex algoritm but usefull to store fingerprint and a easy way to interchange info between AFIS but lately I realized that fingerprint is not good enough and it was replaced with handpalm with format file is JPG2k. Nice video.

[@sb-hf7tw]

Every time I see Zach star, it remembers me Major Prep!❤️ 🙏 U can understand whole yearly syllabus in a video!!!

[@zeitgeisttv5312]

Man if this was taught in math class. I might have paid attention

[@RubixB0y]

That wavelet jazz just blew my mind

[@pokepress]

Even though I learned a lot of this back in college computer science classes, this video was still a nice explanation.

[@officialDragonMap]

The spectrum of gray is definitely continuous and there are definitely not only 254 (+2 for white and black) values (or any other finite color depth).

[@streetrossi4966]

I have been doing a project on compressed sensing in mri woah you explained concepts of kspace, wavelets , edge detection and compression, noise removal in 5 minutes , for which i took couple of days.

[@mathint8221]

Awesome video! This made so many concepts come together. And I finally know what a wavelet is. Thanks for that!

[@NickThePyromaniac]

I really like this, You do a great job of finding a medium between formal lecture and friend explaining cool math to you. It was easy to follow Also, how did you do the transformations from an image to an 2D-plot?

[@majesticwizardcat]

You should add your sources to your videos. It would be great to read the whole paper or read the code that you found.

[@RussellTeapot]

The link for the wavelet algorithm is in the video description

[@zachstar]

Everything I used for this video is in the description. The idea came from a book and the detailed link to the algorithm is there as well as Russell teapot stated

[@majesticwizardcat]

@@zachstarThank you and sorry if I didn't notice it but I was sure I checked before commenting.

[@geoffreyanderson4719]

Our chief engineer of our small company's StoreVision product also innovated in 1996 a way to use wavelet compression to record surveillance video (not photographic stills) comprehensively (not event-driven) of cash tills for our retail customers along with timestamped records from cash tills. We had them using it by 1998. It is a funny thing since it's seemingly the same year approximately (you did not say exacty what year) Los Alamos National Lab did the same thing with fingerprint storage. THe search problem to match against 500 million fingerprints is another video Zach Star might consider to produce. The early 2000s saw the advent of locality sensitive hashing using landmarks in the fingerprint, like swirls and junctions. This would work very well, and is probably how they do it since the early 2000s at the FBI. Secondly, it was a great advance to get that level of compression but now with deep neural networks in particular there's a lot more possible IMO than 20-1 compression. The early 2012+ period to present (ImageNet dataset and GPUs and better algorithms) saw the advent of machine learning using deep neural networks using transfer learning from pretrained large networks like ResNet50 as an automatic feature detector, and variational autoencoders to produce bespoke data-specific compression algorithms to be automatically learned instead of hand coded by human experts. I bet 20 to 1 compression on fingerprint images can be beat by a lot using a combination of the elements I just described. THat's for compression. As for search, I am limited currently in my insights to do better than LSH. LSH is a generic algorithm that does not use deep neural network learning which arose after (at least 5 years).

[@geoffreyanderson4719]

On second thought the dimension-reduced encoded vector that the above deep neural VAE will have created for image compression would also work great for the basis of comparison for search. That's how I would do it, at least what data to search for instead of searching the original picture database. As for algorithm to do the search on the encoded vectors, LSH might still be among the best, not sure at the moment. It's worth a try.

[@simonmultiverse6349]

The thumbnail is wrong! "All images are made of sine waves." No, they're not. All images *CAN* be turned into a sum of sine waves... BUT... you can also make them by adding square waves together. There are Laplace transforms and wavelet transforms and other (linear) transforms which means you can make ANY picture by adding carefully-chosen amounts of your favorite set of waveforms. There just happen to be some neat, fast and efficient algorithms to deal with sine waves.

[@TravelingMooseMedia]

Wow this is CS and complex real world mathematics at once! Beautiful.

[@hugsun5918]

All the visual artifacts in this video made me cry

[@demetresaghliani9048]

You explained the frequency domain better than my professor managed for the _entire_ computer vision class. Wow.

[@stefm.w.3640]

But I want a deep look at the mathematics behind the compression algorithm!!

[@amir-il2sq]

See how it works on kzbin.info/www/bejne/mnyWiqOeh7KMgJI

[@samwise2588]

Excellent video. As a musician, this usage of term high/low-pass filtering is befuddling. Like I get it, but never thought of it another, non-tonal frequency, context. Now I'm wondering what a high/low-pass filtering would like for other senses, lol.

[@renesperb]

These are really fascinating applications of mathematics !

[@Beateau]

I could see a huge market of Fourier transfermations of famous images and memes.

[@tomgroover1839]

OK so the FT graph shown at 6:13, I presume each one of those points corresponds to one entry of an array, and the value of that array entry is the amplitude. The sign will take care of which of two 'in phases' 180 degrees apart. But like in the more common FT, there must be a quadrature entry so that the phase can be controlled over the full 360 deg. Does that mean that points above the horizontal axis are say 'in phase' and below the horizontal axis at quadrature? Ok one more thing> Is not the matrix implied by that cartesian appearing graph actually defining polar coordinates for the data points, so that frequency resolution for all angles of the graph are identical?

[@PrivateSi]

From a digita computing perspective I think a 1 bit GIF with RLE compression would be simplest for fingerprints. Can't see the point of all the sine functions in this case. Could be stored as a series of arcs but I'm not sure it would be higher compression. For advanced graphics analysis I'm sure its useful but realtime decompression prefers simple operations. Sine functions are slow.

[@TURNKEYiNK]

This would have made Marh class sooo much more interesting; more so than: Jonny wanted to plant a garden 3x6, and 1foot deep, how much dirt does he need?

[@TheScreamingFedora]

Too bad you have to learn basic multiplication before you can understand Fourier Transforms.

[@obbavyakti5805]

@@TheScreamingFedora I don't think he referred to the level as much as the degree of context given

[@DUTCHPOTATO]

I need to come back to this when I learn what the heck is going on

[@brianevans4]

Bob Muller: any more detailed analysis of the mathematics behind it is beyond my purview

[@CharlesMacKay88]

Wow I got my bachelors degree in electrical engineering but I never heard this way of explaining digital signal processing. Nice work. Very cool.

[@Imnothere59]

I memorized HPF is Edge detection filter now i understand

[@nunyabidness117]

When I was an 8 year old cub scout we visited the FBI on a field trip. We were all fingerprinted without parental permission.

[@ZimZam131]

This is pretty interesting. It's like an analog version of image creation that can be transmitted digitally just by sharing coefficients.

[@closetweeb8492]

this is fucking insane, math is incredible, this is the most interesting video i have seen in a very long time.

[@cmyk8964]

This works for fingerprint data because pixel perfect precision is not important at all. They don’t need a lot of fine details either, at least compared to most photographs.

[@crewrangergaming9582]

converting the lines of a fingerprint in SVG would have been a breakthrough.

[@DaulphinKiller]

How about using a GAN to learn the most efficient way of compressing these finger print images, and use the alpha/beta powers of the "fingerprint matching test" as metric to minimise the loss of information in the latent space that would be used for storage?

[@davidflores909]

For a second I was already expecting a video about bricks.