Looking through Objects - How Tomography Works!

Рет қаралды 22,010

3 жыл бұрын

During my studies, I became really fascinated by the math and visual illustrations in biomedical imaging. I hope that I can share my passion about this topic with you in this video. The idea of 3b1b's "Summer of Math Exposition" was quite motivating to make this project happen.
Resources used for this video:
* Lecture notes from DESY: Milan Zvolský www.desy.de/~garutti/LECTURES...
* Lecture notes from University Göttingen: Prof. Tim Salditt
* Digital Image Processing: Rafael C. Gonzalez
* Rose CT data by microphotonics, • 5 Minute Micro-CT Scan...
* Animation Software: Manim, www.manim.community
Special thanks to Veerangna Kohli for aesthetic advice, mental support and help with the audio recording.
I really appreciate the people who took time for reviewing this video and giving me technical feedback:
Rishabh Jha,
Martin Krzywinski (mkweb.bcgsc.ca/),
Oliver Schön, and
Matthias Schröter.
Lastly, I would also like to thank the great people in the Manim Community and the Institute for X-Ray Physics in Göttingen.
Small typo at 13:40:
p̃(s,ϕ), not p̃(ω,s).
p̃(s,π*m/M), not p̃(π*m/M,s)
imgur.com/a/qsZwJdI (corrected proof as an image)

Пікірлер: 51

@parhamzolfaghari7394 4 ай бұрын

Mind blowing!!! I wish most professors and lecturers stop teaching and just play videos from people like you. Thank you for your fantastic explanation.

@benjaminhezrony5761 4 ай бұрын

This is SUCH a great video on the topic. Fantastic animations! I do research in CT super resolution, so this provided a lot of good background and visualizations on the source of the images I super resolve

@stoyantodorov1917 16 күн бұрын

Brilli ant explanation! Thanks a lot!

@phonix6494 3 жыл бұрын

Thank you for this video, it really remindet me how connected everything is, so many concepts that I already had a glimce at shining in a new light. Aesome video music and Visuals

@jubieralonsojimenezcamargo5732 9 ай бұрын

Amazing; Thanks for taking the time to doing this

@kphk3428 2 жыл бұрын

I always wanted to learn about this! The animations are amazing. You put a lot of effort into it. It saddens me that it isn't getting more views...

@MariaJose-ub9rt 2 жыл бұрын

Thank you so much! i study Nuclear Medicine and this part of tomographic images is so hard to understand! but the video really helped me. Greetings from Argentina

@Asu-cr9sb 17 күн бұрын

You are the man!

@ahmadayoubi1830 4 ай бұрын

YOUR EXPLANATION IS PERFECT WOW! you made a complicated idea sound so easy thank you so much

@shailesh4673 11 ай бұрын

Thank you very much for this video!! my friends and I were struggling on a past year problem for our medical imaging class and this video cleared everything up

@rohitkumarsaini221 8 ай бұрын

I have been facing problems with removing the tomography effect from OPG dental image. Anybody can help me please

@alirezasheikhsofla2764 2 ай бұрын

The video was so great and informative for the basic concepts of tomography. Thanks!

@NoNTr1v1aL 2 жыл бұрын

Absolutely amazing video! Subscribed.

@tilkesh 7 күн бұрын

Thanks

@Caspar__ 3 жыл бұрын

Wow, this is great. I am really looking forward to when I learn fourrier Transforms next semester, so I can appreciate the beauty at play here. I have been thinking about going into medical physics and I appreciate, that even there many mathematical concepts are at play.

@AForce295 2 жыл бұрын

Amazing video, well explained! Helped me in studying for my medical imaging exam :D

@camilogomez775 5 ай бұрын

Hi. This has been very usefull for me. You did a sublime work. You are a great teacher. Thank you so much. 😄

@error200http 2 жыл бұрын

Excellent animations!

@SirTravelMuffin 2 жыл бұрын

So good!

@zign2044 5 ай бұрын

Merci infiniment pour cette vidéo!

@thebees955 2 жыл бұрын

Very cool video!

@lavimuia7612 7 ай бұрын

Excellent lecture.

@BrianAmedee 3 жыл бұрын

The visualisations were really satisfying to watch, and thanks big time. I have never 'understood' how CT scanners actually work. This makes so much sense now!

@vishalnimesh3846 9 ай бұрын

Amazing

@Marie-yx7qs 6 ай бұрын

Danke Bruder

@matthewjames7513 11 ай бұрын

Thanks so much for this video. I learned a lot. At 13:41 you make a discrete approximation for the inverse radon transform. I'm interested in coming up with a matrix representation for the Radon Transform [R] and Inverse Radon transform [R]^-1 such that: [R]f = p and [R]^-1p = f Do you know what expressions I can use for [R] and [R]^-1 can be? As context: I'm running an optimization algorithm where I need to calculate [R][R]^T f. I have no idea how to find [R][R]^T though.

@corentink3887 7 ай бұрын

you genius

@MooImABunny 2 жыл бұрын

I can't find a formula for the Shepp-Logan filter online it looks from what you graphed and the fact that it should start like |w|, that its 2|sin(w/2)| for -pi

@shervinnia7456 2 жыл бұрын

Hello! This animation is extremely useful, and I'd like to publish some parts of it to open-source resources for understanding tomography in the context of structural biology. Would I be able to post parts of this video with credit given and a link back to the channel? I'd also love to have a look at the source code if you're open to that. Thank you!

@Kolibril 2 жыл бұрын

Thanks for your feedback! That sounds like a really nice project, and I would like to make my animations available to it. Further details we can discuss via direct message.

@someonetoogoodforyou 6 ай бұрын

Thanks for the video. I see you made it using manim! May I access the code somehow?

@matthewjames7513 7 ай бұрын

Thanks for the video! I was following the proof very carefully. I believe you've made a small typo at 13:16 on the second last tline. I believe p_tilde is a function of phi and s. Whereas you have written p_tilde(w,s). This is because once you evaluate the inverse FFT the w should get removed. The next line, you just integrate out the phi and leave the s untouched. But s is a function of phi as well so I think the final summation should look different too, right?

@Kolibril 7 ай бұрын

good spot! it sould be p̃(s,ϕ), not p̃(ω,s). p̃(s,π*m/M), not p̃(π*m/M,s) imgur.com/a/qsZwJdI (corrected proof as an image)

@matthewjames7513 7 ай бұрын

@@Kolibril Thanks for your quick reply! Although I still think the very last line is wrong. Since s = s(phi) = xcos(phi) + ysin(phi), this needs to also be in the discrete sum. Right?

@user-vl6bt6st4x 4 ай бұрын

Wait. When we have circle (2:50) and rectangle (3:50) as objects in a sinogram we get some shit picture. But when we have Pi letter object we get an image of Pi (4:10 ). Did I miss something? And what is the difference between what we do here (4:10) and there (2:40) ?

@MyDum 10 ай бұрын

Can you share code of this video, please?

@71sephiroth 3 жыл бұрын

nice! but... why do we use integration? (6:15 and onward)

@Kolibril 2 жыл бұрын

Imagine a snail race. And now imagine the "pi" symbol would be made out of salad. On their paths, each snail would eat all the salad that it comes across. When the snails reach the finish line, you see how much weight they gained, but you can not see anymore, where along their lines the salad was. Similar, the integration "collects" all the intensities along the u-axis (as shown at 6:59). Note, that the function p(s,ϕ) is not u dependent. Because we integrate over "du", all points along the u-axis are projected.

@71sephiroth 2 жыл бұрын

@@Kolibril Thank you!

@byG027 Жыл бұрын

@@Kolibril Shouldn't the integration showed at 6:37 be over ds instead?

@atlasxatlas 2 жыл бұрын

Why no english subtitles? Why yt's auto generated subtitles in German?! I'm so confused

@Kolibril 2 жыл бұрын

I just changed the video settings, now there should be English subtitles as well.

@moesterer 3 жыл бұрын

Sequel: diffraction tomography?

@Kolibril 2 жыл бұрын

I already have the script for another sequel "Artifacts in Tomography" : nosy image, moving sample, misaligned rotation axis and missing wedge. But making these animations takes really a lot of time. Maybe sometime in the future.

@fuckyoutubengoogle2 2 жыл бұрын

4:20 frequencies of what?

@fuckyoutubengoogle2 2 жыл бұрын

Explanation is out of order.

@aymaneelfahsi8048 2 жыл бұрын

can i contact you. Needa help for my research

@simonmaverick9201 Жыл бұрын

I have got a headache...

@alexkart9239 2 жыл бұрын

4:30 poor explanation. there is no any info about this "frequency" and wtf is these -150~150 values. i cant see anything negative on the picture, i see only positive brightness from 0.0 (black) to 1.0 (white)