Thats really great. But what exactly is f(x,y)? I understand it as an Absorption function at location x and y of the Objekt, related to the density and content of the object
@Abbasali-st3qb Жыл бұрын
Can you send me this presentation?
@NoahSpurrier Жыл бұрын
Which video discusses Filtered Back Projection?
@poppetrurazvan3900 Жыл бұрын
Hi. Try to do some ultrasonic solution. It will work 100 %. Thanks.
@scrumptious9673 Жыл бұрын
Fantastic work
@ahmeda.al-tameemi8001 Жыл бұрын
Hello dear, very interesting course my I know what i have to do with Macbook pro ?
@KrishnaKumar-dx7si Жыл бұрын
Super explain 🙏
@naukadladzieci Жыл бұрын
Each point on the 'object domain'? In English world no one uses that complex terminology to explain relatively simple things.
@user-bc9kk3kb8u Жыл бұрын
Saya tidak percaya ia boleh menjadi sebaik ini
@jamesdavid52242 жыл бұрын
I'm doing my final year project on this and it has help me so much in understanding what my equations are actually doing. Thank you!!!!!
@radtechstudybuddy2 жыл бұрын
Good video
@Davifornication2 жыл бұрын
Thanks for this explenation. I have a question: Is it possible to perform a reconstruction using existing .TIF files (radiographs) from a real scanner with the astra toolbox? Thank you
@markmcla2 жыл бұрын
I really like the part of your video that mentions that a delta function in the (x,y) plane is transformed to a sine wave in the (t,theta) plane. Does frequency of the sine wave provide information about the position of the delta function? Thanks for providing me with a starting point for how to make sense of this amazing transform!
@AGLubang Жыл бұрын
No, because the scanning lasts one cycle, thus you only see one sine period. What provides info about the position of delta function would be 1) an angle of detector function where you can find the dot. This angle, along with the "t" where the dot is located, can provide the "actual" angle of the delta with respect to the coordinate system. We still lack the distance of the delta from the origin, so we also need 2) the amplitude of the sine wave. If your range of "t" results in a sine wave that doesn't have both the crest and through of the wave (similar to what is called "clipping" by audio/EE people), then the distance of the delta to origin is already outside the range of "t". Hope this helps. Note that t=0 means that the ray starting from the detector line function (the p_theta(t)) passes though the origin, so the red line in 0:38 IS t=0. Many t values correspond to the dashed red line rays in 1:23. So the "outside the range of "t"" I wrote above means that the location of the delta *can be* "out of range" of the dashed red line rays on some internal values of theta.
@markmcla Жыл бұрын
@@AGLubang Yes, that's very helpful! Thank you for spending the time to answer my question. My intuition is that since the Radon transform is a linear transform, and since a delta function is transformed into an orthogonal function (like a sine wave), then you can preserve the information about the position of a delta function. The original object that is scanned can be thought of as a superposition of many delta functions. So the inverse transform is possible. -These CT scans look like magic to me. 🙂
@AGLubang Жыл бұрын
@@markmcla Yes, that's correct. Sorry I made a mistake about the "distance of the delta to origin". See my edit. I think I still cannot fully explain it in words only.
@WillBilliam2 жыл бұрын
Oh this was just perfect thank you!
@manik51452 жыл бұрын
Clean and nice explanation
@praveendissanayaka18252 жыл бұрын
Very good
@markmcla2 жыл бұрын
Thanks for making this wonderful video. The Fourier Slice Theorem is astounding! You have provided a nice conceptual guide for me to work out the details for myself. Thanks again!
@14959787072 жыл бұрын
Good vid, but I’ll say that it would improve your videos if you could remove the reverb. Clear crisp audio is most pleasant to listen to technical stuff with
@malekalabed40052 жыл бұрын
Thank you is not enough for this amazing elaboration !
@aliibrahem36912 жыл бұрын
Great content 👍 ThX
@Caspar__2 жыл бұрын
Wow, I did not know about the algebraic approach. Really cool.
@chinhnguyen52752 жыл бұрын
Some segments in the video are stamped not adjacent to each other
@fahimafyzee47202 жыл бұрын
Thank you so much!!! Really easy to understand the basic concept and idea behind it.
@christerranaldo9062 жыл бұрын
Such an intuitive explanation. My teacher spends 2 hours explaining it and I still didn't get it!
@mauricioalbertoledesmavill96552 жыл бұрын
Excelente video! Muchas gracias. Do You now why a bullet in the Brain appears very bright and provoque a Ring ring in the imagen? I am currently working on CT with brain bullets impact and I am having problems with this? Thanks
@scrumptious9673 Жыл бұрын
Metal artefacts? Have a look at Metal Artefact Reduction techniques for CT
@christerranaldo9062 жыл бұрын
Thanks! Very clearly explained. I was only familair with 1D fourier so it seemed a little abstract but now I understand it.
@FTOedu2 жыл бұрын
Great series!! The video description does not have the links to the Fourier transformations has promised in the video.
@hossein22042 жыл бұрын
Very well explained!
@chokfrancisco20083 жыл бұрын
Are we measuring the intensity of radiation from the projector to the detector to interpret the density of the object?
@limebasil89393 жыл бұрын
뭐라는거야 씹;;
@chaoyinggu7473 жыл бұрын
Nice video! clear and easy
@yonatan3653 жыл бұрын
Great explanation, thanks!
@guilhermesilveira52543 жыл бұрын
CT is an important technology in medicine.
@TheLazyEngineer3 жыл бұрын
Is the significant increase in time needed for each projection when using the Strip kernel really that big of a deal? Once the detectors pick up the attenuated beams, storing that data should be easy. The computations (which from my understanding is really just a post processing of the collected detector readings) can come later using modern day computers. I'm picturing a 512 X 512 X 512 voxel image. Thats a lot of voxels, but with a super computer I expect it to be doable. Maybe I dont have a good idea of the scale of the computations. Great videos so far!
@raichu56k2 жыл бұрын
yo i've seen one of your videos before, good stuff
@amirenrique45743 жыл бұрын
please tell us about maximum constraint.. how about that ?
@drvanon3 жыл бұрын
Seriously this is gold.
@ayushikeshare3983 жыл бұрын
Very well explained 👍
@leahstella7853 жыл бұрын
Do you have any tutorials/material on how to change the ray order in ART/SART in python? I have been struggling to code it myself as I am quite new
@ubermensch54723 жыл бұрын
0:49 ok, you lost me already
@aliabrar92284 жыл бұрын
this is amazing video, but anyone can tell me that whats the difference back projection and forward projection? Please give me answer if you know ?
@colanuss49854 жыл бұрын
Great series, please continue elaborating on these topics. The precision and destilled visualization is better then every book I read about projection reconstruction.
@sleepygrumpy4 жыл бұрын
Amazing presentation --> automatic follow
@junkLAVENDER4 жыл бұрын
can you or anyone do tutorial on linear back projection please...
@laurensgoyvaerts84804 жыл бұрын
How does the equation of the points on L hold, for the figure that is being shown?
@AGLubang Жыл бұрын
It is not quite explained, but "x cos(theta) + y sin(theta) = t" can be derived as an equation of a line using trigonometry, with theta being the angle with respect to the y-axis (as shown in the figure), and "t" being the (perpendicular) distance of that line to the origin (0,0). I am sorry this is quite difficult without a visualization. In the figure, one could say that t = 0 there because the line crosses the origin, and change the value of "t" means moving the red line "up" or "down" while still parallel to the red line.
Пікірлер
Thanks for tthis video
This word is used in my dental hygienist class
Brief and clear. Thanks a lot! :)
Thats really great. But what exactly is f(x,y)? I understand it as an Absorption function at location x and y of the Objekt, related to the density and content of the object
Can you send me this presentation?
Which video discusses Filtered Back Projection?
Hi. Try to do some ultrasonic solution. It will work 100 %. Thanks.
Fantastic work
Hello dear, very interesting course my I know what i have to do with Macbook pro ?
Super explain 🙏
Each point on the 'object domain'? In English world no one uses that complex terminology to explain relatively simple things.
Saya tidak percaya ia boleh menjadi sebaik ini
I'm doing my final year project on this and it has help me so much in understanding what my equations are actually doing. Thank you!!!!!
Good video
Thanks for this explenation. I have a question: Is it possible to perform a reconstruction using existing .TIF files (radiographs) from a real scanner with the astra toolbox? Thank you
I really like the part of your video that mentions that a delta function in the (x,y) plane is transformed to a sine wave in the (t,theta) plane. Does frequency of the sine wave provide information about the position of the delta function? Thanks for providing me with a starting point for how to make sense of this amazing transform!
No, because the scanning lasts one cycle, thus you only see one sine period. What provides info about the position of delta function would be 1) an angle of detector function where you can find the dot. This angle, along with the "t" where the dot is located, can provide the "actual" angle of the delta with respect to the coordinate system. We still lack the distance of the delta from the origin, so we also need 2) the amplitude of the sine wave. If your range of "t" results in a sine wave that doesn't have both the crest and through of the wave (similar to what is called "clipping" by audio/EE people), then the distance of the delta to origin is already outside the range of "t". Hope this helps. Note that t=0 means that the ray starting from the detector line function (the p_theta(t)) passes though the origin, so the red line in 0:38 IS t=0. Many t values correspond to the dashed red line rays in 1:23. So the "outside the range of "t"" I wrote above means that the location of the delta *can be* "out of range" of the dashed red line rays on some internal values of theta.
@@AGLubang Yes, that's very helpful! Thank you for spending the time to answer my question. My intuition is that since the Radon transform is a linear transform, and since a delta function is transformed into an orthogonal function (like a sine wave), then you can preserve the information about the position of a delta function. The original object that is scanned can be thought of as a superposition of many delta functions. So the inverse transform is possible. -These CT scans look like magic to me. 🙂
@@markmcla Yes, that's correct. Sorry I made a mistake about the "distance of the delta to origin". See my edit. I think I still cannot fully explain it in words only.
Oh this was just perfect thank you!
Clean and nice explanation
Very good
Thanks for making this wonderful video. The Fourier Slice Theorem is astounding! You have provided a nice conceptual guide for me to work out the details for myself. Thanks again!
Good vid, but I’ll say that it would improve your videos if you could remove the reverb. Clear crisp audio is most pleasant to listen to technical stuff with
Thank you is not enough for this amazing elaboration !
Great content 👍 ThX
Wow, I did not know about the algebraic approach. Really cool.
Some segments in the video are stamped not adjacent to each other
Thank you so much!!! Really easy to understand the basic concept and idea behind it.
Such an intuitive explanation. My teacher spends 2 hours explaining it and I still didn't get it!
Excelente video! Muchas gracias. Do You now why a bullet in the Brain appears very bright and provoque a Ring ring in the imagen? I am currently working on CT with brain bullets impact and I am having problems with this? Thanks
Metal artefacts? Have a look at Metal Artefact Reduction techniques for CT
Thanks! Very clearly explained. I was only familair with 1D fourier so it seemed a little abstract but now I understand it.
Great series!! The video description does not have the links to the Fourier transformations has promised in the video.
Very well explained!
Are we measuring the intensity of radiation from the projector to the detector to interpret the density of the object?
뭐라는거야 씹;;
Nice video! clear and easy
Great explanation, thanks!
CT is an important technology in medicine.
Is the significant increase in time needed for each projection when using the Strip kernel really that big of a deal? Once the detectors pick up the attenuated beams, storing that data should be easy. The computations (which from my understanding is really just a post processing of the collected detector readings) can come later using modern day computers. I'm picturing a 512 X 512 X 512 voxel image. Thats a lot of voxels, but with a super computer I expect it to be doable. Maybe I dont have a good idea of the scale of the computations. Great videos so far!
yo i've seen one of your videos before, good stuff
please tell us about maximum constraint.. how about that ?
Seriously this is gold.
Very well explained 👍
Do you have any tutorials/material on how to change the ray order in ART/SART in python? I have been struggling to code it myself as I am quite new
0:49 ok, you lost me already
this is amazing video, but anyone can tell me that whats the difference back projection and forward projection? Please give me answer if you know ?
Great series, please continue elaborating on these topics. The precision and destilled visualization is better then every book I read about projection reconstruction.
Amazing presentation --> automatic follow
can you or anyone do tutorial on linear back projection please...
How does the equation of the points on L hold, for the figure that is being shown?
It is not quite explained, but "x cos(theta) + y sin(theta) = t" can be derived as an equation of a line using trigonometry, with theta being the angle with respect to the y-axis (as shown in the figure), and "t" being the (perpendicular) distance of that line to the origin (0,0). I am sorry this is quite difficult without a visualization. In the figure, one could say that t = 0 there because the line crosses the origin, and change the value of "t" means moving the red line "up" or "down" while still parallel to the red line.
We can now have greater than 128 slices.
poor. Inconsistent notation.
i love you man