What a very clever presentation - so often they are fudged and nobody, maybe including the presenter, comes out understanding. Thank you for this - and well done!
To those of you who say the algorithm doesn't work for anything more than a 2x2 array: For this size, only 4 total scans are necessary. A larger array will require more scans at differing angles to get a better picture of the object being scanned.
our teacher gave us a problem for 4x4 array and l don't have any idea how to solve that. He didn't tell us anything, just gave us this video and now we have to solve it.
Doing an offset (subtracting 16) at the end is actually here a way of doing a high pass filter. Since there are only two possible frequencies for each axis, then subtracting lowers DC (frequency 0) which makes the other frequency (nyquist) relatively higher. Only works in this particular case.
Our college teacher made us to watch this video. I became big fan of Dr.Physics. you're making me love physics. Thanks indeed for your help sir. Could you do more A2 past paper questions on your channel please. Thanks again. And I would much appriciate you if you could do a video for course work preparation.
Ah yes I've explored your page thank you very much. Understanding is the key, I think I'll have a greater chance of getting an A in the summer because of your helpful videos!
WAJEIH RAJPOOT, fanned out x-ray beam is used to gather full slice data at particular moment of exposure for greater resolution. First xray machines in fact used single focused beam to gather data, but as computer data processing capabilities rise, it was possible to use fan-type beam and use detector array insted of just one.
Hey, Thanks for the clear and concise explanation. I have 2 queries. 1. Are the computed voxel values directly interpretated as image pixel intensities which is what we see as the CT image? 2. As per my understanding, the detector will record the intensities of the received beam whereas the numbers that you mention in the voxel's are attenuation coefficients. So, more the attenuation coefficient or a voxel lesser will be the intensity recorded. What exactly do the summed values 7, 9, etc. represent? Are they the attenuation coefficients or the intensities recorded by the detector? Thanks in advance!
I'm not sure which part of the video you are referring to, but I suspect I mean the ability and extent of the Xray to penetrate the material through which it is passing.
Any processor that can do floating point operations will do. But if you want fast results, you need a decent processor. Any entry-level processor and some nice memory would work quite well.
Hello thank you! And how is the final results of the matrix transformed in an image like the black pages the laboratories give you as fault ? Thank you
I'm puzzled by the apparent additive nature of the voxels rather than multiplicative. If I shine a light through a two filters that individually block out 50% of the light, I'd expect that combining the two would block out 1 - .5*.5 = 75% of the light, not 100%. Do XRays operate differently, or is the percentage of X rays blocked so small that using addition is an acceptable approximation for multiplication?
What do you call this kind of CT reconstruction?? Because we have different kinds of CT reconstruction - Back projection, Iterative, and Analytic Method. What is this kind?
Thx for the awesome vid, but I'm not sure what method this is for image reconstruction? Filtered Back Projection (FBP) or the iterative method? It's helps me a lot if you or someone knew! :)
Hi, I think more precisely it is the simple back projection method. The filtered method applies some form of filtering (such as convolution) on the projected profiles before it is back projected. Correct me if i'm wrong :) Cheers
hbale18 The idea is to substract the whole atenuation of the initial body (in this case the initial table). Which is 16 in every emission direction: 7+9=16, 4+11+1=16, 4+12=16, 3+5+8=16...
Hello Doctor Physics, thank you for the fantastic videos. Is there any chance you would be able to make a video on Magnetic Fields? or recommend any links or other videos?
I still can't understand why you did the sum only for three projection(why did you left remaining projection) and dividing your fellow answer with three? CT scan doesn't stop with scanning three projection right?? it scans the whole body,it means it pixel value changes throughout the 360° right? so you can't divide it with three..will you divide it with 6??
+Shimshon Winograd No. The algorithm gets much more complicated which is why computers are needed. If you do the 2x2 with a,b,c and d you will see why this particular algorithm works.
Great video. But can you please *FAST* explain if you got a 4x4 I have followed the first steps. But when I subtract the combined of the first "scanning" from the calculated values, some become negative? What am I doing wrong?
Christian Engkebølle I appreciate this is way too late for you, but someone else might need to know. I suspect that you're still only doing 4 scans. To solve for more voxels you're going to need more information. I've not worked through the maths, but my intuition is that you need at least as many scans as you have voxels. I think that if you were to simulate doing 16 scans, all at different angles, then you'd be able to solve for 16 voxels.
this algorithm works fine for this particular 2x2 matrix but if you scale it up to 3x3 using the numbers 1-9 it fails resulting in negative intensities?
Very nice description. But I think you need to emphasize that you solver the *forward* problem. That is, given the voxel absorption values, find the absorptions of the 4 beams. Actually going into hospital and getting a CT scan and reconstructing the voxel values from it is the *inverse* problem. Is the inverse solution unique? Often they are not.
2021 and still the best video out there about CT calculation.
Respect!
This explanation is simply the best one i have seen. you're doing a great job in explaining all these things. you are truly a life-saver
After 11 years, 2023, this still helps people, thanks mate.
I'm learning this in my third year physics degree and you have explained it way better than my professor
I honestly don’t know how to thank you enough. Your videos have been so easy to follow and understand. God bless you!!!
I have the same washing machine as you bro, according to the subtle background noise haha
Lmao
What a very clever presentation - so often they are fudged and nobody, maybe including the presenter, comes out understanding. Thank you for this - and well done!
Indeed there is. Well spotted. On other videos you can also hear my dog bark and the kitchen clock which has a cow instead of a cuckoo.
Does contrast between the tissues depends on the difference in average atomic number? (For CT)
An awesome explanation. I could not find many videos and I am glad I spent my time on this video. You just made it so simple.
I wanna cry, I was so stressed about this (cause my physics prof sucks) but you made it so easy! Thank you so much!!
I love the way you broke this down. Very easy to understand the basic principles.
After all these years, it helped me to clear my doubts. Thank you!
Education never gets old 11yrs ago I was in grade 3 but today you helped sir in my A Level thank you
To those of you who say the algorithm doesn't work for anything more than a 2x2 array: For this size, only 4 total scans are necessary. A larger array will require more scans at differing angles to get a better picture of the object being scanned.
But you also have to replace subtracting by 16 with proper ramp filtering.
णत़ो
our teacher gave us a problem for 4x4 array and l don't have any idea how to solve that. He didn't tell us anything, just gave us this video and now we have to solve it.
Perfect and clear explanation. By far the best one! Thank you so much for sharing.
The algorithm is fantastic! Thanks for explaining this!
The best explanation I have ever seen kudos to your dedication
This is such a good explanation. This is exactly what I was looking for. Thanks a lot!
A Vary simple easy to understand video about the basic tenets of CT scanning, Very very good
Realyyyy very veryyyyyy much thank you sir for this wonderful explanation thank you so much...... no one literally no one explained like you
Thank you so much for making this video, it wasn't completely clear to me before but now I fully understand!
Doing an offset (subtracting 16) at the end is actually here a way of doing a high pass filter. Since there are only two possible frequencies for each axis, then subtracting lowers DC (frequency 0) which makes the other frequency (nyquist) relatively higher. Only works in this particular case.
Hi. Thanks for comments. Have you seen my 2 videos on Electromagnetism?
Our college teacher made us to watch this video.
I became big fan of Dr.Physics. you're making me love physics. Thanks indeed for your help sir. Could you do more A2 past paper questions on your channel please. Thanks again. And I would much appriciate you if you could do a video for course work preparation.
I finally understand why my physics lecturer is a pure rubbish after watching this 👍
My teacher literally just plays this video in class as if it was 'his' lecture
fantastic, I never thought it was so simple, in fact I always thought it was magic!
thank you DrPhysicsA.... no one could've explained that any better
Thanks for this. My Year 13's and me are very grateful!!
i just did this today at school.thank you soo much i understand it way better now!
keep up the good work,you got another sub :)
0:25 its Dota
Really appreciated ❤❤
You are indeed a legend,boss
very good presentation it easy, simple and clear..... thank you
Awesome video, gonna use the example on my oral radiology test next week.
Ah yes I've explored your page thank you very much. Understanding is the key, I think I'll have a greater chance of getting an A in the summer because of your helpful videos!
Did u get the A?
Excellent tutorial - Better than my Imperial College lecturers.
2020 and this video is still amazingly useful
Fantastic video. Thank you sir. Your students are very fortunate to have a great teacher. Happy new year.
Thank you very much, I've laways searched for a physics explaination like this!
Now I know way more than I need to. Thank you!
That's awesome it really helps you understand stuff like this better
WAJEIH RAJPOOT, fanned out x-ray beam is used to gather full slice data at particular moment of exposure for greater resolution. First xray machines in fact used single focused beam to gather data, but as computer data processing capabilities rise, it was possible to use fan-type beam and use detector array insted of just one.
Thank you for sharing your knowledge. I appreciate it!
wow thanks alot sir. You even explain better than my college teacher! :D
Thanku so much for explaining it really help me in radiology subject
Sir, I don't understand why a deduction of 2X2 box with 7 7 9 9 is made? Is there a more complicated explanation to this?
awsum.... but i have a question why cat-scanner shows "fanned-out" array of x-ray beams....directed through patients?
whoever came up with this algorithm was a smart cookie
Awesome vid. The first step is the Radon transform
First class explaination!
Thank you!
Hey,
Thanks for the clear and concise explanation.
I have 2 queries.
1. Are the computed voxel values directly interpretated as image pixel intensities which is what we see as the CT image?
2. As per my understanding, the detector will record the intensities of the received beam whereas the numbers that you mention in the voxel's are attenuation coefficients. So, more the attenuation coefficient or a voxel lesser will be the intensity recorded. What exactly do the summed values 7, 9, etc. represent? Are they the attenuation coefficients or the intensities recorded by the detector?
Thanks in advance!
super clear cut explanation. thank you
I'm not sure which part of the video you are referring to, but I suspect I mean the ability and extent of the Xray to penetrate the material through which it is passing.
DrPhysicsA somya
What kind of computer of processor would a CT scanner use to add all this up? So much computation needed for just one voxel, insane !
Any processor that can do floating point operations will do. But if you want fast results, you need a decent processor. Any entry-level processor and some nice memory would work quite well.
Thank you so much! such a clear explanation!
at 10:07 do we just divide by a common factor; such as for the this example the common factor was 3?
Hi, one of the question mentioned "background reading". May I know what that is?
The sum of the densities
Hello thank you! And how is the final results of the matrix transformed in an image like the black pages the laboratories give you as fault ? Thank you
Nice explanation, thank you! One question: how to get from voxels to pixels to produce the image of that slice?
Does contrast between the tissues depends on the difference in average atomic number? (For CT)
Thank you very much, I've laways searched for a physics explaination like this! is there an algoritm for more block greater than 2x2? thanks again!
I'm puzzled by the apparent additive nature of the voxels rather than multiplicative. If I shine a light through a two filters that individually block out 50% of the light, I'd expect that combining the two would block out 1 - .5*.5 = 75% of the light, not 100%. Do XRays operate differently, or is the percentage of X rays blocked so small that using addition is an acceptable approximation for multiplication?
these numbers are in a logarithmic scale, adding logarithms of numbers is the same as multiplying the numbers
Is that an simplification for the filtered back projection (FBR)?
Great way of explaining!
Thank you.
What do you call this kind of CT reconstruction?? Because we have different kinds of CT reconstruction - Back projection, Iterative, and Analytic Method. What is this kind?
Is there a washing maschine running in the background?
Thx for the awesome vid, but I'm not sure what method this is for image reconstruction? Filtered Back Projection (FBP) or the iterative method? It's helps me a lot if you or someone knew! :)
DeltaSlayer Hi, It's the Filtered Back Projection (FBP) method!
Hi, I think more precisely it is the simple back projection method. The filtered method applies some form of filtering (such as convolution) on the projected profiles before it is back projected. Correct me if i'm wrong :) Cheers
Thanks for the simple explanation. What is the reasoning behind subtracting the sum total of 7 and 9 from the table before the final result?
Can you remind me the time on the video at which this occurs please?
hbale18 The idea is to substract the whole atenuation of the initial body (in this case the initial table). Which is 16 in every emission direction: 7+9=16, 4+11+1=16, 4+12=16, 3+5+8=16...
Hello Doctor Physics, thank you for the fantastic videos.
Is there any chance you would be able to make a video on Magnetic Fields? or recommend any links or other videos?
Machismo which method is this?
sir what do you mean by when you said 'INTENSITY' of the x ray??
Does contrast between the tissues depends on the difference in average atomic number? (For CT)
I still can't understand why you did the sum only for three projection(why did you left remaining projection) and dividing your fellow answer with three? CT scan doesn't stop with scanning three projection right?? it scans the whole body,it means it pixel value changes throughout the 360° right? so you can't divide it with three..will you divide it with 6??
Does this algorithm should work for tables bigger than 2X2?
I couldn't make it work...
+Shimshon Winograd No. The algorithm gets much more complicated which is why computers are needed. If you do the 2x2 with a,b,c and d you will see why this particular algorithm works.
Is this an iterative method of image reconstruction?
Yes sunny
Thank you for explaining!
how did you do it can you share with me , thank you
Really appreciable...thank you Sir could you please mention the name of this book in which this method is given please Sir ... Humble request...
Great! explained very well. Thanks
Great video. But can you please *FAST* explain if you got a 4x4 I have followed the first steps. But when I subtract the combined of the first "scanning" from the calculated values, some become negative? What am I doing wrong?
Christian Engkebølle I appreciate this is way too late for you, but someone else might need to know.
I suspect that you're still only doing 4 scans. To solve for more voxels you're going to need more information. I've not worked through the maths, but my intuition is that you need at least as many scans as you have voxels.
I think that if you were to simulate doing 16 scans, all at different angles, then you'd be able to solve for 16 voxels.
ima need this with a 3x3, have never been asked to do one below a 3x3.
Y it's 16 to subtract and 3 to divide??
This was really helpful. Thanks!
Helps a lot man thank you ❤️
How does this scale from a 2 by 2 to an N by N grid?
thanks for sharing such helpful video ! Much appreciated :)
You are brilliant. Thank you!
n u r beautiful,thnk u !
Why do we have to rotate it in 4 directions? can it done in any other number of directions?
DrPhysicsA, CT means Computerized axial Tomography right?or does Computed Tomography mean the same?
+Shanice Leitch (Ms. Curly) I am not too sure about the above post which is why I asked...
at 0:30 is that the dota 2 logo? hahaha
hahaha :DDD
this algorithm works fine for this particular 2x2 matrix but if you scale it up to 3x3 using the numbers 1-9 it fails resulting in negative intensities?
by the way, are you boiling water when you were doing the video?
sounded like a washing machine
Sounds like a CT scanner gantry ramping up to speed and back down!
Very nice description. But I think you need to emphasize that you solver the *forward* problem. That is, given the voxel absorption values, find the absorptions of the 4 beams. Actually going into hospital and getting a CT scan and reconstructing the voxel values from it is the *inverse* problem. Is the inverse solution unique? Often they are not.
Wonderfullllllllllll physicssss lovelyyy explanation sir
Well.... If I take a 3by 3 box then from how many angles I need to project??? Plz reply... Is there any formula for that..?
Thank you! Great revision video. ^_^
very helpful
Sir can u please make a video about iterative reconstruction
is he washing ? or is it a blender?
definitely washing
thanks a loooooooot, sir! you r a life saver
Does contrast between the tissues depends on the difference in average atomic number? (For CT)
What is the name of this method ?
Why is the background reading the sum of attenuation for one scan??? And why is everything divided by 3 in the final step?????
Who came up with the formula?
Very good video! Thank you very much :D
Does contrast between the tissues depends on the difference in average atomic number? (For CT)