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.
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!
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.
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.
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!
respected sir there is a point in the syllabus that understand how the image of 8-voxel can be developed using CT scan You explained 4-voxel, please explain it
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.
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!
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.
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.
Does not work with 4x4 grid. The sum of right side attenuation numbers is larger than 60% of final grids values. Therefore subtraction gives me negative atenuation values. But one thing is kind a working -> values which are the largest in my case are still positive after subtraction.
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??
The two persons who invented this method receives a nobel prize in Physiology or Medicine in 1979 , for this invention. They were : Sir Godfrey Hounsfield , and Allan MacLeod Cormack .
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 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
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?
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?
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
![Дон ДОН, Алаудинов и СБЕЖАВШИЕ из под Курска ахматовцы 😁 [Пародия]](http://i.ytimg.com/vi/dEfCf5IK26Q/mqdefault.jpg)
2021 and still the best video out there about CT calculation.
Respect!
After 11 years, 2023, this still helps people, thanks mate.
I have the same washing machine as you bro, according to the subtle background noise haha
Lmao
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
I honestly don’t know how to thank you enough. Your videos have been so easy to follow and understand. God bless you!!!
I'm learning this in my third year physics degree and you have explained it way better than my professor
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.
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)
Hi. Thanks for comments. Have you seen my 2 videos on Electromagnetism?
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!
I wanna cry, I was so stressed about this (cause my physics prof sucks) but you made it so easy! Thank you so much!!
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.
Perfect and clear explanation. By far the best one! Thank you so much for sharing.
I love the way you broke this down. Very easy to understand the basic principles.
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
Education never gets old 11yrs ago I was in grade 3 but today you helped sir in my A Level thank you
After all these years, it helped me to clear my doubts. Thank you!
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.
The algorithm is fantastic! Thanks for explaining this!
Realyyyy very veryyyyyy much thank you sir for this wonderful explanation thank you so much...... no one literally no one explained like you
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
The best explanation I have ever seen kudos to your dedication
Thank you so much for making this video, it wasn't completely clear to me before but now I fully understand!
very good presentation it easy, simple and clear..... thank you
fantastic, I never thought it was so simple, in fact I always thought it was magic!
You are indeed a legend,boss
thank you DrPhysicsA.... no one could've explained that any better
Awesome video, gonna use the example on my oral radiology test next week.
0:25 its Dota
Thanks for this. My Year 13's and me are very grateful!!
2020 and this video is still amazingly useful
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.
Excellent tutorial - Better than my Imperial College lecturers.
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?
super clear cut explanation. thank you
Thank you very much, I've laways searched for a physics explaination like this!
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 :)
Fantastic video. Thank you sir. Your students are very fortunate to have a great teacher. Happy new year.
Now I know way more than I need to. Thank you!
Thank you so much! such a clear explanation!
That's awesome it really helps you understand stuff like this better
whoever came up with this algorithm was a smart cookie
Thank you for explaining!
Awesome vid. The first step is the Radon transform
respected sir there is a point in the syllabus that understand how the image of 8-voxel can be developed using CT scan
You explained 4-voxel, please explain it
Thank you for sharing your knowledge. I appreciate it!
wow thanks alot sir. You even explain better than my college teacher! :D
old is gold
Wonderfullllllllllll physicssss lovelyyy explanation sir
First class explaination!
Thank you!
ima need this with a 3x3, have never been asked to do one below a 3x3.
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
Y it's 16 to subtract and 3 to divide??
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?
Great way of explaining!
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!
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.
at 0:30 is that the dota 2 logo? hahaha
hahaha :DDD
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.
Great! explained very well. Thanks
This was really helpful. Thanks!
wow so ct is using x ray
and it builds a 3d image
that is so interesting
thanks !
Does not work with 4x4 grid. The sum of right side attenuation numbers is larger than 60% of final grids values. Therefore subtraction gives me negative atenuation values. But one thing is kind a working -> values which are the largest in my case are still positive after subtraction.
Helps a lot man thank you ❤️
thanks for sharing such helpful video ! Much appreciated :)
You are brilliant. Thank you!
n u r beautiful,thnk u !
Thank you! Great revision video. ^_^
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??
Who came up with the formula?
awesome!! who came with the mathematical model , its genius..
The two persons who invented this method receives a nobel prize in Physiology or Medicine in 1979 , for this invention.
They were : Sir Godfrey Hounsfield , and Allan MacLeod Cormack .
Please explain Iterative reconstruction
Why is the background reading the sum of attenuation for one scan??? And why is everything divided by 3 in the final step?????
seems like it would be much more fun to rotate the person 🤣 thank you and great info...
Thank You So Much
thank you for these information
nice lecture
Really appreciable...thank you Sir could you please mention the name of this book in which this method is given please Sir ... Humble request...
Very good video! Thank you very much :D
Does contrast between the tissues depends on the difference in average atomic number? (For CT)
I never knew about the initial subtraction part after accumulating the values in the voxels. I assumed you just compute the average (ie div by 4).
Hi, one of the question mentioned "background reading". May I know what that is?
The sum of the densities
Amazing !! :)))
Amazing!!!
very helpful
Sir can u please make a video about iterative reconstruction
I don't understand why the algorithm is done? Thank you.
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!
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...
at 10:07 do we just divide by a common factor; such as for the this example the common factor was 3?
Awesome one
thanks a loooooooot, sir! you r a life saver
Does contrast between the tissues depends on the difference in average atomic number? (For CT)
thanks
THANK YOU SO MUCH!
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
thanks you sier
Thank you Dr Physics :)
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?
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
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