Some image and audio compression like PNG or FLAC no use this method but replace same data value with shorter version. Compression no equal JPEG, mp3, or ogg but can store all data exact.
Great. Thank You so much. just one thing to point out : the JPEG Compression standard used the DCT transform on the block level of an image (usually 8x8) it's based on Fourier's idea but a bit advanced in some sense that it de-correlates the input data (frequency information of pixels) to make it easier to Quantify (reduce) the higher frequencies and still get almost the same image with less volume.
Wonderful content. I think the fact that compression works depends on the fact that the Discrete Fourier Transform, and hence its inverse, are unitary operators, hence they preserve distances between vectors. If I am eliminating a little noise in a vector in the Fourier space, I get a new denoised vector whose distance to the first one is negligible, hence the distance between the original image and the the "compressed" image shall itself be negligible.
@@yuurishibuya4797 well, I have everything i need, you name it...except a job in engineering field for which I had left my previous stable-cum-peaceful job.
Great video. Very good level of explanation for educational purposes, but also for professionals. Congratulations! Looking forward for the wavelet analysis and S-transform if it possible sometime.
Likely some variation on this: black room, solid color background, special neon markers, camera behind *pane of glass,* and the picture is reversed (i.e., horizontally reflected) either before or after recording. Make sense?
@@danielsteel5251 Thanks. That explains. Sometimes he also includes his computer screen on the board. Guess there would be another projector involved. Anyways, it's really cool to see it. It looks so nice.
@@danielsteel5251 That's unlikely, since he is precisely pointing to the right codes and images while he demonstrates the code implementations. It's gonna be really difficult to pretend something exists there while explaining very accurately and add the actual stuffs later.
@@xiezhang1741 His screen is being recorded and he can see it in a monitor while recording as he can be seen looking off camera into a monitor and it is then later edited in (and out) in post-production (post/post-prod) as necessary. If I'm wrong feel free to offer an alternate theory, but this seems the most likely and is what I would do.
So after thresholding do the large-amplitude components tend to sit on a compactly supported set as you kind of suggest in your sketches, or are they scattered all over Fourier space? Thanks for the great lectures!
They would be pretty heavily localized, but depend a lot from image to image. A picture of a white square on a black background would look kind of like a puddle after a rock was dropped in, with circles emmanating from the center.
you could design an image to scatter over the fourier space, but regardless, the inverse operation to form the image only keeps the coefficients needed for the higher values, aka, you store their coordinates from the fourier space although one could totally design a way to store the coefficients that best fit the described set in the sketch, but you would need to study a very particular use case to apply it (like maybe how the fourier space looks on cartoony images or just compressing for text)
Professor can you please explain difference between and FFT and DCT, why DCT is used in JPEG Compression and can you please explain python code for JPEG COMPRESSION . Thank you.
Hi, Great video as usual. Lately I have heard of Haline which is used in image processing and it is 100 times faster than Matlab, I wonder if Haline using another algorithm differs from that of FFT, and another question is how we can return the signal word to the image(image=signal!!)?
the fast fourier transform is a discrete transform meaning that the values it receives are in a discrete domain, it's not a continuous signal. it's extensively used in computing because of the discrete nature of digital stuff like audio and video
The middle is low frequency waves. The very center is what's called the DC term, which is the overall average brightness of the image. The edges would be terms that are alternating every pixel, so you would only see those if you did something like took a picture of a screen door.
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Some image and audio compression like PNG or FLAC no use this method but replace same data value with shorter version. Compression no equal JPEG, mp3, or ogg but can store all data exact.
Great. Thank You so much.
just one thing to point out : the JPEG Compression standard used the DCT transform on the block level of an image (usually 8x8) it's based on Fourier's idea but a bit advanced in some sense that it de-correlates the input data (frequency information of pixels) to make it easier to Quantify (reduce) the higher frequencies and still get almost the same image with less volume.
yes was just about to type this. @steve maybe you should mention it
Excellent video. It was especially interesting to understand image compression in the context of Parseval's Theorem.
Wonderful content.
I think the fact that compression works depends on the fact that the Discrete Fourier Transform, and hence its inverse, are unitary operators, hence they preserve distances between vectors. If I am eliminating a little noise in a vector in the Fourier space, I get a new denoised vector whose distance to the first one is negligible, hence the distance between the original image and the the "compressed" image shall itself be negligible.
Great Steve! There was the Parsevals theorem related to FFT we talked about a few videos ago. Very nice example and explanation!!!
wow steve all your videos are way too great I'm buying your book as soon as I can.
Very clear and easy to understand!
It's 2 AM in New Delhi and you have made my day. Thank you Steve!
Get a life!
@@yuurishibuya4797 well, I have everything i need, you name it...except a job in engineering field for which I had left my previous stable-cum-peaceful job.
Brilliant video, very concise, and clear.
Would be nice to see effects of various animations on the FFT.
Just do it yourself in python.
This video have FFT history and animación:
m.ua-cam.com/video/nmgFG7PUHfo/v-deo.html
Great Video. Very good explanation. it's clear my concept about wavelet transformation.
Great video. Very good level of explanation for educational purposes, but also for professionals. Congratulations! Looking forward for the wavelet analysis and S-transform if it possible sometime.
Hi Professor Steve, Thanks.....
Thank you sir
This was really good. Great job.
أستاذ رائع ومميّز.... Great Video
This is a great video.
might be a bit advanced but the bit I'm interested in is zero-padding. thanks great vids as always
Great video
Thanks!
I am curious how the "transparent" board works.
Likely some variation on this: black room, solid color background, special neon markers, camera behind *pane of glass,* and the picture is reversed (i.e., horizontally reflected) either before or after recording.
Make sense?
@@danielsteel5251 Thanks. That explains. Sometimes he also includes his computer screen on the board. Guess there would be another projector involved. Anyways, it's really cool to see it. It looks so nice.
@@xiezhang1741 _... Guess there would be another projector involved. ..._
I'd guess that it was video editing, after the fact; not a projector.
@@danielsteel5251 That's unlikely, since he is precisely pointing to the right codes and images while he demonstrates the code implementations. It's gonna be really difficult to pretend something exists there while explaining very accurately and add the actual stuffs later.
@@xiezhang1741 His screen is being recorded and he can see it in a monitor while recording as he can be seen looking off camera into a monitor and it is then later edited in (and out) in post-production (post/post-prod) as necessary. If I'm wrong feel free to offer an alternate theory, but this seems the most likely and is what I would do.
Another great video and well explained. Doesn't JPEG use the DCT instead of the full FFT?
Yes JPEG uses the DCT instead. The energy compaction of the DCT is much better than the Fourier Transform.
JPEG uses the DCT with blocks of pixels instead of the whole image at once. That's why badly jpg'd images have the odd blocky appearance.
great video, thanks
what is the range of frequencies used for the FFT ?
So after thresholding do the large-amplitude components tend to sit on a compactly supported set as you kind of suggest in your sketches, or are they scattered all over Fourier space? Thanks for the great lectures!
They would be pretty heavily localized, but depend a lot from image to image. A picture of a white square on a black background would look kind of like a puddle after a rock was dropped in, with circles emmanating from the center.
@@Miyelsh thanks!
you could design an image to scatter over the fourier space, but regardless, the inverse operation to form the image only keeps the coefficients needed for the higher values, aka, you store their coordinates from the fourier space
although one could totally design a way to store the coefficients that best fit the described set in the sketch, but you would need to study a very particular use case to apply it (like maybe how the fourier space looks on cartoony images or just compressing for text)
I'm excited to learn more about this!
Professor can you please explain difference between and FFT and DCT, why DCT is used in JPEG Compression and can you please explain python code for JPEG COMPRESSION . Thank you.
Hi, Great video as usual. Lately I have heard of Haline which is used in image processing and it is 100 times faster than Matlab, I wonder if Haline using another algorithm differs from that of FFT, and another question is how we can return the signal word to the image(image=signal!!)?
an image is simply a set of points(x,y) which they could be plotted like a signal
the fast fourier transform is a discrete transform meaning that the values it receives are in a discrete domain, it's not a continuous signal.
it's extensively used in computing because of the discrete nature of digital stuff like audio and video
Thanks good
Great. Thank you very much sir.
Question. In the middle of fft2 image
There are low frequensy sinewaves, or there are high amplitude sinewaves?
The middle is low frequency waves. The very center is what's called the DC term, which is the overall average brightness of the image. The edges would be terms that are alternating every pixel, so you would only see those if you did something like took a picture of a screen door.
7:05 this doesn't have to be true but this is true!! Lol 🤣
I'm here first... Awesome video... 😁
The board doesnt really help with visualizing the process. I wish there were better graphics.
Peppa!!! What are you doing in Steve's video??
hello >>>thank you for this فhe interesting lecture. Can I communicate with you by email about the same topic