7 ms·

Discrete Cosine Transform in Video Compression – Explain Like I'm Five

121 points by ponderingfish 6y ago

djmips 6y ago
If this stuff intrigues you please try out Steve Brunton's extensive set of videos on Data Science that include superb lectures on Fourier Series, the Fourier Transform and the Fast Fourier Transform with examples in Matlab and Python. Can't recommend this guy enough. https://www.youtube.com/channel/UCm5mt-A4w61lknZ9lCsZtBw https://www.youtube.com/channel/UCm5mt-A4w61lknZ9lCsZtBw
rrao84 6y ago
Fantastic explanation of transforms and the example of 20 questions and DCT totally did it for me. The rest of the explanation is hard to grok if aren't a programmer or not interested in image & video compression. YMMV
Diti 6y ago
This is DEFINITELY NOT explained like I’m five. More like late high school level (mathematical planes, frequencies) and above (matrixes). I appreciate the author’s attempt at vulgarization but the title is wrong.
- mwexler 6y ago
  Props for use of "vulgarization"; I hadn't seen this word as a noun or process before but it seems to fit nicely in context.
  - ponderingfish 6y ago
    Never seen this word before :) Simple explanation of the concept and the use of DCT though. Perhaps, written for a person who is Five times 5? :)
- LandR 6y ago
  You mean you didn't understand this when you were 5? > In simple terms, the Discrete Cosine Transform takes a set of N correlated (similar) data-points and returns N de-correlated (dis-similar) data-points (coefficients) in such a way that the energy is compacted in only a few of the coefficients M where M << N. Did you even nursery?
- olx_designer 6y ago
  Is this can be used as a feature extraction for image recognition task ? I read some time ago someone used jpeg compression as a feature extraction before DNN.
  - ponderingfish 6y ago
    Can be for sure by examining the coefficients. It's a little hard but can be a way to do feature detection in the frequency transform.
  - qayxc 6y ago
    This depends on the kind of features you're interested in. If the features lead to clustering in the frequency domain, then yes. Otherwise it'd be detrimental. Examples for features that'd work well are edges and lines. Features based on gradients wouldn't work well.
walagran 6y ago
Pretty cool! I would add Computerphile's Youtube Video as a watch after this: https://www.youtube.com/watch?v=Q2aEzeMDHMA https://www.youtube.com/watch?v=Q2aEzeMDHMA. This is a part of their 4-video series on JPEG:https://www.youtube.com/playlist?list=PLQfOC23r609kmgOr_V8sfUnr0r3pOI9gT https://www.youtube.com/playlist?list=PLQfOC23r609kmgOr_V8sf...
- djmips 6y ago
  Those are great! For a more in depth series of videos on the transforms themselves I haven't found anything better than videos from Steve Brunton. Here's a link jumping in at Fourier Series. Best set of videos I've seen on the subject. https://www.youtube.com/watch?v=MB6XGQWLV04&list=PLMrJAkhIeNNRjxJ_sMtJ02geqw_-vuB7O&index=47 https://www.youtube.com/watch?v=MB6XGQWLV04&list=PLMrJAkhIeN...
miccah 6y ago
Not DCT, but this website [1] has been on my TODO list for awhile. It explains DFT using interactive visualizations. [1] https://jackschaedler.github.io/circles-sines-signals/index.html https://jackschaedler.github.io/circles-sines-signals/index....
- ponderingfish 6y ago
  Nice .. this is definitely something to bookmark.
JackFr 6y ago
Maybe I'm dense, but I didn't find this useful at all. The author spends the bulk of the article explaining what transform means (not typically the sticking point) and then uses terms like "pixel-domain", "frequency-domain", "decorrelating", "energy compacting" without explanation or definition. The author could spend a little less time on the former and more on the latter IMHO.
- OneGuy123 6y ago
  This, it's funny how the author talks about views/transforms and all other stuff EXCEPT the actual intuition behind the DCT.
  - mrspeaker 6y ago
    It let me understand views and transforms! I've read countless articles that talk about transforms and I realized I previously didn't properly understand them until at all!
  - ponker 6y ago
    That’s because it’s the hardest thing to grok. I have two electrical engineering degrees from a highly regarded university and still don’t.
- raxxorrax 6y ago
  To be fair, the terms in literature are all over the place. image space and spectral space is what I read most often (not necessarily in English). I personally would prefer just source and target space, especially since we have imaging as an application. I think the explanation was quite good, but I implemented a DCT once as a student (with shitty code and slow as hell, don't roll your own matrix multiplication). The Wikipedia article was bad at the time, but it has really good info now. The topic can take a while to get it. I think looking at the base functions helps a lot. Every image is basically an overlap of these base functions which are each parameterized through an amplitude and phase. I transformed some images with basic shapes with Matlab until it really clicked.
  - 6y ago
ssawyer06 6y ago
Being familiar with the DCT but having no idea how to explain to a five year-old, I clicked. This does not ELI5 the DCT.
- anticristi 6y ago
  This. I'm not even sure why anyone would bother ELI5-ing the DCT with images. Here is an attempt to explain the DCT using audio: The DCT converts music into key presses on a piano. When playing back those keys on the piano, you lose the text of the music, but you sure hear the melody. There! Way more ELI5-ish.
  - ponderingfish 6y ago
    huh? if you throw away 70% of the melody, do you get back the text? If not, you haven't explained the DCT.
    - anticristi 6y ago
      In my ELI5 analogy, the DCT "throws away" the voice. You can still recognize the song.
    - Jasper_ 6y ago
      In this analogy, you are throwing away the instrumentation, like whether it was played on a piano or a tuba, but the raw melody is still there. This is the advantage of working in the frequency space. If we were in the time space, throwing away 70% of the data would throw away 70% of the melody.
      - ponderingfish 6y ago
        And a 5 year old understands instrumentation, melody, piano, and the tuba?
- Aardwolf 6y ago
  How about this analogy: You have a tap with a hot handle and a cold handle. You can make medium lukewarm water by making hot and cold equally strong. To maintain temperature but increase flow, you must increase both handles After DCT, the tap instead has a handle controlling the temperature, and another handle controlling the flow. You can make all the same combinations of flow and temperature, but it's controlled in a different way. Medium lukewarm water is now made by having the temperature handle halfway, and the flow then increased by increasing only the other handle. Not sure if this analogy works for America since American showers have, afaik, a single rotational dial that somehow controls both temperature and flow (???), but in Europe the distinction between the sinks with a red and a blue handle, vs the thermostatic tap with temperature handle and flow handle, is very common :)
andi999 6y ago
Actually even if you are not 5 this totally misses the point about the DCT. Especially the AC components are not explained.
EForEndeavour 6y ago
The main reason why this article wasn't intuitive to me is that the toy example is trivial, and the next example (a real image) is very nontrivial. The first example shows through three lines of runnable Matlab code (sadly, I don't have Matlab and it's not free, but whatever) that if you start with an 8-by-8 matrix of 255 and run the discrete cosine transform, you end up with a sparse matrix with just one nonzero value in the first entry, because "the DCT has compacted the energy of the matrix into the first element referred to as the DC coefficient. The rest of the coefficients are called the AC coefficients." Cool? This doesn't help any more than just telling me that sentence directly. Also, the article doesn't even expand on this fingerhold of familiarity: DC and AC? Like direct current and alternating current, so that first element is in some sense the zero-frequency ("direct current") term, and if the starting example had any variation at all beyond a perfectly uniform field of 255's, you'd start to see "energy" showing up in the "alternating-current" entries? That would start to give some intuition. I guess what I'm saying is this article works, but it works by frustrating the reader just enough that they modify and play with the code (porting it from Matlab if they have to), thereby gaining the intuitive understanding that the article promises.
- mindcrime 6y ago
  (sadly, I don't have Matlab and it's not free, but whatever) What about Octave[1]? [1]:https://www.gnu.org/software/octave/ https://www.gnu.org/software/octave/
cevans01 6y ago
For those that have already worked with the FFT a bit, there are ways to use the FFT to calculate a DCT: https://dsp.stackexchange.com/questions/2807/fast-cosine-transform-via-fft https://dsp.stackexchange.com/questions/2807/fast-cosine-tra...
golergka 6y ago
> In simple terms, the Discrete Cosine Transform takes a set of N correlated (similar) data-points and returns N de-correlated (dis-similar) data-points (coefficients) in such a way that the energy is compacted in only a few of the coefficients M where M << N. That's not simple terms.
cdavid 6y ago
I am not convinced it is eli5. I am too lazy to write a blog post w/ illustration, but for audio signals, which I am more familiar with, the intuition behind DCT (and MDCT, used e.g. for mp3) is straightforward. Assuming you understand that a Fourier transform is an operation to go from from time domain to the frequency domain, the problem solved by DCT, DST, etc. is related to the fact that digital signal processing are finite, and without any care, you introduce 'irregularities' if you use a 'normal' Fourier transform. So the main idea of DCT/DST/etc. is to implicitly 'copy' and/or mirror the signal, to reduce the artefacts/irregularities introduced by Fourier Transform. Reducing irregularities intuitively leads to more regular signals, and the more regular your signal, the quicker the high frequencies decrease, which is the compression effect of DCT. More mathematically, but still very informally: DCT/DST is about boundary conditions. Using DFT (the 'normal' Fourier transform for digital signals) will imply discontinuities at the boundaries. For continuous time signals, an intuitive way to define regularities is to measure the decay of successive derivative of a function f(t), by looking at convergence convergence of t^n f(t) as t -> inf for n. That implies that regular functions have bounded Fourier transforms, and the more regular, the faster the Fourier transform decays. The DST/DCT, by mirroring/copying the signal, reduce irregularities, and hence their coefficients decrease faster.
- ponderingfish 6y ago
  Amazing explanation!!
- jerf 6y ago
  ELI5 was a mistake. ELI12 would have made much more sense. ELI5 is so obviously absurd that people seem to subconsciously just discard the criterion and put all sorts of things in that no conceivable 5-year-olds would understand, not even the genius ones we occasionally read about. ELI5 is extremely restrictive. ELI12 would be much more sensible. An ELI12 explanation would be possible, but it wouldn't be able to casually assume "frequency domain" or related concepts are things that could be assumed; it would first have to show how you can break images down into frequency components.
  - cdavid 6y ago
zackmorris 6y ago
Here's the page that got me interested in the DCT 15 years ago: https://www.mathworks.com/help/images/discrete-cosine-transform.html https://www.mathworks.com/help/images/discrete-cosine-transf... Although I must admit that I haven't fully internalized it (it's easy to forget how it works). It might help to learn some of the more mainstream ones like the Fourier transform first: https://www.mathworks.com/help/images/fourier-transform.html https://www.mathworks.com/help/images/fourier-transform.html https://www.mathworks.com/help/images/image-transforms.html https://www.mathworks.com/help/images/image-transforms.html MATLAB (or GNU Octave which is free) is the only language I've used that maps abstractions to code in close to a 1:1 fashion. I think of code bloat as roughly these orders of magnitude: Math/Matrix languages (MATLAB) 1:1 Scripting languages (JavaScript, PHP, Python, etc) 10:1 Bare metal languages (Rust, C++, Assembly) 100:1 Unfortunately I have yet to find a functional programming language that is 1:1 in the same way that MATLAB is. One would think that Lisp/Haskell/Scala/Julia/Clojure/Erlang would be concise. But in practice, I've found them to generally be write-only languages that are quite difficult to grok. The only thing that comes close is spreadsheets, but due to their 2D nature, they can't really scale beyond a certain level of complexity. Honestly, I think that the lack of adoption of functional programming languages (due to their own obstinance) is one of the great problems of our time. Anyway, for the past 5-10 years or so, I solve most problems in my head in a data-driven way that looks like a hybrid between MATLAB and spreadsheets, piping data between classes written in an Actor model style (I learned this from a very good teacher during a contract at HP). I use rules of thumb like no mutable data (stored state), mostly higher-order functions, and framing concepts in terms of transformations rather than class inheritance. Then I translate that to whatever language I have to use for the client, which is probably PHP, JavaScript or C# (Unity). I highly recommend this sort of approach for keeping abstractions separate from implementations. Unfortunately since nobody else seems to follow this method, it makes for some friction in the workplace. People talk past me all of the time because they don't realize that I'm coming from this place of experience. They don't see the need for this clean separation when they are "trying to get things done". They may get things done faster, but if you want bug-free implementations, this is the way to go IMHO. Edit: I'm on the fence about TensorFlow. It's arguably more advanced than MATLAB, but vastly more opaque. So I'm not sold on any advantage it provides, other than perhaps better performance or usefulness in certain domains like machine learning. Oh and any perceived lack of performance with MATLAB is an implementation detail. I can't understand why it's not fully parallelized and running on the GPU by now.
anovikov 6y ago
Good description of how you use it for image compression, but nothing about video compression - that is, how similarity between consecutive frames is used.
rsync 6y ago
"Explain Like I'm Five" Oh my god - are you all right ? Where are your parents ?
master_yoda_1 6y ago
Looks like everyone at hackernews have intelligence of a five year old :) Sad to see for so many human being their brain never evolve.
hinkley 6y ago
3Blue1Brown ELI15 the Fast Fourier Transform, which sets up the problem domain: https://www.youtube.com/watch?v=spUNpyF58BY https://www.youtube.com/watch?v=spUNpyF58BY
justjonathan 6y ago
This is an explanation (from the amazing three blue one brown) of the DFT not the DCT, but this was the first thing that ever really made sense to me. It is explained by someone who really knows math incredibly well and is an amazing teacher, with amazing visuals: https://www.youtube.com/watch?v=spUNpyF58BY https://www.youtube.com/watch?v=spUNpyF58BY

121 points by ponderingfish 6y ago

If this stuff intrigues you please try out Steve Brunton's extensive set of videos on Data Science that include superb lectures on Fourier Series, the Fourier Transform and the Fast Fourier Transform with examples in Matlab and Python. Can't recommend this guy enough. https://www.youtube.com/channel/UCm5mt-A4w61lknZ9lCsZtBw https://www.youtube.com/channel/UCm5mt-A4w61lknZ9lCsZtBw

rrao84 6y ago

Fantastic explanation of transforms and the example of 20 questions and DCT totally did it for me. The rest of the explanation is hard to grok if aren't a programmer or not interested in image & video compression. YMMV

Diti 6y ago

This is DEFINITELY NOT explained like I’m five. More like late high school level (mathematical planes, frequencies) and above (matrixes). I appreciate the author’s attempt at vulgarization but the title is wrong.

mwexler 6y ago
Props for use of "vulgarization"; I hadn't seen this word as a noun or process before but it seems to fit nicely in context.
- ponderingfish 6y ago
  Never seen this word before :) Simple explanation of the concept and the use of DCT though. Perhaps, written for a person who is Five times 5? :)
LandR 6y ago
You mean you didn't understand this when you were 5? > In simple terms, the Discrete Cosine Transform takes a set of N correlated (similar) data-points and returns N de-correlated (dis-similar) data-points (coefficients) in such a way that the energy is compacted in only a few of the coefficients M where M << N. Did you even nursery?
olx_designer 6y ago
Is this can be used as a feature extraction for image recognition task ? I read some time ago someone used jpeg compression as a feature extraction before DNN.
- ponderingfish 6y ago
  Can be for sure by examining the coefficients. It's a little hard but can be a way to do feature detection in the frequency transform.
- qayxc 6y ago
  This depends on the kind of features you're interested in. If the features lead to clustering in the frequency domain, then yes. Otherwise it'd be detrimental. Examples for features that'd work well are edges and lines. Features based on gradients wouldn't work well.

walagran 6y ago

Pretty cool! I would add Computerphile's Youtube Video as a watch after this: https://www.youtube.com/watch?v=Q2aEzeMDHMA https://www.youtube.com/watch?v=Q2aEzeMDHMA. This is a part of their 4-video series on JPEG:https://www.youtube.com/playlist?list=PLQfOC23r609kmgOr_V8sfUnr0r3pOI9gT https://www.youtube.com/playlist?list=PLQfOC23r609kmgOr_V8sf...

djmips 6y ago
Those are great! For a more in depth series of videos on the transforms themselves I haven't found anything better than videos from Steve Brunton. Here's a link jumping in at Fourier Series. Best set of videos I've seen on the subject. https://www.youtube.com/watch?v=MB6XGQWLV04&list=PLMrJAkhIeNNRjxJ_sMtJ02geqw_-vuB7O&index=47 https://www.youtube.com/watch?v=MB6XGQWLV04&list=PLMrJAkhIeN...

miccah 6y ago

Not DCT, but this website [1] has been on my TODO list for awhile. It explains DFT using interactive visualizations. [1] https://jackschaedler.github.io/circles-sines-signals/index.html https://jackschaedler.github.io/circles-sines-signals/index....

ponderingfish 6y ago
Nice .. this is definitely something to bookmark.

JackFr 6y ago

Maybe I'm dense, but I didn't find this useful at all. The author spends the bulk of the article explaining what transform means (not typically the sticking point) and then uses terms like "pixel-domain", "frequency-domain", "decorrelating", "energy compacting" without explanation or definition. The author could spend a little less time on the former and more on the latter IMHO.

OneGuy123 6y ago
This, it's funny how the author talks about views/transforms and all other stuff EXCEPT the actual intuition behind the DCT.
- mrspeaker 6y ago
  It let me understand views and transforms! I've read countless articles that talk about transforms and I realized I previously didn't properly understand them until at all!
- ponker 6y ago
  That’s because it’s the hardest thing to grok. I have two electrical engineering degrees from a highly regarded university and still don’t.
raxxorrax 6y ago
To be fair, the terms in literature are all over the place. image space and spectral space is what I read most often (not necessarily in English). I personally would prefer just source and target space, especially since we have imaging as an application. I think the explanation was quite good, but I implemented a DCT once as a student (with shitty code and slow as hell, don't roll your own matrix multiplication). The Wikipedia article was bad at the time, but it has really good info now. The topic can take a while to get it. I think looking at the base functions helps a lot. Every image is basically an overlap of these base functions which are each parameterized through an amplitude and phase. I transformed some images with basic shapes with Matlab until it really clicked.
- 6y ago

ssawyer06 6y ago

Being familiar with the DCT but having no idea how to explain to a five year-old, I clicked. This does not ELI5 the DCT.

anticristi 6y ago
This. I'm not even sure why anyone would bother ELI5-ing the DCT with images. Here is an attempt to explain the DCT using audio: The DCT converts music into key presses on a piano. When playing back those keys on the piano, you lose the text of the music, but you sure hear the melody. There! Way more ELI5-ish.
- ponderingfish 6y ago
  huh? if you throw away 70% of the melody, do you get back the text? If not, you haven't explained the DCT.
  - anticristi 6y ago
    In my ELI5 analogy, the DCT "throws away" the voice. You can still recognize the song.
  - Jasper_ 6y ago
    In this analogy, you are throwing away the instrumentation, like whether it was played on a piano or a tuba, but the raw melody is still there. This is the advantage of working in the frequency space. If we were in the time space, throwing away 70% of the data would throw away 70% of the melody.
    - ponderingfish 6y ago
      And a 5 year old understands instrumentation, melody, piano, and the tuba?
Aardwolf 6y ago
How about this analogy: You have a tap with a hot handle and a cold handle. You can make medium lukewarm water by making hot and cold equally strong. To maintain temperature but increase flow, you must increase both handles After DCT, the tap instead has a handle controlling the temperature, and another handle controlling the flow. You can make all the same combinations of flow and temperature, but it's controlled in a different way. Medium lukewarm water is now made by having the temperature handle halfway, and the flow then increased by increasing only the other handle. Not sure if this analogy works for America since American showers have, afaik, a single rotational dial that somehow controls both temperature and flow (???), but in Europe the distinction between the sinks with a red and a blue handle, vs the thermostatic tap with temperature handle and flow handle, is very common :)

andi999 6y ago

Actually even if you are not 5 this totally misses the point about the DCT. Especially the AC components are not explained.

EForEndeavour 6y ago

The main reason why this article wasn't intuitive to me is that the toy example is trivial, and the next example (a real image) is very nontrivial. The first example shows through three lines of runnable Matlab code (sadly, I don't have Matlab and it's not free, but whatever) that if you start with an 8-by-8 matrix of 255 and run the discrete cosine transform, you end up with a sparse matrix with just one nonzero value in the first entry, because "the DCT has compacted the energy of the matrix into the first element referred to as the DC coefficient. The rest of the coefficients are called the AC coefficients." Cool? This doesn't help any more than just telling me that sentence directly. Also, the article doesn't even expand on this fingerhold of familiarity: DC and AC? Like direct current and alternating current, so that first element is in some sense the zero-frequency ("direct current") term, and if the starting example had any variation at all beyond a perfectly uniform field of 255's, you'd start to see "energy" showing up in the "alternating-current" entries? That would start to give some intuition. I guess what I'm saying is this article works, but it works by frustrating the reader just enough that they modify and play with the code (porting it from Matlab if they have to), thereby gaining the intuitive understanding that the article promises.

mindcrime 6y ago
(sadly, I don't have Matlab and it's not free, but whatever) What about Octave[1]? [1]:https://www.gnu.org/software/octave/ https://www.gnu.org/software/octave/

cevans01 6y ago

For those that have already worked with the FFT a bit, there are ways to use the FFT to calculate a DCT: https://dsp.stackexchange.com/questions/2807/fast-cosine-transform-via-fft https://dsp.stackexchange.com/questions/2807/fast-cosine-tra...

golergka 6y ago

> In simple terms, the Discrete Cosine Transform takes a set of N correlated (similar) data-points and returns N de-correlated (dis-similar) data-points (coefficients) in such a way that the energy is compacted in only a few of the coefficients M where M << N. That's not simple terms.

cdavid 6y ago

I am not convinced it is eli5. I am too lazy to write a blog post w/ illustration, but for audio signals, which I am more familiar with, the intuition behind DCT (and MDCT, used e.g. for mp3) is straightforward. Assuming you understand that a Fourier transform is an operation to go from from time domain to the frequency domain, the problem solved by DCT, DST, etc. is related to the fact that digital signal processing are finite, and without any care, you introduce 'irregularities' if you use a 'normal' Fourier transform. So the main idea of DCT/DST/etc. is to implicitly 'copy' and/or mirror the signal, to reduce the artefacts/irregularities introduced by Fourier Transform. Reducing irregularities intuitively leads to more regular signals, and the more regular your signal, the quicker the high frequencies decrease, which is the compression effect of DCT. More mathematically, but still very informally: DCT/DST is about boundary conditions. Using DFT (the 'normal' Fourier transform for digital signals) will imply discontinuities at the boundaries. For continuous time signals, an intuitive way to define regularities is to measure the decay of successive derivative of a function f(t), by looking at convergence convergence of t^n f(t) as t -> inf for n. That implies that regular functions have bounded Fourier transforms, and the more regular, the faster the Fourier transform decays. The DST/DCT, by mirroring/copying the signal, reduce irregularities, and hence their coefficients decrease faster.

ponderingfish 6y ago
Amazing explanation!!
jerf 6y ago
ELI5 was a mistake. ELI12 would have made much more sense. ELI5 is so obviously absurd that people seem to subconsciously just discard the criterion and put all sorts of things in that no conceivable 5-year-olds would understand, not even the genius ones we occasionally read about. ELI5 is extremely restrictive. ELI12 would be much more sensible. An ELI12 explanation would be possible, but it wouldn't be able to casually assume "frequency domain" or related concepts are things that could be assumed; it would first have to show how you can break images down into frequency components.
- cdavid 6y ago

zackmorris 6y ago

Here's the page that got me interested in the DCT 15 years ago: https://www.mathworks.com/help/images/discrete-cosine-transform.html https://www.mathworks.com/help/images/discrete-cosine-transf... Although I must admit that I haven't fully internalized it (it's easy to forget how it works). It might help to learn some of the more mainstream ones like the Fourier transform first: https://www.mathworks.com/help/images/fourier-transform.html https://www.mathworks.com/help/images/fourier-transform.html https://www.mathworks.com/help/images/image-transforms.html https://www.mathworks.com/help/images/image-transforms.html MATLAB (or GNU Octave which is free) is the only language I've used that maps abstractions to code in close to a 1:1 fashion. I think of code bloat as roughly these orders of magnitude: Math/Matrix languages (MATLAB) 1:1 Scripting languages (JavaScript, PHP, Python, etc) 10:1 Bare metal languages (Rust, C++, Assembly) 100:1 Unfortunately I have yet to find a functional programming language that is 1:1 in the same way that MATLAB is. One would think that Lisp/Haskell/Scala/Julia/Clojure/Erlang would be concise. But in practice, I've found them to generally be write-only languages that are quite difficult to grok. The only thing that comes close is spreadsheets, but due to their 2D nature, they can't really scale beyond a certain level of complexity. Honestly, I think that the lack of adoption of functional programming languages (due to their own obstinance) is one of the great problems of our time. Anyway, for the past 5-10 years or so, I solve most problems in my head in a data-driven way that looks like a hybrid between MATLAB and spreadsheets, piping data between classes written in an Actor model style (I learned this from a very good teacher during a contract at HP). I use rules of thumb like no mutable data (stored state), mostly higher-order functions, and framing concepts in terms of transformations rather than class inheritance. Then I translate that to whatever language I have to use for the client, which is probably PHP, JavaScript or C# (Unity). I highly recommend this sort of approach for keeping abstractions separate from implementations. Unfortunately since nobody else seems to follow this method, it makes for some friction in the workplace. People talk past me all of the time because they don't realize that I'm coming from this place of experience. They don't see the need for this clean separation when they are "trying to get things done". They may get things done faster, but if you want bug-free implementations, this is the way to go IMHO. Edit: I'm on the fence about TensorFlow. It's arguably more advanced than MATLAB, but vastly more opaque. So I'm not sold on any advantage it provides, other than perhaps better performance or usefulness in certain domains like machine learning. Oh and any perceived lack of performance with MATLAB is an implementation detail. I can't understand why it's not fully parallelized and running on the GPU by now.

anovikov 6y ago

Good description of how you use it for image compression, but nothing about video compression - that is, how similarity between consecutive frames is used.

rsync 6y ago

"Explain Like I'm Five" Oh my god - are you all right ? Where are your parents ?

master_yoda_1 6y ago

Looks like everyone at hackernews have intelligence of a five year old :) Sad to see for so many human being their brain never evolve.

hinkley 6y ago

3Blue1Brown ELI15 the Fast Fourier Transform, which sets up the problem domain: https://www.youtube.com/watch?v=spUNpyF58BY https://www.youtube.com/watch?v=spUNpyF58BY

justjonathan 6y ago

This is an explanation (from the amazing three blue one brown) of the DFT not the DCT, but this was the first thing that ever really made sense to me. It is explained by someone who really knows math incredibly well and is an amazing teacher, with amazing visuals: https://www.youtube.com/watch?v=spUNpyF58BY https://www.youtube.com/watch?v=spUNpyF58BY