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Image Compression


A 1 hour movie in full high definition (1080p).
That is a-lot-of data. How much exactly?

When not compressed:
- 24 bits for each RGB pixel (8 bits for each of the 3 primary light colors: Red, Green, and Blue)
- A frame resolution of 1920 * 1080 = 2073600 pixels (16:9 widescreen)
- A frame rate of 24 fps (24 images in each second)
- One hour, that's 60*60 = 3600 seconds.
- Not including: sound, subtitles, and such.

The amount of bits is:
24 * 2073600 * 24 * 3600 = 4299816960000 bits
The amount of 24 bits RGB pixels is:
2073600 * 24 * 3600 = 179159040000 RGB pixels
The amount of 8 bits channel pixels is:
2073600 * 24 * 3 * 3600 = 537477120000 channel pixels
The amount of frames is:
24 * 3600 = 86400 frames

How many GigaBytes is that?
Calculated using 1024 per kilo:
4299816960000 / 8 / 1024 / 1024 / 1024 = 500.56 GB
And that will NOT fit on one DVD (4.7 GB, or 8.5 GB dual layer)
Nor will it fit on one Blu-ray disc! (25 GB, or 50 GB dual layer)

To get this 1 hour movie on one dual layer Blu-ray disc, it must be compressed to even less than 50 GB, because the sound and such need to fit on the same disc.
Let's say this movie may be no more than 20 GB large.
From 500GB to only 20GB. That's a compression ratio of 500 / 20 = 25

The amount of bits that on average may be spend on 1 pixel is only:
24 / 25 = 0.96 bits
How can that be done?!
One RGB pixel needs 24 bits. One bit can make 1 out of 2 colors, while we need to get one out of 16777216 colors!


How many 1 hour movies are there, in theory?
Of exactly this size.
The amount is not invite.
The amount is exactly 2 ^ 4299816960000
Don't bother trying to calculate that. It may freeze your computer!

The library of all possible movies this size, contains every movie that has been made, but also all movies that can be made in the future, and all movies that have not been made in the past! All real movies, all fantasy movies, all cartoons, any movie you can imagine.
And that's not all. All these movies occupy only an extremely small part of the whole movie space. Most movies contain what we call: noise. A boring soup of random colors.
The "movie space" is the name of this library.
Each different size movie has its own movie space.

It is impossible to store this movie space library
But it is equal to the result of a very simple formula:
A) First frame = all black (all pixels have a value of zero, and together form one large number)
B) Next frame = previous frame +1
C) Repeat step B, until all pixels are white.

Instead of storing a movie on your hard disk, you could only store the address of this movie in the movie space. Smart! That will save a lot of bits! No. No it won't. The size of your address is exactly as large as your movie!
But you can save bits if you can reduce the size of the movie space.
If you can reduce the size of the movie space down to 1/2 the original size, you will save... 1 bit. Just 1 bit. So instead of 4299816960000 bits, you're now down to 4299816959999 bits. And oh yea; you now have to store how you reduced the movie space, which will cost you at least 1 bit.

Why is that so? Well; imagine a tiny space of 16 unique combinations of 4 bits. Each combination is like an unique answer. To each unique answer is a unique question. The amount of information in the questions (library address) is equal to the amount of information in the answers (library locations).

Is it possible to reduce the size of your address? If so, can it get as far reduced as can be done with lossless compression, or better?
This I think of as a very interesting question! It can have great consequences if extreme "compression" can be reached this way.

Can the size of the image space be reduced extremely, without having to write down much about how it was done? If the answer is yes, then we can enter a new chapter in the coming history of computing.

Giesbert Nijhuis

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