How much information can a small image contain?

Svenstaro 4 years ago |

Many moons ago, I wondered what it would look like if you iteratively generated every possible image. It doesn't sound very useful at all (and it certainly isn't) but I learned C++ and SDL that way.

This is probably terrible code by anybody's standards but maybe someone wants to take a look: https://github.com/svenstaro/infinerator

quacked 4 years ago | |

I've thought about this as well; it's one of those weird things where you realize that with enough pixel count and shading options, every image you can think of exists within the total set of generated images.

jodrellblank 4 years ago | | |

"enough" hides a surprising amount of work. Mobilise the entire planet's computers for a decade, assuming a generous Moore's law increase as well, and you might count through seventeen 8-bit grayscale pixels in that decade.

Annihilate the Sun and you won't get enough energy to drive a simple counter through thirty 8-bit grayscale pixels.

https://security.stackexchange.com/a/6149/

alanbernstein 4 years ago | |

A story about the text version of this concept: https://en.wikipedia.org/wiki/The_Library_of_Babel

smnrchrds 4 years ago | | |

Check out this one too if you haven't: https://en.wikipedia.org/wiki/The_Nine_Billion_Names_of_God

iggldiggl 4 years ago | | |

An an online version based on that story: https://libraryofbabel.info/

jcun4128 4 years ago | |

I think about it from the perspective of ideas, once we figure out something (how to fly, electricity) we know it. How do you brute force find that info through random/massive computation. Specifically to find the next things we don't know like jumping dimensions or FTL, etc...

sysihyk 4 years ago |

Very very misleading.

First, article tried to assess information capacity in Shannon style, completely disregarding what signal is (a) two-dimensional and (b) highly redundant, that is, ignoring the traits of being an image.

Second, article taken too much liberties while mixing photorealistic and pixel-art images. The latter is really an art, since there is no formally defined ("machine") transform between these two types. And last but not least these types have significantly different information density profiles.

No DSP curiosity here.

necovek 4 years ago |

The introduction has lost me completely: such a long winded way to say that 32x32x3 bytes can represent 2^(32x32x3x8) different values.

p1necone 4 years ago | |

I think the point of the article is that there isn't 2^(32x32x3x8) meaningful images that can be encoded - there's far less than that because so many of the possible arrangements of the data are just meaningless noise, or millions of versions of the same thing with slightly altered color values etc.

The article is saying that neural networks are cool, because part of what they do is finding which images actually contain meaningful visual information.

goldenkey 4 years ago | | |

But they don't, they often conflate noise with actual features, as long as the noise has some statistical bias, which given enough random generations, will. Try it yourself, generate random images using a uniform distribution (not gaussian) and run a SOTA classifier on them. Eventually you'll hit some minor false positives.

It errs in the same way we often see objects in clouds or constellations.

necovek 4 years ago | | |

I got the point quickly enough (from the title and initial table of snapshots?), but author has lost me as a reader due to saying little with too many words before they could elaborate on the point.

keithnz 4 years ago |

I sort of came at the combinations of small images from a slightly different angle when I was a teenager, I was imagining that if there was a movie of your life (and everyone elses, in fact every possible life you could live) then you could produce every still image of that video if you restricted the bounds of the image to something small but understandable. I was very quickly was disappointed at how big the numbers get :)

thro1 4 years ago |

Up to infinity ? (depends of person interpreting it - "a picture is worth a thousand words")

sloshnmosh 4 years ago |

I was hoping this was an article about packing different executables into images like I saw on Twitter.

brijeshpatel007 4 years ago |

wonderful, it looks like people are talking with Zoom, kidding. a image can contain lot more information if it is designed by an professional artist. an image have an message for everyone.

dukeofdoom 4 years ago |

Would this be a good way to avoid censorship. Encode an image by mixing it with a private key image, maybe xor the cells or something like that. Post online. Anyone with the key image can decode.

vdqtp3 4 years ago | |

This is encryption and/or steganography.

nixpulvis 4 years ago |

N^M, clearly.

chunkyks 4 years ago | |

Amateur.

Use the whole space [32x32x3 bytes = 3072 bytes] to encode a Busy Beaver.

H8crilA 4 years ago | | |

It's still at most n^m different images.

chunkyks 4 years ago | | |

True, but the posed question was "how much information can a small image contain", not "how many unique images are there"

H8crilA 4 years ago | | |

Those are the same things ...

https://en.m.wikipedia.org/wiki/Information_theory

jstanley 4 years ago | | |

What's the distinction?

Specifying an element from a set of 2^n members seems equivalent to encoding n bits of information.

nobrains 4 years ago |

> "Machine learning tries to do by math what we are able to do by instinct"

...except that we also do it by math. It is just so fast and optimized, that we refer to it as instinct.

weird-eye-issue 4 years ago | |

That's like saying gravity works because it uses math. No, we just applied our version of math to it