How to estimate GIF file size?

Question

We\'re building an online video editing service. One of the features allows users to export a short segment from their video as an animated gif. Imgur has a file size limit

Answer 1

The GIF image format uses LZW compression. Infamous for the owner of the algorithm patent, Unisys, aggressively pursuing royalty payments just as the image format got popular. Turned out well, we got PNG to thank for that.

The amount by which LZW can compress the image is extremely non-deterministic and greatly depends on the image content. You, at best, can provide the user with a heuristic that estimates the final image file size. Displaying, say, a success prediction with a colored bar. You'd can color it pretty quickly by converting just the first frame. That won't take long on 384x216 image, that runs in human time, a fraction of a second.

And then extrapolate the effective compression rate of that first image to the subsequent frames. Which ought to encode only small differences from the original frame so ought to have comparable compression rates.

You can't truly know whether it exceeds the site's size limit until you've encoded the entire sequence. So be sure to emphasize in your UI design that your prediction is just an estimate so your user isn't going to disappointed too much. And of course provide him with the tools to get the size lowered, something like a nearest-neighbor interpolation that makes the pixels in the image bigger. Focusing on making the later frames smaller can pay off handsomely as well, GIF encoders don't normally do this well by themselves. YMMV.

Answer 2

There's no simple answer to this. Single-frame GIF size mainly depends on image entropy after quantization, and you could try using stddev as an estimator using e.g. ImageMagick:

identify -format "%[fx:standard_deviation]" imagename.png

You can very probably get better results by running a smoothing kernel on the image in order to eliminate some high-frequency noise that's unlikely to be informational, and very likely to mess up compression performance. This goes much better with JPEG than with GIF, anyway.

Then, in general, you want to run a great many samples in order to come up with something of the kind (let's say you have a single compression parameter Q)

STDDEV   SIZE W/Q=1   SIZE W/Q=2    SIZE W/Q=3 ...
value1   v1,1         v1,2          v1,3

After running several dozens of tests (but you need do this only once, not "at runtime"), you will get both an estimate of, say, , and a measurement of its error. You'll then see that an image with stddev 0.45 that compresses to 108 Kb when Q=1 will compress to 91 Kb plus or minus 5 when Q=2, and 88 Kb plus or minus 3 when Q=3, and so on.

At that point you get an unknown image, get its stddev and compression @Q=1, and you can interpolate the probable size when Q equals, say, 4, without actually running the encoding.

While your service is active, you can store statistical data (i.e., after you really do the encoding, you store the actual results) to further improve estimation; after all you'd only store some numbers, not any potentially sensitive or personal information that might be in the video. And acquiring and storing those numbers would come nearly for free.

Backgrounds

It might be worthwhile to recognize images with a fixed background; in that case you can run some adaptations to make all the frames identical in some areas, and have the GIF animation algorithm not store that information. This, when and if you get such a video (e.g. a talking head), could lead to huge savings (but would throw completely off the parameter estimation thing, unless you could estimate also the actual extent of the background area. In that case, let this area be B, let the frame area be A, the compressed "image" size for five frames would be A+(A-B)*(5-1) instead of A*5, and you could apply this correction factor to the estimate).

Compression optimization

Then there are optimization techniques that slightly modify the image and adapt it for a better compression, but we'd stray from the topic at hand. I had several algorithms that worked very well with paletted PNG, which is similar to GIF in many regards, but I'd need to check out whether and which of them may be freely used.

Some thoughts: LZW algorithm goes on in lines. So whenever a sequence of N pixels is "less than X%" different (perceptually or arithmetically) from an already encountered sequence, rewrite the sequence:

     018298765676523456789876543456787654
     987678656755234292837683929836567273

here the 656765234 sequence in the first row is almost matched by the 656755234 sequence in the second row. By changing the mismatched 5 to 6, the LZW algorithm is likely to pick up the whole sequence and store it with one symbol instead of three (6567,5,5234) or more.

Also, LZW works with bits, not bytes. This means, very roughly speaking, that the more the 0's and 1's are balanced, the worse the compression will be. The more unpredictable their sequence, the worse the results.

So if we can find out a way of making the distribution more **a**symmetrical, we win.

And we can do it, and we can do it losslessly (the same works with PNG). We choose the most common colour in the image, once we have quantized it. Let that color be color index 0. That's 00000000, eight fat zeroes. Now we choose the most common colour that follows that one, or the second most common colour; and we give it index 1, that is, 00000001. Another seven zeroes and a single one. The next colours will be indexed 2, 4, 8, 16, 32, 64 and 128; each of these has only a single bit 1, all others are zeroes.

Since colors will be very likely distributed following a power law, it's reasonable to assume that around 20% of the pixels will be painted with the first nine most common colours; and that 20% of the data stream can be made to be at least 87.5% zeroes. Most of them will be consecutive zeroes, which is something that LZW will appreciate no end.

Best of all, this intervention is completely lossless; the reindexed pixels will still be the same colour, it's only the palette that will be shifted accordingly. I developed such a codec for PNG some years ago, and in my use case scenario (PNG street maps) it yielded very good results, ~20% gain in compression. With more varied palettes and with LZW algorithm the results will be probably not so good, but the processing is fast and not too difficult to implement.