There's something really fishy about the "balloon" example in the paper. Allegedly it's a 512x512 image, but if you look at it it's plainly 64x64. (If I view the article using Firefox's pdf.js, then it's upscaled in some kinda-smooth way; if I open it in a dedicated PDF viewer then the big pixels are clearly visible.) And then the fractally-compressed-and-decompressed images have miraculously created detail that wasn't there before, and have smoothed out the blocky edges of the balloon (for instance) into nice high-resolution smooth curves.
If it really did that, then it would be badly wrong because for all the compressor knows it's destroying lots of useful information by rounding off all the corners. And it would be miraculous because what it's actually done turns out to make something physically plausible, when there are any number of ways of filling in the missing detail that fit the data in the 64x64 image equally well, as far as anything short of full AI could tell.
But I don't really believe it did really do that, because (1) from Barnsley's description of the algorithm it seems fantastically unlikely that it could, (2) the paper says explicitly that the original and reconstructed images are both 512x512 pixels, and (3) if fractal compression were really doing something so miraculous then Barnsley's article would have made a lot more noise about it (and in particular the discussion of "fractal zoom" that follows wouldn't make any sense if Barnsley thought he had just showed a spectacular 8x fractal zoom already).
I'm guessing that something very bad happened to Figure 2, and that the image that was actually compressed and decompressed to produce Figure 3 looked a lot more like Figure 3 than it did like Figure 2 as shown in the paper.
I, too, was at Iterated Systems in its early days.
See the correction after the comment below - Good reason to be confused. Fig 2 is actually the first step in decoding.
You are missing the significance of the 64x64. The point was that the picture was split into squares that were bigger than single pixels before encoding. In this case, the regions were 8x8, so there are 64x64 of them in the original 512x512 image. If the basic elements were 1x1 pixel the linear transformation encoding would have made the encoding bigger than the original! The images illustrate some of the steps in the iterative decoding process, which always starts with single intensity blocks in the basic elements (so 64x64 blocks) but iteratively gets closer to the original, finer grained image. It looks like magic, but the fractal theory is sound. It is a lossy process, so there is no guarantee that the encoded image has both limited losses and is small in size.
I was an algorithm developer, not in sales. For sales purposes they clearly could have chosen example images that were more naturally fractal at a scale below a pixel, so blowing them up looked good. I do not know how generally good the zooming in was.
The image is captioned as "Original 512 x 512 grayscale image, with 256 gray levels for each pixel, before fractal compression.".
So, if what your saying is true the caption is wrong? Are you saying it is the first stage of decompression? That this is the input data to the decompressor?
I'm assuming therefore that the compressor actually does use a full undownsampled (not blocky) image as it's input. Or uses it as part of it's iterative compression process. Is that correct?
Good point. The caption for Figure 2 is wrong. The picture is of the first step in decompression of a 512 x 512 image. A pity you do not actually see the original that they refer to.
I think that actually the caption is "correct", and they must have simply included the wrong image, because the text says "Figure 2 shows the
original digital image of Balloon, which is of dimensions
512 pixels by 512 pixels, with 256
gray levels at each pixel."
I'm in two minds about this. That was my own first interpretation, for the same reasons as you. And you could well be right, in fact I'd say there's a 70% probability.
But the nature of iterated fractal functions is that they generate information, which is how we can get such elaborate pictures of ferns from such a small amount of starting information. When we squint at a pixelated image, we're deliberately trading off optical distortion in order to get a sense of the underlying pattern - it's not more accurate because we're inventing stuff, but it is giving us an answer to the question of 'what function would generate these shapes in a low-resolution picture?' and then going on to iterate that same function.
So while acknowledging the likelihood that you're right and I'm wrong, I'm not totally ready to come off this limb because I'm also thinking of what it was that made the resolution scaling of this technology so good - there was something more complex than mere interpolation going on. I'll have a look through the text again and think about it further.
I used the software when it first became available in the early 90s, but with a focus on resolution independence rather than reverse entropy (which is why it's more likely than not that I'm wrong).
It's certainly not a scam, Barnsley's a respected researcher in this field of mathematics - http://en.wikipedia.org/wiki/Barnsley_fern At worst this is a rendering problem in the PDF and some nostalgic over-enthusiasm on my part.
I'm very shortsighted (about -8). When I squint, my eyelashes act as a rudimentary lens and make the image clearer. The image is distorted differently when I squint, but less blurred. I suggest that those with better eyesight may also squint in order to see details on a retina display, and the squinter sees a higher res image (albeit a distorted one).
If it really did that, then it would be badly wrong because for all the compressor knows it's destroying lots of useful information by rounding off all the corners. And it would be miraculous because what it's actually done turns out to make something physically plausible, when there are any number of ways of filling in the missing detail that fit the data in the 64x64 image equally well, as far as anything short of full AI could tell.
But I don't really believe it did really do that, because (1) from Barnsley's description of the algorithm it seems fantastically unlikely that it could, (2) the paper says explicitly that the original and reconstructed images are both 512x512 pixels, and (3) if fractal compression were really doing something so miraculous then Barnsley's article would have made a lot more noise about it (and in particular the discussion of "fractal zoom" that follows wouldn't make any sense if Barnsley thought he had just showed a spectacular 8x fractal zoom already).
I'm guessing that something very bad happened to Figure 2, and that the image that was actually compressed and decompressed to produce Figure 3 looked a lot more like Figure 3 than it did like Figure 2 as shown in the paper.