That's quite a complex question a priori.

There's a widespread myth that since there's only a limited number of pixels, the accuracy can't be much improved over cubic resizing. And without thinking much about it, as a user I also thought along those lines at first. But then, someday I realized that since I could imagine when looking at an image what it should look like when zoomed that there had to be a way to write an algorithm that zooms better and that's how I come to write Imagiris. The truth is, with new advances in mathematics (last 50 years), the limits to image zooming are much farther that our first intuition dictates.

So what are the limits ?

Let's start wit a simple answer: it depends on the image.

More exactly it depends on the regularity of the image.

New theories such as compressive sampling have emerged. The idea behind them is that a minimal energy function can be used to represent the image. Zooming in that situation simply comes down to minimizing this function.

Now this may seems a bit complicated, but the idea is simple. There's a regularity, an underlying structure to the image. This proved that the famous Fourrier sampling limit is in fact a lower bound, not an upper bound. Just as reminder, the Fourrier limit indicates that a signal is represented accurately only if it's sample at twice its highest frequency.

Just to give you a concrete example, let's take an image which underlying structure is a line. Then knowing two distinct points on that line is sufficient to reproduce all the points in the line. In other words, if you have a model for your image, a few points are sufficient to capture a lot of information, sometimes all of it.

Now back to image processing, if the image has a lot of regularity, that means lines, curves, edges, then theoritically it can modeled as a set of simple equations which would insure infinte zoom. Those equations are describing self-similarity, and they are often given the name of fractals. In practice, however, images also contain areas of fine details which have no self similarity. For example, the skin texture looks like the grand canyon when looked under a microscope while looked at from a distance, it looks smooth. So obviously, for such cases, there's no magic, without knowing what the area represent, there's no way to zoom in much and the effective limit is indeed the pixel limit.

Like stated above, reguarlity is key. So Imagiris technology focuses on that aspect. That's why the images look so much more precise than other techniques. Note that Imagiris doesn't use a pure fractal model, that would over-exagerate regularity (like a commercial fractal zoom package). However good the results currently are, I can achieve even better quality in my current development branch. The incredible thing about regularity is that algorithms can find some patterns that initially escaped the human eye and that effectively make image enlargement reveal new details. New progress on my algorithms are continually made available, so quality is constantly improved.