Since the dawn of digital photography, practitioners of the art have been barred from a creative freedom enjoyed by their image-making predecessors. Oil and watercolor painters, printmakers, and, yes, chemically-based photographers could make an image any shape they wanted to. Not so in the digital world. When cropping a raster image, a digital photographer must either leave an entire pixel in, or take it out. The result is that the aspect ratio of the cropped photograph is limited to the ratios of the integer dimensions of a rectangular subset of the pixels in an image.
An example with a small image will make this clear. Let’s say that the original image is 3×4 pixels. The possible aspect ratios that can be cropped from this image are 3:4 (the entire image), 1:1 (3×3, 2×2, and 1×1 pixel crops), 1:4, 1:3, 1:2, 3:1, 2:1, 3:2, 2:3, and so on. 4:5, a common photographic aspect ratio, is simply not available. As the size of the original image, measured in pixels, increases, the choices grow, but it’s never been enough for the truly creative photographer.
As often happens this time of year, the inspired geniuses at Lirpa Labs, the wholly-owned research subsidiary of the Sloof Lirpa Corporation, have invented a solution to a problem that many of us didn’t even know we had. Some of Sloop Lirpa’s previous breakthroughs include the DED-backlit LCD and the 4×5 cellphone.
This year, the Lirpa researchers took a look at what they could do to increase the limited selection of aspect ratios available to photographers. They explored the obvious, such as increasing the resolution of images to gain a wider variety of ratios. That wasn’t good enough for the Lirpalites. True, the number of aspect ratios available through that stratagem is infinite. But mathematicians have hierarchies of infinities, and the set of rational numbers, which the set of aspect ratios you can get by scaling and cropping, is the lowliest of infinities, the countable kind.
There is a much larger infinity out there, the set of all real numbers. How could the Lirpa scientists make that entire set available to photographers, both as aspect ratios and as both horizontal and vertical dimensions? Pixels are integrally addressed by definition, so the number of pixels in each direction are integers, and the ratio of those integers must be a rational number.
The breakthrough came when the researchers explored the ramifications of the fact that pixels don’t have to be square. Their unsquareness is not itself the breakthrough; such pixels are used often in moving images. But the aspect ratio of the pixel has always been rational. The new Lirpa pixels can have any real number for their aspect ratio, and thus, images composed of these pixels can themselves have any real number for their aspect ratio.
And here’s the great thing about the invention; the new type of pixels can be entirely implemented through the addition of a few new metadata fields. Rather than indicating the pixel aspect ratio with a number, which, in order to be representable in binary form must perforce be rational, the new fields allow the specification of an algorithm for calculating the aspect ratio in a programming language created for the purpose in a manner similar to the PostScript language. In order to make the specification of some useful aspect ratios simpler, commonly used ones such as e, pi, and the square root of two are predefined and may be invoked by reference.
Well, there you have it. A host of new possibilities are now available to you. The engineers on the parent company, Sloof Lirpa, who are responsible for making practical the Lirpa Labs discoveries, are hard at work on creating displays and printers whose pixel dimensions are irrational. And the researchers, always staying at the forefront of human knowledge — and sometimes considerably beyond — have set their sights on complex aspect ratios.
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