It was only after a conversation with Larry Sromovsky (involving Leigh as well) that I came to understand how much processing lies behind these "images." Several techniques were required to bring out what are, in fact, very subtle (but clearly coherent) details.

The left image is actually composed of 117 exposures, the right 118. It has become quite common in astronomy to take large numbers of images at a fairly rapid rate and then stack them (or a subset of the sharpest ones) in order to bring out details. "Stacking" essentially means that you carefully align the images and then average them. This method accomplishes two things: it helps reduce the effects of random noise, and it sharpens the images.

Sromovsky explained that they did stack the images, but not before doing some preliminary work. Uranus rotates pretty quickly. The images shown here are about 350 pixels across, so Uranus' circumference is roughly 1000; divide that by the 17-hour rotation rate and you get roughly 60 pixels per hour, or one per minute. The smallest features I see here are a few pixels across; they'd be hopelessly smeared after a few minutes of imaging unless the rotation were accounted for.

That's pretty easy to fix, in a bit of work that's quite common in image processing. You "reproject" the images to flat maps. A view of Uranus from Earth is essentially an orthographic map projection. Convert each image from an orthographic to some cylindrical map projection. Then shift images left or right to account for Uranus' rotation. (I should be able to figure out whether it's left or right as time increases but Uranus, with its upside-down or retrograde-ness, gets me tied up in directional knots and I'd be guaranteed to pick the wrong one.)

But wait, it's more complicated than that. Uranus' visible "surface" is not a solid body; it's a hydrodynamically circulating atmosphere. Like all self-respecting giant planets, its winds move at different rates at different latitudes. So there's a second-order correction that the astronomers had to do, warping the image by shifting lines of pixels at different latitudes left or right, depending upon the observed zonal wind speeds. What are the wind speeds on Uranus? In fact, it's the same group of astronomers who figured out the answer to that question, publishing the (currently) definitive paper on Uranus' wind speeds as observed from cloud motions. Here's the graph: