In photographs of Jupiter, the limb seems extremely definite. Being a gas giant, my naive self thinks that the atmosphere should have a more gradual cut off, creating a hazy effect similar to that on Titan. I am aware of Jupiter's immense size, so each pixel in the linked photograph is likely tens or hundreds of kilometers. Even so, wouldn't there be some small smudge? Does perhaps Jupiter's terrific gravity have any effect on the apparent edge of its atmosphere?
Your first inclination is correct. It's a matter of scale. Jupiter is HUGE. I'll resist quoting Douglas Adams here, but the human brain just isn't equipped to deal with those sort of dimensions. Add to that the distance from which that photograph was taken. You are actually beyond the orbit of the moon Io in that picture, so scale will be even more set off than usual.
In looking at the specific photograph you posted, there may have been some post processing effects as well in terms of colour and clarity (due to some pixelation effects on the limb), although in this case I may have to claim some ignorance. However, there have been experiments done where the Galileo probe actually watched a star as it passed the limb of Jupiter, and measured the atmospheric extent. I can't find that exact experiment, but here is a UV shot that again appears pretty defined, until you realize the distances you are dealing with.
Image Source: NASA
This picture does show some apparent haze, but I only have a few details on it (i.e. New Horizon's image courtesy NASA as posted on the Boston Globe). I have no idea the wavelength or any other parameters.
So again, our scale of perspective is thrown off because of the huge size of the planet.
[Great answer, Larian. Just wanted to add a bit.]
Some graphs that didn't make the cut for this paper show the density of a self-gravitating sphere in hydrostatic equilibrium as a function of radius. A defining feature of the equations that determine the structure of a fluid sphere like Jupiter (or stars, white dwarfs, neutron stars, etc.) is that the pressure and density hold relatively steady for a while and then exhibit this crash to zero.
With the caveat that you have to be prepared to evaluate words like "thick," "thin," "fast," and "crash" on not-human scales, as Larian mentioned, the crash to zero pressure and density is quite fast in the sense that it happens within a very thin, uppermost layer of the sphere.
EDIT: Aha! But one of them made it into this paper. See figure 8, bold line.