I think better cameras and helmet mount systems can remove a lot of shake... but I don't have any expensive gear. I also think there is a reason that the best cycling videos are not shot from the first person perspective. There are, however, FREE (I am incapable of typing the word 'FREE' without capitalizing it... hmmm...) after-the-fact remedies for all the shake and vibration inherent to inexpensive setups like mine (and theirs). The remedies I speak of are two bits of FREE software; VirtualDub and a plugin for it called Deshaker. I forget where I got them, but just google 'em up, they weren't hard to find. What was hard to find was a mix of deshaker settings that worked well with the moving camera on my bike, which I finally found after much trial and error. This stuff isn't perfect. The edges of the video get weird. The improvement, however, is remarkable. I'm going to show you some before and after video now, of course! Watch the whole thing... there's a 'happening' near the end that's kind of funny.
Please know that when I was riding by, that kid was laughing her head off over something, so no worries on the shove. Now, the deshaked version:
I don't want to bore everybody with the details of setting up deshaker. If you have an interest, email me and I will send you screenshots of the deshaker configuration screens and try to explain the process.
Shake It Only When You Should,