Is there such a thing as an 'Indie'/Alternative anime scene? Having followed anime for some time, one thing I have noticed, at least from my perspective, is that there is no equivalent of the Indie/Alternative scene when it comes to anime.

What I mean by this is that the vast majority of anime seems to be produced and distributed by some corporate production studio(s). While my knowledge of anime production is quite limited, this would seem to hold for most anime.

What reasons are there for this trend or am I wrong in assuming the lack of an alternative scene?

If I am wrong, then what can be considered as Indie anime? 

Notes: In response to Euphorics's comment, 'Anime' in this context refers to any and all forms of Japanese animated media. The form of distribution, length and animation style are the kind of details I'm looking for in the answers.

Additionally, I am aware of the existence of Doujinshi as a form of independently made Manga, although I wasn't aware of the fact that it included music as well (Thank you Rapitor for that) but I am mainly interested in the animated medium in the context of this question.
There's Voices of a Distant Star, which was "directed, written, produced, character designed, storyboarded, cinematographed, edited, and animated by Makoto Shinkai". Essentially an individual effort except for some voice acting that was done by his wife Mika Shinohara. The DVD release had to go through a manufacturer and distributor, of course but I think that's as close as Indie/Alternative as you'll get.

There aren't many anime like that, as anime TV series or movies are very expensive and time consuming to produce. This is why even small anime studios often rely on production and backing from larger companies (like TV studios). Instances like Voices of a Distant Star is rare because it's short, and probably made no money.