One-Way Functions vs. perfectly binding commitments
In a recent work with Rafael Pass, it is shown that without those extra complexity assumptions of Barak-Ong-Vadhan, noninteractive commitments can not be based on one-way functions in a black-box way. In fact even with these extra assumptions (when formalized as some kind of hitting property assumed in addition to one-way-ness) still a black-box separation holds:

http://eprint.iacr.org/2012/523.pdf

(the construction of Barak-Ong-Vadhan is non-black-box).