The "Surge" and the shift to a population-centric COIN strategy obviously did not occur in a vacuum. One of the large contributors to the reduction of violence in Baghdad was the sectarian homogenization of neighborhoods. Take a look at the change from 2003 to mid-2008.
Larger maps covering Baghdad's sectarian layout in 2003, 2006, early 2007, late 2007, and 2008 can be found at the links provided.
A great deal of credit for the dramatic drops in Baghdad violence is given to the change in U.S. strategy, but Shiite militias running out of Sunnis to kill is a significant factor as well.