Collision detection with complex shapes

I am wanting to make a game that has each level loaded from an image. I want to draw up the whole level in Photoshop, and then set it as the background and allow the player to walk over it. I want another invisible image to go over top which will be black in all places that I want to collide with.

The reason I don't want to use tiles, which are much easier with rectangle collision and such, is because there will be complex corners and not everything will be rectangle.

Is this a good idea, and is it possible to do easily? Would this be a big CPU hog or is there a better way to do this?

Level image

Obstacles shown in red