How can I initiate OS X installation from a dmg in Windows on a Mac?
As far as I know, you can't "launch" the installation directly from Windows. From there, you have two choices :


Normally, you should have a recovery partition on your Mac. Boot on this one, you'll be able to repair or reinstall OS X.
Create a bootable USB stick with OS X on it to reinstall your main partition. There are lots of tutorials that show how to create a bootable OS X USB stick on Google, it's pretty easy to find. 


Good luck