How to delete photos off of my iPhone?

I have an iPhone 5 with iOS 7.0.4. I'm trying to delete some photos I transferred from my computer (so the trash can is grayed out when trying to delete them from the photos app). When I plug my phone into iTunes and try to delete them like that, the album doesn't show up in iTunes for me to delete. How can I delete them without resetting my phone?

Sync an Empty folder to the iPhone. It'll erase all the albums.
Means set the default image directory to an empty DIR in itunes.