I need some help with a lot of the symbols in these series of equations.

http://i5.photobucket.com/albums/y17...e/equation.jpg

I'm assuming \Delta g(x,y) is some kind of array or matrix. I need to know how exactly |g1(x,y) - g2(x,y)| is calculated.

Also for equation 2, I'm at lose for how to solve for mx and my.

For equation 3, is \delta ^ 2 some kind of weird symbol for second derivative? \delta is introduced so suddenly I don't really know what to do with it.