How to control white space in figures in presence of text?

My main issue is in including graphs in a two-column article where space is very limited and white space around figure is to be minimized as far as possible. (I am trying to find an automated solution. I am aware of "trim" option of 'includegraphics' in LaTeX.)

I have seen the solution offered in Minimal White Space but it appears that any text that is placed on the figure is not taken into account during the creation of the tight box.

So a piece of code as in

str='$$G$$';
text(x,y,str,'Interpreter','latex')

could end up placing a letter G at position (x,y) but outside the box containing the figure.

I am looking for a code that will create a white box of a certain width H around the figure AND the texts placed on it.