Img = bg;
would assign Img a copy of the handle to the button group. There is no numeric index or image associated with a button group.
You are trying to use callbacks as if they are functions that return values. The only kinds of callbacks that ever return values are the callbacks that act as position filters, such as a Position Constraint callback for an imroi. Callbacks for uicontrol, uipanel, axes, button groups, plots, surfaces, contour plots, patches: it is impossible for any of those to return a value. Likewise, graphics objects do not return values either. You can ask what the current state of a graphics object is.
Perhaps you need to read How To Share Variables in Callbacks
