Your ab muscles run right around your back, like a girdle. That's why people (like me) prattle on about core stability, that's the muscles we are referring to, as well as the muscles of your torso.
Abs are half the story. There are some great books on abs and back workouts. I would seriously consider getting a swiss or fit ball. They are fabulous, versatile and inexpensive, and you can do a range of exercises not only for your abs but for you whole body.
I have found since doing core training for four months, my back is loads stronger, and my back pain has all but disappeared.
Visualising your tummy button going to your back bone is a legitimate abs training technique. You can do that any time!!! Unless you wanna take a giant ball into your office
You do realise though, that stregthening the abs will help with your overall strength and fitness it won't decrease the size of your tummy. Any strength training needs to be accompanied by cardio, and in my experience, for a big tummy (I own one too) a lot of it.