To take pictures without using the button, you must first activate the voice commands to applications. Press the 'Menu' button and then go to 'Settings'.
Scroll down the menu again until 'Language and input' appears.
Go to Category 'Voice cmd for applications' and slide the button 'OFF' to 'ON' so that it remains green, as in the attached image.
Now run the camera on your Samsung Galaxy SIII and when you're ready, say 'Shoot'. Automatically, the phone takes a photo.