How do I take a full image backup of an Android device? I am trying to do a full system image backup of a Samsung Galaxy Tab 4.
It is unrooted at present, and is running Android Kitkat 4.4.2 . I have no desire of rooting it as of now. 

I have tried creating a full image backup of the device using the ADB (Android Debug Bridge) method (adb backup -apk -shared -all -f C:\backup.ab), which looks like it works, but when it completes, no backup files are created (Although the backup process is shown as having been completed).

Can anyone either offer advice on why the adb method doesn't work, or present an alternative solution to this? The end result should be a full backup image (including all apps and data) that I can use to restore the device back to its exact backup state.
Yes, you can, by taking a full NANDroid backup. This takes a backup of everything, including the app data, the accounts, the system, etc. with the exclusion of the files stored on the SD cards (both internal and external). 

Such NANDroid backups are usually taken with the help of a custom recovery, like the CWM (ClockWorkMod) recovery and the TWRP (TeamWin Recovery Project) recovery. If any custom recovery such as the ones mentioned here, or any other custom recovery based on them; is installed on your phone, then, you can proceed to do so. 

For more information, and some helpful resources you might want to see, please visit here and here.