I have a big .png file with 2160x1224 dimensions. I create hello world cpp project and replace HelloWorld.png with my big one. Run the app on my Android device and it shows nothing instead of showing my image. The rest such as labels, close button work OK. When I resize the image to become 1920x1080, image becomes visible. Why it does not show the image? See details here: http://stackoverflow.com/questions/26561282/android-how-to-know-maximal-size-of-the-image-that-the-device-can-load
This max texture size is device dependent. In my apps, I originally had 2048x2048 as my max texture sizes until I found some android devices that only supported 1024x1024!
To get around this, I break up large backgrounds into two pieces and automatically switch to the two piece version if a one piece does not exist.