Track warping & moving objects in After Effects and replace them with another object.

Threw this together in about 2 minutes. Create a comp from the footage, add a solid that is the same size as the image you want to apply to the paper, pre-compose the solid layer but do not move all attributes to the new comp so you get a pre-comp that is the same size as the solid, add grid to the solid in the pre-comp, return to the main comp and apply mesh warp to the pre-comp and adjust it so that the perspective closely matches. When you get the mesh perfected then all you have to do is return to the pre-comp, drop the replacement image in the pre-comp and animate its Y position to match the speed of the paper coming out of the printer. A black to white gradient filled shape layer as an overlay using the screen or add blend mode and your new image is now on the paper. Here's the start:

This isn't perfect but it could be perfect with a little tweaking of the mesh and a couple of keyframes. No fancy tracking required. Pretty much what Mylenium suggested.

Wrong approach. Build a warp at comp size usingt Mesh Warp based on a pre-comp where the image is moving from top to bottom. The edges can easily be cut off suing masks or linear wipes. Of course you may need to apply additional effects for tiny corrections and you will have to figure out ways to re-create the shading for the highlights etc., but otherwise this should be simple enough.

Mylenium