The Camera Map modifier (object-space version) lets you blend an object into the background in a single frame.
This modifier works by assigning planar mapping coordinates based on the current frame and a specific camera in the scene. This differs from the Camera Map (WSM) modifier, which updates the object's mapping coordinates at every frame.
Left: The texture of an object with a Camera Map modifier matches the background when seen by the camera the modifier uses.
Right: When seen by a camera not used by Camera Map, the object’s texture is based on object geometry.
Blending an Object into the Background
The topic To Use the Camera Map Modifier (Object Space) shows how to blend an object into the background. If the background uses the same image as the object's texture map, then the object blends with the background at the frame where the modifier is applied and a camera is specified. The object becomes visible if either the camera or object moves. To make the illusion work, you must assign the same map to the background that you assign to the object.
If you want to move the camera and maintain the match to the background, use Camera Map (WSM) instead.
Mapping Coordinates
Because the accuracy of mapped objects depends partly on the complexity of the mesh, the "blend to background" effect works best when applied to an object with a relatively high density of triangular faces. The necessary density also depends on the distance of the object from the camera.
A simple box might look fine when it occupies only a small portion of the background, but up close the mapping will look distorted without adequate tessellation. Some experimentation is required to get an ideal mapping and still minimize the complexity of the geometry. (In general, for a box object that's filling a quarter of the screen, a tessellation of 4x4x4 works well.)