Perspective mapping takes the world space coordinates and divides the X and Y coordinates by the Z coordinate (Figure 1). One way this is useful is by using a texture with this projection as the distribution, with black border mode. You can also use it for camera mapping. The same change as the other projections applies here: the image is mapped to (-1, -1) – (1, 1), so by default, offsets are not needed to use this mapping for projectors or camera mapping. The following image is from the Standalone version of Octane (figure 1).
Figure 1: The Perspective projection node orienting a Checks texture
Figure 2: Perspective projection applied to a box, cylinder, and sphere