The motivation for homographic modeling arose through the process of marking a reference frame with text or simple graphics, where it was noted that by calculating and matching homographies of the plane, an illusory rigid planar patch appeared to hover upon objects in the real-world, giving rise to a form of computer-mediated reality which was described in.
In homographic modeling, a spouse may leave a virtual ``Post-it'' note upon the entrance to a department store , (Fig 6),
Figure 6: Recipient of the virtual ``Post-It'' note approaches entrance to the grocery store and sees the message through his ``smart sunglasses''. Illusion of attachment (registration); the virtual note appears to be truly attached to the ``Star Market'' sign. (Thanks to Jeffrey Levine for ongoing collaboration on this project. )
or one might leave a grocery list on the refrigerator, that would be destined for a particular individual (not everyone wearing the special glasses would see the message -- only those wearing the glasses and on the list of intended recipients).
Note that the message is sent right away, but ``lives'' dormant on the recipient's WearComp until an image of the desired planar surface ``wakes up'' the message, at which point it appears in frames that lie within the same orbit of the projective group of coordinate transformations in which it was placed.
When the incoming video falls into the orbit (as defined by the projectivity + gain group of coordinate transformations) of one of the templates, the comparison switches modes from comparing each incoming frame with all of the templates to comparing each incoming frame with just the one that has been identified as being in the orbit.