View Invariants for Three-Dimensional Points with Constrained Observer Motion

Images from cameras are a common source of navigation information for a variety of vehicles. Such navigation often requires the matching of observed objects (e.g., landmarks, beacons, stars) in an image to a catalog (or map) of known objects. In many cases, this matching problem is made easier through the use of invariants. However, if the objects are modeled as three-dimensional points in general position, it has long been known that there are no invariants for a camera that is also in general position. This work discusses how invariants are introduced when the camera's motion is constrained to a line, and proves that this is the only camera path along which invariants are possible. Algorithms are presented for computing both the invariants and the location for a camera undergoing rectilinear motion. The applicability of these ideas is discussed within the context of trains, aircraft, and spacecraft.