View Invariants for Three-Dimensional Points with Constrained Observer Motion

Author:

McKee Paul D.1,Derksen Harm2,Christian John A.3ORCID

Affiliation:

1. Rensselaer Polytechnic Institute, Troy, New York 12180

2. Northeastern University, Boston, Massachusetts 02115

3. Georgia Institute of Technology, Atlanta, Georgia 30332

Abstract

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.

Funder

National Science Foundation

Publisher

American Institute of Aeronautics and Astronautics (AIAA)

Subject

Applied Mathematics,Electrical and Electronic Engineering,Space and Planetary Science,Aerospace Engineering,Control and Systems Engineering

Reference44 articles.

1. KohS. S., Invariant Theory, Springer, Berlin, 1987, pp. 1–7. 10.1007/BFb0078801

2. SpringerT. A., Invariant Theory, Springer, Berlin, 1977, Vol. 585, pp. 1–14. 10.1007/bfb0095644

3. Invariant Theory

4. Encyclopaedia of Mathematical Sciences;Derksen H.,2015

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