Reconstructing the Euclidean Geometry of One Point Viewed by an Uncalibrated Moving Camera

This paper addresses the problem of reconstructing the trajectory of a point viewed by an uncalibrated moving camera, in which at each frame all that is known is the 3D position of the camera. When the camera's inner parameters are also given it is trivial to reconstruct a xed point in space, which is the intersection of the rays given by the camera's centers and the viewed pixels. When the 3D points are restricted to move along a certain type of trajectory, such as a line or a conic it is also (nonlinearly) possible to reconstruct the speci c line or conic and the 3D positions of points viewed in each frame. If only the camera matrices are given, the reconstruction is up to a projective transformation. In this case of a moving point in 3D space, no corresponding relationship may be available. The Euclidean geometry of the trajectory of a xed point or a point moving along a straight line or a conic in 3D space can also be computed from uncalibrated views of this moving point. Each view is taken from a di erent position of a moving camera whose internal parameters are xed but unknown.