Abstract
A method is proposed to recover three-dimensional structure and motion of a moving rigid object. It is assumed that one can observe velocity fields generated at temporally discrete intervals by orthographic projection of a set of points belonging to one object whose rotational velocity component is constant.
From the condition of rigidity, an instantaneous rigidity condition is derived which states that the relative position vector between any two points is orthogonal to the corresponding relative velocity vector.
From the condition of constant rotational velocity component, each of the projected relative velocity vectors depicts a similar elliptical trajectory, the direction of whose longer axis is one and the same.
Then one can determine the equations of the ellipses by observing only two points in three views or three points in two views. The solution is obtained from a set of linear equations. The determined length of the longer axis enables one to determine the relative velocity and then the instantaneous rigidity condition is used to obtain the relative position. The special cases where the rotational axis is either perpendicular to or parallel with the image plane are discussed.
The above results are discussed in relation to the relevant psychophysical observations as well as the other theoretical studies.
