Estimating three-dimensional motion parameters of a rigid planar patch

We present a new direct method of estimating the three-dimensional motion parameters of a rigid planar patch from two time-sequential perspective views (image frames). First, a set of eight pure parameters are defined. These parameters can be determined uniquely from the two given image frames by solving a set of linear equations. Then, the actual motion parameters are determined from these pure parameters by a method which requires the solution of a sixth-order polynomial of one variable only, and there exists a certain efficient algorithm for solving a sixth-order polynomial. Aside from a scale factor for the translation parameters, the number of real solutions never exceeds two. In the special case of three-dimensional translation, the motion parameters can be expressed directly as some simple functions of the eight pure parameters. Thus, only a few arithmetic operations are needed.