A Non-Iterative Solution to the Four-Point Three-Views Pose Problem in Case of Collinear Cameras

We give a non-iterative solution to a particular case of the four-point three-views pose problem when three camera centers are collinear. Using the well-known Cayley representation of orthogonal matrices, we derive from the epipolar constraints a system of three polynomial equations in three variables. The eliminant of that system is a multiple of a 36th degree univariate polynomial. The true (unique) solution to the problem can be expressed in terms of one of real roots of that polynomial. Experiments on synthetic data confirm that our method is robust enough even in case of planar configurations.