We study the challenging problem of estimating the relative pose of three
calibrated cameras. We propose two novel solutions to the notoriously difficult
configuration of four points in three views, known as the 4p3v problem. Our
solutions are based on the simple idea of generating one additional virtual
point correspondence in two views by using the information from the locations
of the four input correspondences in the three views. For the first solver, we
train a network to predict this point correspondence. The second solver uses a
much simpler and more efficient strategy based on the mean points of three
corresponding input points. The new solvers are efficient and easy to implement
since they are based on the existing efficient minimal solvers, i.e., the
well-known 5-point relative pose and the P3P solvers. The solvers achieve
state-of-the-art results on real data. The idea of solving minimal problems
using virtual correspondences is general and can be applied to other problems,
e.g., the 5-point relative pose problem. In this way, minimal problems can be
solved using simpler non-minimal solvers or even using sub-minimal samples
inside RANSAC.
In addition, we compare different variants of 4p3v solvers with the baseline
solver for the minimal configuration consisting of three triplets of points and
two points visible in two views. We discuss which configuration of points is
potentially the most practical in real applications