Handling Repeated Solutions to the Perspective Three-Point Pose Problem

Abstract

In the Perspective 3-Point Pose Problem (P3P), with the three control points equidistant from each other, a repeated solution occurs when and only when a certain equation is satisfied. When the setup only approximately satisfies this equation, two nearly equal solutions can introduce substantial calculation errors. To better handle this circumstance, it may be preferable to behave as though the equation holds precisely, and invert a certain two-dimensional transformation to obtain the repeated solution. The inversion involves only a few basic arithmetic operations and square roots. This approach is much more efficient and more reliable, than the standard quartic equation approach to solving P3P, at least in this special case.