Geometric Stratification for Singular Configurations of the P3P Problem via Local Dual Space

This paper investigates singular configurations of the P3P problem. Using local dual space, a systematic algebraic-computational framework is proposed to give a complete geometric stratification for the P3P singular configurations with respect to the multiplicity μ of the camera center O: for μ≥ 2, O lies on the ``danger cylinder'', for μ≥ 3, O lies on one of three generatrices of the danger cylinder associated with the first Morley triangle or the circumcircle, and for μ≥ 4, O lies on the circumcircle which indeed corresponds to infinite P3P solutions. Furthermore, a geometric stratification for the complementary configuration O^prime associated with a singular configuration O is studied as well: for μ≥ 2, O^prime lies on a deltoidal surface associated with the danger cylinder, and for μ≥ 3, O^prime lies on one of three cuspidal curves of the deltoidal surface.