New extensions of the 3-simplex for exterior orientation

Object pose may be determined from a set of 2D image points and corresponding 3D model points, given the camerapsilas intrinsic parameters. In this paper, two new exterior orientation algorithms are proposed and then compared against the Efficient PnP method and orthogonal iteration algorithm. As an alternative to the homogeneous transformation, both algorithms utilize the 3-simplex as a pose parameterization. One algorithm uses a semidefinite program and the other a Gauss-Newton algorithm.