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.

[1]  Jean B. Lasserre,et al.  Global Optimization with Polynomials and the Problem of Moments , 2000, SIAM J. Optim..

[2]  Richard I. Hartley,et al.  Minimizing algebraic error in geometric estimation problems , 1998, Sixth International Conference on Computer Vision (IEEE Cat. No.98CH36271).

[3]  Gregory D. Hager,et al.  Fast and Globally Convergent Pose Estimation from Video Images , 2000, IEEE Trans. Pattern Anal. Mach. Intell..

[4]  Kostas Daniilidis,et al.  Linear Pose Estimation from Points or Lines , 2002, ECCV.

[5]  Berthold K. P. Horn,et al.  Closed-form solution of absolute orientation using unit quaternions , 1987 .

[6]  Johan Löfberg,et al.  YALMIP : a toolbox for modeling and optimization in MATLAB , 2004 .

[7]  Vincent Lepetit,et al.  Accurate Non-Iterative O(n) Solution to the PnP Problem , 2007, 2007 IEEE 11th International Conference on Computer Vision.

[8]  Long Quan,et al.  Linear N-Point Camera Pose Determination , 1999, IEEE Trans. Pattern Anal. Mach. Intell..

[9]  Berthold K. P. Horn,et al.  Closed-form solution of absolute orientation using orthonormal matrices , 1988 .

[10]  Jos F. Sturm,et al.  A Matlab toolbox for optimization over symmetric cones , 1999 .

[11]  Paul D. Fiore,et al.  Efficient Linear Solution of Exterior Orientation , 2001, IEEE Trans. Pattern Anal. Mach. Intell..

[12]  J. Lofberg,et al.  YALMIP : a toolbox for modeling and optimization in MATLAB , 2004, 2004 IEEE International Conference on Robotics and Automation (IEEE Cat. No.04CH37508).