. Author manuscript; available in PMC: 2021 Sep 22.

Published in final edited form as: Med Image Comput Comput Assist Interv. 2009;12(Pt 2):466–473. doi: 10.1007/978-3-642-04271-3_57

Algorithm 3.

Gram-Schmidt procedure applied to $J e_{1}$ , $J e_{2}$ , and $J e_{3}$

1:	Initialize $v_{i} = J e_{i}$ for 1 ≤ i ≤ 3
2:	compute u₁: u₁ = v_l
3:	compute $u_{2} : u_{2} = v_{2} - {proj}_{u_{1}} v_{2}$ , where proj_ab = (a^Tb)a/(a^Ta)
4:	compute $u_{3} : u_{3} = v_{3} - {proj}_{u_{1}} v_{3} - {proj}_{u_{2}} v_{3}$
5:	compute $e_{1}^{'}$ , $e_{2}^{'}$ , and $e_{3}^{'} : e_{1}^{'} = u_{1} / ‖ u_{1} ‖$ , $e_{2}^{'} = u_{2} / ‖ u_{2} ‖$ , and $e_{3}^{'} = u_{3} / ‖ u_{3} ‖$