Table 3. Comparison of resultant matrices computed from 3-point change of basis technique and 5-point linear least squares method. The matrices are presented from CRW-to-MidACPC and the reverse as 3 x 4, where the 3 x 3 components are the rotational vectors and the last column is the translation. One can observe that the matrices are very similar and a simple delta, subtraction, between each is presented. Analysis of the 3 x 3 vector component of each matrix by orthonormality and orthogonality are close to 1 and 0, respectively, which would be expected in this affine system.

CRW = Cosman-Roberts-Wells; Mid-ACPC = Middle of Anterior Commissure (AC) and Posterior Commissure (PC); AP = Antero-Posterior; LAT = Lateral; VERT = Vertical.

CRW-					MidACPC-
MidACPC	Matrix 1:				CRW	Matrix 2:
Change of Basis	0.993792	-0.03941	0.104036	2.05		0.993792	0.032717	-0.106	-1.726
3-points	0.032717	0.997329	0.065298	2.5		-0.03941	0.997329	-0.061	-2.185
	-0.10633	-0.06149	0.992428	3.7		0.104036	0.065298	0.9924	-4.049
	Matrix 3:					Matrix 4:
Linear Least Squares	0.993983	-0.04348	0.104011	2.021192		0.993471	0.036872	-0.107	-1.707
5-points	0.033201	0.995652	0.065853	2.472828		-0.03998	0.998827	-0.062	-2.161
	-0.10593	-0.06087	0.992991	3.680035		0.103533	0.065161	0.9919	-4.021
Delta	-0.00019	0.004065	2.51E-05	0.028808		0.000322	-0.00415	0.0002	-0.018
	-0.00048	0.001677	-0.00056	0.027172		0.000563	-0.0015	0.0006	-0.024
	-0.0004	-0.00062	-0.00056	0.019965		0.000503	0.000137	0.0005	-0.028
		Orthonormality	Orthonormality	Orthonormality	Orthogonality	Orthogonality	Orthogonality
		AP	LAT	VERT	AP-LAT	LAT-VERT	AP-VERT
	Matrix 1	1	1	1	-1.39E-15	1.19E-15	3.25E-15
	Matrix 2	1	1	1	1.26E-15	-1.33E-15	-2.73E-15
	Matrix 3	1.000711	0.996762	1.000959	-0.00344	0.00127	0.000633
	Matrix 4	0.999687	1.003105	0.998815	0.003722	-0.0006	-0.00038