(
A,B) Structure of Hessian matrix used during optimisaton in the Lucas–Kanade framework in the parameter formulation used by (
A)
Greenberg and Kerr (2009) and (
B) in this work for the 3D (x, y, z) case with 10 realignment points in total. Grey and white checkerbox indicate elements of the Hessian Matrix. Blue squares indicate matrix elements associated with the second realignment position, red squares indicate matrix elements associated with the third realignment position and yellow squares indicate matrix elements associated with both the second and third realignment position. (
C) Time required for realignment of the 512 × 512 × 51 3D intensity data shown in
Figure 7 using 15 realignment points per z position (2295 parameters in total) and 51 time points using (i) conventional factorisation, (iii) banded factorisation and (iii) banded factorisation with GPU computation of the error function and Jacobian.