Research Article

Evaluation of Interpolation Effects on Upsampling and Accuracy of Cost Functions-Based Optimized Automatic Image Registration

Table 6

The joint entropy for the registered images of matrix size of 256 × 256 × 120 using interpolations of trilinear, B-spline 3rd order, B-spline 4th order, cubic Lagrange, quintic Lagrange, heptic Lagrange, windowed Sinc, and cost functions of CR, LS, NCC, and NMI. Their entropies were achieved using mutual information.

InterpolationCost function Entropy

TrilinearCorrelation ratio2.3723
TrilinearLeast squares2.3718
TrilinearNormalized cross-correlation2.3704
TrilinearNormalized mutual information2.3787
B-spline 3rd orderCorrelation ratio2.4499
B-spline 3rd orderLeast squares2.4486
B-spline 3rd orderNormalized cross-correlation2.4489
B-spline 3rd orderNormalized mutual information2.4529
B-spline 4th orderCorrelation ratio2.3874
B-spline 4th orderLeast squares2.3889
B-spline 4th orderNormalized cross-correlation2.3891
B-spline 4th orderNormalized mutual information2.3881
Cubic LagrangeCorrelation ratio2.3649
Cubic LagrangeLeast squares2.3613
Cubic LagrangeNormalized cross-correlation2.3615
Cubic LagrangeNormalized mutual information2.3636
Quintic LagrangeCorrelation ratio2.3527
Quintic LagrangeLeast squares2.3559
Quintic LagrangeNormalized cross-correlation2.3534
Quintic LagrangeNormalized mutual information2.3544
Heptic LagrangeCorrelation ratio2.3549
Heptic LagrangeLeast squares2.3561
Heptic LagrangeNormalized cross-correlation2.3511
Heptic LagrangeNormalized mutual information2.3517
Windowed SincCorrelation ratio2.3425
Windowed SincLeast squares2.3452
Windowed SincNormalized cross-correlation2.3434
Windowed SincNormalized mutual information2.3443