Registration Protocol

The following registration protocol was used to produce the registration results using the method described in [17] and summarized in Section 3. The values of $\sigma =1.0$, $\alpha = 0.1$, $\beta =0.1$ , $\gamma = 0.0$ and $\rho = 0.00125$ in Eqs. 5 and 7 were fixed for all experiments. For the consistent linear-elastic registration, the following values of $\chi = 2500$, $\chi = 600$, and $\chi = 2500$, were used for the phantom, CT, and MRI experiments, respectively. The values for $\sigma$, $\rho$ and $\chi$ are chosen by experimentation to give the desired trade off between inverse consistency error and squared intensity registration error.

The phantoms were registered at the $128 \times 128$ resolution. The registration started by estimating the lowest frequency basis coefficients ( $d_1=d_2=d_3=1$) in the transformation parameterization, Eq. 8. The number of frequency basis coefficients estimated was increased every 250 iterations, and the algorithms were run until a total of 1500 iterations. The run time was less than 5 minutes on a DCG AlphaPC using a single 667 MHz, alpha 21264 processor.

The CT data were registered for 2000 iterations at 1/8 resolution, 2000 iterations at 1/4 resolution, 100 iterations at 1/2 resolution, and 10 iterations at full resolution. The initial maximum harmonic was set at one and was increased by one after every 400 iterations at 1/8 resolution, 400 iterations at 1/4 resolution, and 50 iterations at 1/2 resolution. The number of harmonics was not increased at the full resolution. The large number of iterations at the low resolution assured convergence of the gradient descent at each resolution. The total run time took approximately 3 hours.

The protocol for the MRI data registrations was similar to that of the CT data except that only 500 iterations were used at the 1/8 and 1/4 resolutions and the harmonics were incremented every 100 iterations at these resolutions. The total run time for the MRI data was approximately 1.5 hours.

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