registrations is preferred over training using cross-sectional data. Vice versa, training FPIR on cross-sectional data for cross-sectional registrations is preferred over training using longitudinal data. Comparisons are with respect to registration results obtained by numerical optimization (i.e., LDDMM).

Regression

:   As for regression, we compare linear models fitted to atrophy scores over time, where scores are either obtained from FPSGR or optimization-based SGR. Additionally, we study correlations between atrophy scores and diagnostic groups. Our hypothesis is that FPSGR is accurate enough to achieve comparable performance to optimization-based SGR, at much lower computational cost, in both situations.

Training of the prediction models
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We use a randomly selected set of 120 patients’ MRI images from `ADNI` for training the prediction models and to test the performance of FPIR. We use all of the `ADNI` data for our regression experiments.\
**Training for registration.** We randomly selected 120 subjects from `ADNI-1` and registered their baseline images to their 24 month follow-up images. We used the first 100 subjects for training and the remaining 20 subjects for testing. For *longitudinal training*, we registered the baseline image of a subject to the subject’s 24-month image. For *cross-sectional training*, we registered a subject’s baseline image to 