However, as both FPIR and SGR are based on LDDMM, they naturally integrate and hence result in our proposed [*fast predictive simple geodesic regression (FPSGR)*]{} approach.

1ex Our *contributions* can be summarized as follows:\

Predictive geodesic regression

:   We use a fast predictive registration approach for image geodesic regression. Different to [@quicksilver], we specifically validate that our approach can indeed capture the frequently subtle deformation trends of *longitudinal* image data.

Large-scale dataset capability

:   Our predictive regression approach facilitates large-scale image regression within a short amount of time on a single GPU, instead of requiring months of computation time for standard optimization-based methods on a single computer, or on a compute cluster.

Accuracy

:   We assess the accuracy of FPSGR by (1) studying linear models of atrophy scores (which are derived from the nonlinear SGR model) over time, as well as (2) correlations between atrophy scores and various diagnostic groups.

Validation

:   We demonstrate the performance of FPSGR by analyzing $>6000$ images of the `ADNI-1` / `ADNI-2` datasets. For comparison, we also perform SGR using numerical optimization for the registrations, again on the complete `ADNI-1` / `ADNI-2` datasets.

1ex This work is an extension of a recent conference paper [@ding2017]. 