Tensor-based morphometry can recover three-dimensional longitudinal brain changes over time by nonlinearly registering baseline to follow-up MRI scans of the same subject. Here, we compared the anatomical distribution of longitudinal brain structural changes, over 12 months, using a subset of the ADNI dataset consisting of 20 patients with Alzheimer's disease (AD), 40 healthy elderly controls, and 40 individuals with mild cognitive impairment (MCI). Each individual longitudinal change map (Jacobian map) was created using an unbiased registration technique, and spatially normalized to a geometrically-centered average image based on healthy controls. Voxelwise statistical analyses revealed regional differences in atrophy rates, and these differences were correlated with clinical measures and biomarkers. Consistent with prior studies, we detected widespread cerebral atrophy in AD, and a more restricted atrophic pattern in MCI. In MCI, temporal lobe atrophy rates were correlated with changes in mini-mental state exam (MMSE) scores, clinical dementia rating (CDR), and logical/verbal learning memory scores. In AD, temporal atrophy rates were correlated with several biomarker indices, including a higher CSF level of p-tau protein, and a greater CSF tau/beta amyloid 1-42 (ABeta42) ratio. Temporal lobe atrophy was significantly faster in MCI subjects who converted to AD than in non-converters. Serial MRI scans can therefore be analyzed with nonlinear image registration to relate ongoing neurodegeneration to a variety of pathological biomarkers, cognitive changes, and conversion from MCI to AD, tracking disease progression in 3-dimensional detail.