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Longitudinal analysis of anatomical changes is a vital component in many personalized-medicine applications for predicting disease onset, determining growth/atrophy patterns, evaluating disease progression, and monitoring recovery. Estimating anatomical changes in longitudinal studies, especially through magnetic resonance (MR) images, is challenging because of temporal variability in shape (e.g. from growth/atrophy) and appearance (e.g. due to imaging parameters and tissue properties affecting intensity contrast, or from scanner calibration). This paper proposes a novel mathematical framework for constructing subject-specific longitudinal anatomical models. The proposed method solves a generalized problem of joint segmentation, registration, and subject-specific atlas building, which involves not just two images, but an entire longitudinal image sequence. The proposed framework describes a novel approach that integrates fundamental principles that underpin methods for image segmentation, image registration, and atlas construction. This paper presents evaluation on simulated longitudinal data and on clinical longitudinal brain MRI data. The results demonstrate that the proposed framework effectively integrates information from 4-D spatiotemporal data to generate spatiotemporal models that allow analysis of anatomical changes over time.