It is widely known that the optimization of imaging systems based on objective, or task-based, measures of image quality via computer-simulation requires use of a stochastic object model (SOM). However, the development of computationally tractable SOMs that can accurately model the statistical variations in anatomy within a specified ensemble of patients remains a challenging task. Because they are established by use of image data corresponding a single patient, previously reported numerical anatomical models lack of the ability to accurately model inter- patient variations in anatomy. In certain applications, however, databases of high-quality volumetric images are available that can facilitate this task. In this work, a novel and tractable methodology for learning a SOM from a set of volumetric training images is developed. The proposed method is based upon geometric attribute distribution (GAD) models, which characterize the inter-structural centroid variations and the intra-structural shape variations of each individual anatomical structure. The GAD models are scalable and deformable, and constrained by their respective principal attribute variations learned from training data. By use of the GAD models, random organ shapes and positions can be generated and integrated to form an anatomical phantom. The randomness in organ shape and position will reflect the variability of anatomy present in the training data. To demonstrate the methodology, a SOM corresponding to the pelvis of an adult male was computed and a corresponding ensemble of phantoms was created. Additionally, computer-simulated X-ray projection images corresponding to the phantoms were computed, from which tomographic images were reconstructed.