Methods and systems for modeling objects and object image data using medial atoms are disclosed. Objects and object image data can be modeled using medial atoms. Each medial atom includes at least two vectors having a common tail and extending towards an implied boundary of a model. The medial atoms may be aligned along one or more medial axes in the model. The model may include multiple sub-components, referred to as figures. The model and each of its figures may be represented in model-based and figure-based coordinates. The model may be automatically deformed into target image data using a hierarchy of geometric or probabilistic transformations.