1. A system for detecting deviations from an orthodontic treatment plan, the system comprising: at least one processor; and a computer readable medium including instructions that when executed cause the at least one processor to: receive a tracking model comprising a digital representation of an actual arrangement of a patient's teeth after an orthodontic treatment plan has begun for the patient for comparison to a plan model comprising a pre-determined planned arrangement of the patient's teeth; perform an alignment between the plan model and the tracking model using a partial region beyond a tooth crown of the plan model and a partial region beyond a tooth crown of the tracking model such that stationary elements of each of the plan model and the tracking model are aligned with one another, the alignment including detecting the partial region of each of the tracking model and the plan model based on a polygon formed from predetermined points on at least some of the teeth in the plan model and a polygon formed from predetermined points on at least some of the teeth in the tracking model; and detect one or more positional differences between the actual arrangement of the patient's teeth and the pre-determined planned arrangement of the patient's teeth.