A computer-implemented method of simulating orthodontic treatment, the method comprising: receiving a captured first 2D image, the first 2D image comprising a representation of a patient's face and a patient's teeth of a patient; identifying one or more shapes associated with at least one of the patient's teeth; building a parametric 3D model of the patient's teeth based on the 2D image, using one or more case-specific parameters for the one or more shapes associated with the at least one of the patient's teeth, wherein building the parametric 3D model includes: finding edges of teeth and lips in the first 2D image; aligning a parametric tooth model to the edges of the teeth and lips in the first 2D image to determine the case specific parameters; storing the case-specific parameters of the parametric tooth model that align the parametric tooth model with the edges of the teeth, gingiva, and lips in the first 2D image; and aligning the parametric 3D tooth model to the edges of the teeth, gingiva and lips in the first 2D image; simulating an outcome of a dental treatment plan for the patient's teeth to produce a simulated outcome of the dental treatment plan; modifying the parametric 3D model to provide a modified 3D model representing the simulated outcome of the dental treatment plan; and rendering, using the modified 3D model, a second 2D image representing the patient's face, the second 2D image representing the patient's teeth in accordance with the simulated outcome of the dental treatment plan. receiving a captured first 2D image, the first 2D image comprising a representation of a patient's face and a patient's teeth of a patient; identifying one or more shapes associated with at least one of the patient's teeth; building a parametric 3D model of the patient's teeth based on the 2D image, using one or more case-specific parameters for the one or more shapes associated with the at least one of the patient's teeth, wherein building the parametric 3D model includes: finding edges of teeth and lips in the first 2D image; aligning a parametric tooth model to the edges of the teeth and lips in the first 2D image to determine the case specific parameters; storing the case-specific parameters of the parametric tooth model that align the parametric tooth model with the edges of the teeth, gingiva, and lips in the first 2D image; and aligning the parametric 3D tooth model to the edges of the teeth, gingiva and lips in the first 2D image; finding edges of teeth and lips in the first 2D image; aligning a parametric tooth model to the edges of the teeth and lips in the first 2D image to determine the case specific parameters; storing the case-specific parameters of the parametric tooth model that align the parametric tooth model with the edges of the teeth, gingiva, and lips in the first 2D image; and aligning the parametric 3D tooth model to the edges of the teeth, gingiva and lips in the first 2D image; simulating an outcome of a dental treatment plan for the patient's teeth to produce a simulated outcome of the dental treatment plan; modifying the parametric 3D model to provide a modified 3D model representing the simulated outcome of the dental treatment plan; and rendering, using the modified 3D model, a second 2D image representing the patient's face, the second 2D image representing the patient's teeth in accordance with the simulated outcome of the dental treatment plan. <EOS>