Indiana University-Purdue University Indianapolis (IUPUI) ; Quantification of treatment outcomes (tooth displacement and bony changes) is the key to advance orthodontic research and improve clinical practices. Traditionally, treatment outcome were quantified by using two-dimensional (2D) cephalometric analysis. However, there are problems inherent in 2D analysis, such as tracing errors and inability to detect side-effects. Thus, a reliable three-dimensional (3D) image analysis method for treatment outcome quantification is of high interest. Systematic 3D image analysis methods were developed for digital dental cast models and Cone-Beam Computed Tomography (CBCT) models. A typical analysis procedure includes image reconstruction, landmarks identification, coordinate system setup, superimposition, and displacement or change calculation. The specified procedures for maxillary teeth displacements and anatomical landmarks movements were presented and validated. The validation results showed that these procedures were accurate and reliable enough for clinical applications. The 3D methods were first applied to a human canine retraction clinical study. The purposes of this study were to quantify canines and anchorage tooth movements, and to compare two commonly used canine retraction strategies, controlled tipping and translation. The canine results showed that (1) canine movements were linear with time; (2) the initial load system was not the only factor that controlled the canine movement pattern; and (3) control tipping was significantly faster than translation. The anchorage tooth results showed that (1) anchorage losses occurred even with transpalatal arch (TPA); (2) there was no significant difference in anchorage loss between the two treatment strategies; and (3) compared with removable TPA, fixed TPA appliance can significantly reduce the amount of anchorage loss in the mesial-distal direction. The second clinical application for the 3D methods was a mandibular growth clinical trial. The purposes of this study were to quantify skeletal landmark movements, and compare two widely used appliances, Herbst and MARA. The results showed that (1) the Herbst appliance caused mandibular forward movement with backward rotation; and (2) the treatment effects had no significant differences by using either Herbst or MARA appliances. The two clinical applications validated the methods developed in this study to quantify orthodontic treatment outcomes. They also demonstrated the benefits of using the 3D methods to quantify orthodontic treatment outcomes and to test fundamental hypotheses. These 3D methods can easily be extended to other clinical cases. This study will benefit orthodontic patients, clinicians and researchers.