With computer graphic methods, we develop statistical descriptions of three-dimensional smooth surfaces to describe craniofacial malformations and propose surgical methods for their correction. For the past 16 years, modeling craniofacial malformations and statistical comparisons of these patients with a normal population has been the subject of our work, supported by grants from the National Institutes of Health and several private sources. Computerized tomographic scans of each patient are homology-mapped to a standard model of a normal skull. We devised statistical methods for comparing groups of patients, as well as the individual patient with normal standards. Surgical simulation and optimization software allows precise surgical planning for each patient. Averages of normal skulls appropriate for age, race, and sex serve as the optimization target. Recently, robotic vision system methods and virtual reality techniques have been used in the operating room to assure precise results of these surgical plans. Future applications of automatic homology mapping and statistical comparison with a normal set extend far beyond craniofacial malformations. This work will lead to semiautomatic identification of abnormalities in any organ system based on computerized tomographic and magnetic resonance scans.