The objective of this project is to study "electronic gaging" and create a system for automatic dimensional inspection of mechanical parts. The focus of this project is on developing theories and methods needed for systematically comparing the geometric variations of measured-features with their allowed tolerances. The approach to the data analysis is based on decomposing the measurement data into a set of features, and extracting their measures of imperfection. A set of formal definitions will be developed to express the meaning of such measures of imperfection as size, form, orientation, and position.