An automatic inspection method contactlessly measures the offset of a feature of an object from a theoretical ideal center of the object, and is particularly suited for measuring at an endface of an optical fiber termination the eccentricity of an optical fiber core relative to a theoretical ideal center of the termination. The core is extremely smaller (typically between about 50 and 500 times) in size than the termination boundary. An inspection system for implementing the novel inspection method has a feature imager, one or more boundary segment imagers but preferably four in number, and a machine vision system connected to the foregoing imagers. The feature imager is positioned to capture an image of the feature (e.g., fiber core endface), and the one or more boundary segment imagers are positioned to capture an image of a corresponding boundary segment of the object (e.g., termination endface). The machine vision system determines the offset, or eccentricity, based upon the feature image and the one or more boundary segment images.