Machine vision systems that perform inspection tasks must be capable of making measurements. A vision system measures an image to determine a measurement of the object being viewed. The image measurement depends on several factors, including sensing, image processing, and feature extraction. We consider the error that can occur in measuring the distance between two corner points of the 2D image. We analyze the propagation of the uncertainty in edge point position to the 2D measurements made by the vision system, from 2D curve extraction, through point determination, to measurement. We extend earlier work on the relationship between random perturbation of edge point position and variance of the least squares estimate of line parameters and analyze the relationship between the variance of 2D points.