A Comparison of Digital Length Estimators for Image Features

Image analysis methods for estimating size of object features extract pixel-based measurements, after object segmentation, then convert these to an estimate of actual size; e.g. segmentation of a cell in a randomly located 2-D cross-sectional image, counting no. of pixels on the cell boundary, and converting to an estimate of cell surface area using geometrical formulae. Stereology takes a quite different approach to estimating higher dimensional properties of an object, by using a randomly orientated 2-D specimen section or 2-D projection of a 3-D object. Geometrical properties and sampling theory enable inference of 3-D properties; e.g. feature length is estimated by counting intersections with a randomly superimposed test grid with fixed known spacing. This work compares these two approaches for image feature length estimation, using a simulation study. We generate binary straight line structures and planar curves of known size and compare results from several different estimators of feature length, including a novel estimator which weights pixel count by estimating local curve orientation.