Measurement error in statistical models of shape

Active shape models (ASMs) are popular and sophisticated methods of extracting features in (especially medical) images. Here we analyse the error in placing ASM points on the boundary of the feature. By using replications, a corrected covariance matrix is presented that should reduce the effects of placement error. We show analytically and via simulations that the cumulative variability for a given number of eigenvalues retained in principal components analysis (PCA) ought to be reduced by increasing levels of point-placement error. Results for predicted errors are in excellent agreement with the set-up parameters of two simulated shapes and with anecdotal evidence from the trained experts for real data taken from the OSTEODENT project. We derive an equation for the reliability of placing the points and we find values of 0.79 and 0.85 (where 0 = bad and 1 = good) for the two clinical experts for the OSTEODENT data. These analyses help us to understand the sources and effects of measurement error in shape models.