Sample sufficiency and number of modes to retain in statistical shape modelling

Abstract

Statistical shape modelling is a popular technique in medical imaging, but the issue of sample size sufficiency is not generally considered. Also the number of principal modes retained is often chosen simply to cover a percentage of the total variance. We show that these simple rules are unreliable. We propose a new method that uses bootstrap replication and a t-test comparison with noise to decide whether each mode direction has stabilised. We establish mode correspondence by minimising the distance between the space spanned by the replicates and their mean. By retaining only stable modes, our method distinguishes real anatomical variation from modes dominated by random noise. This provides a lower stopping rule when the sample is small and converges as the sample size increases. We use this convergence to determine sample sufficiency. For validation we use synthetic datasets of the left ventricle generated with a known number of structural modes and added noise. Our stopping rule detected the correct number of modes to retain where other methods failed. The methods were also tested on real 2D (22 points) and 3D (500 points) face data, retaining 24 and 70 modes with sample sufficiency being reached at approximately 50 and 150 samples respectively. For a 3D database of the left ventricle (527 points), 319 samples are not sufficient, but at this level we can retain around 55 stable modes. Our method provides a principled foundation for appropriate selection of the number of modes to retain and determination of sample size sufficiency for statistical shape modelling. © 2008 Springer-Verlag Berlin Heidelberg.