On the adequacy of principal factor analysis for the study of shape variability

Abstract

The analysis of shape variability of anatomical structures is of key importance in a number of clinical disciplines, as abnormality in shape can be related to certain diseases. Statistical shape analysis techniques commonly employed in the medical imaging community, such as Active Shape Models or Active Appearance Models rely on Principal Component Analysis (PCA) to decompose shape variability into a reduced set of interpretable components. In this paper we propose Principal Factor Analysis (PFA) as an alternative to PCA and argue that PFA is a better suited technique for medical imaging applications. PFA provides a decomposition into modes of variation that are more easily interpretable, while still being a linear, efficient technique that performs dimensionality reduction (as opposed to Independent Component Analysis, ICA). Both PCA and PFA are described. Examples are provided for 2D landmark data of corpora callosa outlines, as well as vector-valued 3D deformation fields resulting from non-rigid registration of ventricles in MRI. The results show that PFA is a more descriptive tool for shape analysis, at a small cost in size (as in theory more components may be necessary to explain a given percentage of total variance in the data). In conclusion, we argue that it is important to study the potential of factor analysis techniques other than PCA for the application of shape analysis, and defend PFA as a good alternative.