Statistical 2D and 3D shape analysis using Non-Euclidean metrics

Abstract

The contribution of this paper is the adaptation of data driven methods for non-Euclidean metric decomposition of tangent space shape coordinates. This basic idea is to take extend principal components analysis to take into account the noise variance at different landmarks and at different shapes. We show examples where these non-Euclidean metric methods allow for easier interpretation by decomposition into biologically meaningful modes of variation. The extensions to PCA are based on adaptation of maximum autocorrelation factors and the minimum noise fraction transform to shape decomposition. A common basis of the methods applied is the assessment of the annotation noise variance at individual landmarks. These assessments are based on local models or repeated annotations by independent operators. © Springer-Verlag Berlin Heidelberg 2002.