Statistical shape analysis using non-Euclidean metrics

The contribution of this paper is the adaptation of data driven methods for non-Euclidean metric decomposition of tangent space shape coordinates. The basic idea is to extend principal component analysis (PCA) 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 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. We show that the Molgedey–Schuster independent component analysis is equivalent to the maximum autocorrelation factors. Finally, the different subspace methods are compared using a probabilistic formulation based on their ability to represent the data.