Independent component analysis in statistical shape models

Statistical shape models generally use Principal Component Analysis (PCA) to describe the main directions of shape variation in a training set of example shapes. However, PCA assumes a number of restrictions on the data that do not always hold. In this paper we explore the use of an alternative shape decomposition, Independent Component Analysis (ICA), which does not assume a Gaussian distribution of the input data. Several different methods for performing ICA are available. Three most frequently used methods were tested in order to evaluate their effect on the resulting vectors. In statistical shape models, generally not all the eigenvectors that result from the PCA are used. Vectors describing noise are discarded to obtain a compact description of the data set. The selection of these vectors is based on the natural ordering of the vectors according to the variance in that direction which is inherent to PCA. With ICA, however, there is no natural ordering of the vectors. Four methods for sorting the ICA vectors are investigated. The different ICA-methods yielded highly similar yet not identical results. Vectors obtained with ICA showed localized shape variations, whereas eigenvectors obtained with PCA show global shape variations. From the results of the ordering methods can be seen that PCA is better suited for dimensionality reduction. Of the ordering methods that were tested, the best results were obtained with the ordering according to the locality of the shape variations.