In this work we introduce the usage of bilinear models as a means of factorising the shape variation induced by subject variability and the contraction of the human heart. We show that it is feasible to reconstruct the shape of the heart at a certain point in the cardiac cycle if we are given a small number of shapes representing the same heart at different points in the same cycle, using the bilinear model. Depending on pathology and the ratios between healthy and pathological hearts in the training set, RMS reconstruction errors measured between 1.39 and 16.58 millimetres, with a median of 6.79 and 90th percentile of 9.95 millimetres.

This work is framed in the field of statistical face analysis. In particular, the problem of accurate segmentation of prominent features of the face in frontal view images is addressed. We propose a method that generalizes linear Active Shape Models (ASMs), which have already been used for this task. The technique is built upon the development of a nonlinear intensity model, incorporating a reduced set of differential invariant features as local image descriptors. These features are invariant to rigid transformations, and a subset of them is chosen by Sequential Feature Selection for each landmark and resolution level. The new approach overcomes the unimodality and Gaussianity assumptions of classical ASMs regarding the distribution of the intensity values across the training set. Our methodology has demonstrated a significant improvement in segmentation precision as compared to the linear ASM and Optimal Features ASM (a nonlinear extension of the pioneer algorithm) in the tests performed on AR, XM2VTS, and EQUINOX databases.