Independent component analysis (ICA)-the theory of mixed, independent, non-Gaussian sources-has a central role in signal processing, computer vision and pattern recognition. One of the most fundamental conjectures of this research field is that independent subspace analysis (ISA)-the extension of the ICA problem, where groups of sources are independent-can be solved by a simple ICA followed by grouping the ICA components. The conjecture, called ISA separation principle, (i) has been rigorously proven for some distribution types recently, (ii) forms the basis of the state-of-theart ISA solvers, (iii) enables one to estimate the unknown number and the dimensions of the sources efficiently, and (iv) can be extended to generalizations of the ISA task, such as different linear-, controlled-, post nonlinear-, complex valued-, partially observed problems, as well as to problems dealing with nonparametric source dynamics. Here, we shall review the advances on this field.

Person independent and pose invariant estimation of facial expressions and action unit (AU) intensity estimation is important for situation analysis and for automated video annotation. We evaluated raw 2D shape data of the CK+ database, used Procrustes transformation and the multi-class SVM leave-one-out method for classification. We found close to 100% performance demonstrating the relevance and the strength of details of the shape. Precise 3D shape information was computed by means of Constrained Local Models (CLM) on video sequences. Such sequences offer the opportunity to compute a time-averaged '3D Personal Mean Shape' (PMS) from the estimated CLM shapes, which-upon subtraction-gives rise to person independent emotion estimation. On CK+ data PMS showed significant improvements over AU0 normalization; performance reached and sometimes surpassed state-ofthe-art results on emotion classification and on AU intensity estimation. 3D PMS from 3D CLM offers pose invariant emotion estimation that we studied by rendering a 3D emotional database for different poses and different subjects from the BU 4DFE database. Frontal shapes derived from CLM fits of the 3D shape were evaluated. Results demonstrate that shape estimation alone can be used for robust, high quality pose invariant emotion classification and AU intensity estimation.

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