Extending non-negative matrix factorisation to 3D registered data

© 2016 IEEE. The use of non-negative matrix factorisation (NMF) on 2D face images has been shown to result in sparse feature vectors that encode for local patches on the face, and thus provides a statistically justified approach to learning parts from wholes. However successful on 2D images, the method has so far not been extended to 3D images. The main reason for this is that 3D space is a continuum and so it is not apparent how to represent 3D coordinates in a non-negative fashion. This work compares different non-negative representations for spatial coordinates, and demonstrates that not all non-negative representations are suitable. We analyse the representational properties that make NMF a successful method to learn sparse 3D facial features. Using our proposed representation, the factorisation results in sparse and interpretable facial features.