Patch-Based Low-Rank Matrix Completion for Learning of Shape and Motion Models from Few Training Samples

Statistical models have opened up new possibilities for the automated analysis of images. However, the limited availability of representative training data, e.g. segmented images, leads to a bottleneck for the application of statistical models in practice. In this paper, we propose a novel patch-based technique that enables to learn representative statistical models of shape, appearance, or motion with a high grade of detail from a small number of observed training samples using low-rank matrix completion methods. Our method relies on the assumption that local variations have limited effects in distant areas. We evaluate our approach on three exemplary applications: (1) 2D shape modeling of faces, (2) 3D modeling of human lung shapes, and (3) population-based modeling of respiratory organ deformation. A comparison with the classical PCA-based modeling approach and FEM-PCA shows an improved generalization ability for small training sets indicating the improved flexibility of the model.