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.
KeywordsStatistical modeling High-dimension-low-sample-size problem Low-rank matrix completion Virtual samples
This work was supported by the German Research Foundation (DFG EH 224/6-1).
- 2.Balzano, L., Wright, S.J.: On GROUSE and incremental SVD. In: Computational Advances in Multi-sensor Adaptive Processing (CAMSAP), pp. 1–4 (2013)Google Scholar
- 12.He, J., Balzano, L., Szlam, A.: Incremental gradient on the grassmannian for online foreground and background separation in subsampled video. CVPR 2012, 1568–1575 (2012)Google Scholar
- 14.Kennedy, R., Taylor, C.J., Balzano, L.: Online completion of ill-conditioned low-rank matrices. In: IEEE Global Conference on Signal and Information Processing (GlobalSIP), pp. 507–511 (2014)Google Scholar
- 16.Kumar, R., Banerjee, A., Vemuri, B.C., Pfister, H.: Maximizing all margins: pushing face recognition with kernel plurality. ICCV 2011, 2375–2382 (2011)Google Scholar
- 17.Lai, R.Y., Yuen, P.C.: ProPPA: a fast algorithm for \(\ell _1\) minimization and low-rank matrix completion, May 2012. arXiv preprint arXiv:1205.0088
- 19.Lu, J., Tan, Y.P., Wang, G.: Discriminative multi-manifold analysis for face recognition from a single training sample per person. ICCV 2011, 1943–1950 (2011)Google Scholar
- 21.Mishra, B.: A Riemannian approach to large-scale constrained least-squares with symmetries. Ph.D. thesis, Université de Namur (2014)Google Scholar
- 22.Ngo, T., Saad, Y.: Scaled gradients on grassmann manifolds for matrix completion. NIPS 2012, 1412–1420 (2012)Google Scholar
- 23.Nordstrøm, M.M., Larsen, M., Sierakowski, J., Stegmann, M.B.: The IMM face database-an annotated dataset of 240 face images. Technical report, Technical University of Denmark, DTU Informatics (2004)Google Scholar
- 27.Turk, M.A., Pentland, A.P.: Face recognition using eigenfaces. In: CVPR 1991, pp. 586–591. IEEE (1991)Google Scholar
- 31.Zhu, P., Zhang, L., Hu, Q., Shiu, S.C.K.: Multi-scale patch based collaborative representation for face recognition with margin distribution optimization. In: Fitzgibbon, A., Lazebnik, S., Perona, P., Sato, Y., Schmid, C. (eds.) ECCV 2012, Part I. LNCS, vol. 7572, pp. 822–835. Springer, Heidelberg (2012)Google Scholar