Abstract
In this paper, we compare four different Subspace Multiple Linear Regression methods for 3D face shape prediction from a single 2D intensity image. This problem is situated within the low observation-to-variable ratio context, where the sample covariance matrix is likely to be singular. Lately, efforts have been directed towards latent-variable based methods to estimate a regression operator while maximizing specific criteria between 2D and 3D face subspaces. Regularization methods, on the other hand, impose a regularizing term on the covariance matrix in order to ensure numerical stability and to improve the out-of-training error. We compare the performance of three latent-variable based and one regularization approach, namely, Principal Component Regression, Partial Least Squares, Canonical Correlation Analysis and Ridge Regression. We analyze the influence of the different latent variables as well as the regularizing parameters in the regression process. Similarly, we identify the strengths and weaknesses of both regularization and latent-variable approaches for the task of 3D face prediction.
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Ahmed, A., Farag, A.: A New Statistical Model Combining Shape and Spherical Harmonics Illumination for Face Reconstruction. In: Bebis, G., Boyle, R., Parvin, B., Koracin, D., Paragios, N., Tanveer, S.-M., Ju, T., Liu, Z., Coquillart, S., Cruz-Neira, C., Müller, T., Malzbender, T. (eds.) ISVC 2007, Part I. LNCS, vol. 4841, pp. 531–541. Springer, Heidelberg (2007)
Atick, J., Griffin, P., Redlich, N.: Statistical approach to shape from shading: Reconstruction of three-dimensional face surfaces from single two-dimensional images. Neural Computation 8, 1321–1340 (1996)
Blanz, V., Vetter, T.: A morphable model for the synthesis of 3d faces. In: Proc. SIGGRAPH, pp. 187–194 (1999)
Blanz, V., Vetter, T.: Face recognition based on fitting a 3d morphable model. IEEE Trans. Pattern Anal. Mach. Intell. 25(9), 1063–1074 (2003)
Castelán, M., Smith, W., Hancock, E.: A coupled statistical model for face shape recovery from brightness images. IEEE Transactions on Image Processing 16(4), 1139–1151 (2007)
Castelán, M., Van Horebeek, J.: 3D face shape approximation from intensities using Partial Least Squares. In: Proc. IEEE CVPRW, pp. 1–6 (2008)
Cootes, T., Edwards, G., Taylor, C.: Active appearance models. In: Burkhardt, H., Neumann, B. (eds.) ECCV 1998. LNCS, vol. 1407, pp. 484–498. Springer, Heidelberg (1998)
Frank, I., Friedman, J.: A statistical view of some chemometrics regression tools. Technometrics 25(2), 109–135 (1993)
Geladi, P., Kowalski, B.: Partial least squares regression: a tutorial. Anal. Chim. Acta 185, 1–17 (1986)
Hoegaerts, L., Suykens, J.A.K., Vandewalle, J., De Moor, B.: Kernel PLS variants for regression. In: Proc. of the 11th European Symposium on Artificial Neural Networks, pp. 203–208 (2003)
Hotelling, H.: Relations between two sets of variates. Biometrika 8, 321–377 (1936)
Horn, B., Brooks, M.: Shape from Shading. MIT Press, Cambridge (1989)
Kemelmacher, I., Basri, R.: Molding Face Shapes by Example. In: Leonardis, A., Bischof, H., Pinz, A. (eds.) ECCV 2006. LNCS, vol. 3951, pp. 277–288. Springer, Heidelberg (2006)
Sirovich, L., Kirby, M.: Low-dimensional Procedure for the Characterization of Human Faces. Journal of the Optical Society of America 4, 519–524 (1987)
Lei, Z., Bai, Q., He, R., Li, S.Z.: Face Shape Recovery from a Single Image Using CCA Mapping between Tensor Spaces. In: Proc. IEEE CVPR, pp. 1–7 (2008)
Li, A., Shan, S., Chen, X., Chai, X., Gao, W.: Recovering 3D facial shape via coupled 2D/3D space learning. In: Proc. IEEE International Conference on Automatic Face and Gesture Recognition, pp. 1–6 (2008)
Reiter, M., Donner, R., Langs, G., Bischof, H.: 3d and Infrared Face Reconstruction from RGB Data Using Canonical Correlation Analysis. In: Proc. IEEE ICPR (2006)
Smith, W.A.P., Hancock, E.R.: Recovering Facial Shape Using a Statistical Model of Surface Normal Direction. IEEE Trans. Pattern Anal. Mach. Intell. 28(12), 1914–1930 (2006)
Smith, W.A.P., Hancock, E.R.: Facial shape-from-shading and recognition using principal geodesic analysis and robust statistics. International Journal of Computer Vision 76(1), 71–91 (2008)
Worthington, P.L., Hancock, E.R.: New constraints on data-closeness and needle map consistency for shape-from-shading. IEEE Trans. on Pattern Analysis and Machine Intelligence 21(12), 1250–1267 (1999)
Zheng, Y., Wang, Z.: Robust depth estimation for efficient 3D face reconstruction. In: Proc. IEEE ICIP, pp. 1516–1519 (2008)
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Castelán, M., Puerto-Souza, G.A., Van Horebeek, J. (2009). Using Subspace Multiple Linear Regression for 3D Face Shape Prediction from a Single Image. In: Bebis, G., et al. Advances in Visual Computing. ISVC 2009. Lecture Notes in Computer Science, vol 5876. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10520-3_63
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DOI: https://doi.org/10.1007/978-3-642-10520-3_63
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