We have shown how Supervised Descent Method outperforms state-of-the-art approaches in facial feature detection and tracking in challenging databases
Supervised Descent Method and Its Applications to Face Alignment
CVPR, no. 1 (2013): 532-539
Many computer vision problems (e.g., camera calibration, image alignment, structure from motion) are solved through a nonlinear optimization method. It is generally accepted that 2nd order descent methods are the most robust, fast and reliable approaches for nonlinear optimization of a general smooth function. However, in the context of c...更多
下载 PDF 全文
- Mathematical optimization has a fundamental impact in solving many problems in computer vision.
- There are a large number of different approaches to solve these continuous nonlinear optimization problems based on first and second order methods, such as gradient descent  for dimensionality reduction, Gauss-Newton for image alignment [22, 5, 14] or Levenberg-Marquardt for structure from motion .
- Mathematical optimization has a fundamental impact in solving many problems in computer vision
- The Supervised Descent Method learns a sequence of descent directions that minimizes the mean of Non-linear Least Squares functions sampled at different points
- This paper presents Supervised Descent Method, a method for solving Non-linear Least Squares problems
- Supervised Descent Method learns in a supervised manner generic descent directions, and is able to overcome many drawbacks of second order optimization schemes, such as nondifferentiability and expensive computation of the Jacobians and Hessians
- We have shown how Supervised Descent Method outperforms state-of-the-art approaches in facial feature detection and tracking in challenging databases
- Eq 3 allows to establish a direct connection with existing Parameterized Appearance Models for face alignment, and apply existing algorithms for minimizing it such as Gauss-Newton
- The first experiment compares the SDM with the Newton method in four analytic functions.
- The authors tested the performance of the SDM in the problem of facial feature detection in two standard databases.
- SDM on analytic scalar functions.
- This experiment compares the performance in speed and accuracy of the SDM against the Newton’s method on four analytic functions.
- The authors show how SDM improves state-of-the-art performance for facial feature detection in two “face in the wild” databases [26, 4] and demonstrate extremely good performance tracking faces in the YouTube celebrity database .
- The standard deviations of the scaling and translational perturbation were set to 0.05 and 10, respectively
- It indicates that in two consecutive frames the probability of a tracked face shifting more than 20 pixels or scaling more than 10% is less than 5%.
- The authors have shown how SDM outperforms state-of-the-art approaches in facial feature detection and tracking in challenging databases
- SDM learns in a supervised manner generic descent directions, and is able to overcome many drawbacks of second order optimization schemes, such as nondifferentiability and expensive computation of the Jacobians and Hessians.
- It is extremely fast and accurate.
- Eq 3 allows to establish a direct connection with existing PAMs for face alignment, and apply existing algorithms for minimizing it such as Gauss-Newton
- Table1: Experimental setup for the SDM on analytic functions
- This work is partially supported by the National Science Foundation (NSF) under the grant RI-1116583 and CPS0931999
- K. T. Abou-Moustafa, F. De la Torre, and F. P. Ferrie. Pareto discriminant analysis. In CVPR, 2010. 1
- S. Baker and I. Matthews. Lucas-Kanade 20 years on: A unifying framework. IJCV, 56(3):221 – 255, March 2004. 2
- M. Bartlett, G. Littlewort, M. Frank, C. Lainscsek, I. Fasel, and J. Movellan. Automatic recognition of facial actions in spontaneous expressions. Journal of Multimedia, 1(6):22–35, 2006. 6
- P. N. Belhumeur, D. W. Jacobs, D. J. Kriegman, and N. Kumar. Localizing parts of faces using a consensus of exemplars. In CVPR, 2011. 2, 3, 5, 6
- M. J. Black and A. D. Jepson. Eigentracking: Robust matching and tracking of objects using view-based representation. IJCV, 26(1):63–84, 1998. 1, 2
- V. Blanz and T. Vetter. A morphable model for the synthesis of 3D faces. In SIGGRAPH, 1999. 2
- G. Bradski. The OpenCV Library. Dr. Dobb’s Journal of Software Tools, 2000. 5
- A. Buchanan and A. W. Fitzgibbon. Damped newton algorithms for matrix factorization with missing data. In CVPR, 2005. 1
- R. H. Byrd, P. Lu, and J. Nocedal. A limited memory algorithm for bound constrained optimization. SIAM Journal on Scientific and Statistical Computing, 16(5):1190–1208, 1995. 2
- X. Cao, Y. Wei, F. Wen, and J. Sun. Face alignment by explicit shape regression. In CVPR, 2012. 4, 6
- T. Cootes, G. Edwards, and C. Taylor. Active appearance models. TPAMI, 23(6):681–685, 2001. 2, 4, 6
- T. F. Cootes, M. C. Ionita, C. Lindner, and P. Sauer. Robust and accurate shape model fitting using random forest regression voting. In ECCV, 203
- D. Cristinacce and T. Cootes. Automatic feature localisation with constrained local models. Journal of Pattern Recognition, 41(10):3054–3067, 2008. 3, 6
- F. De la Torre and M. H. Nguyen. Parameterized kernel principal component analysis: Theory and applications to supervised and unsupervised image alignment. In CVPR, 2008. 1, 2
- P. Dollar, P. Welinder, and P. Perona. Cascaded pose regression. In CVPR, 2010. 2, 4
- J. Friedman. Greedy function approximation: A gradient boosting machine. Annals of Statistics, 29(5):1189–1232, 2001. 2, 4
- R. Gross, I. Matthews, J. Cohn, T. Kanade, and S. Baker. Multi-pie. In AFGR, 2007. 6
- Y. Huang, Q. Liu, and D. N. Metaxas. A component-based framework for generalized face alignment. IEEE Transactions on Systems, Man, and Cybernetics, 41(1):287–298, 2011. 3
- M. J. Jones and T. Poggio. Multidimensional morphable models. In ICCV, 1998. 2
- M. Kim, S. Kumar, V. Pavlovic, and H. Rowley. Face tracking and recognition with visual constraints in real-world videos. In CVPR, 2008. 2, 6
- D. Lowe. Distinctive image features from scale-invariant keypoints. IJCV, 60(2):91–110, 2004. 2
- B. Lucas and T. Kanade. An iterative image registration technique with an application to stereo vision. In Proceedings of Imaging Understanding Workshop, 1981. 1, 2
- I. Matthews and S. Baker. Active appearance models revisited. IJCV, 60(2):135–164, 2004. 6
- S. Rivera and A. M. Martinez. Learning deformable shape manifolds. Pattern Recognition, 45(4):1792–1801, 2012. 3
- E. Sanchez, F. De la Torre, and D. Gonzalez. Continuous regression for nonrigid image alignment. In ECCV, 2012. 3
- J. Saragih. Principal regression analysis. In CVPR, 2011. 2, 3, 5, 6
- J. Saragih and R. Goecke. A nonlinear discriminative approach to AAM fitting. In ICCV, 2007. 2, 4
- J. Saragih, S. Lucey, and J. Cohn. Face alignment through subspace constrained mean-shifts. In ICCV, 2009. 3
- P. Tresadern, P. Sauer, and T. F. Cootes. Additive update predictors in active appearance models. In BMVC, 2010. 2, 4
- G. Tzimiropoulos, S. Zafeiriou, and M. Pantic. Robust and efficient parametric face alignment. In ICCV, 2011. 2
- X. Zhu and D. Ramanan. Face detection, pose estimation, and landmark localization in the wild. In CVPR, 2012. 3
- K. Zimmermann, J. Matas, and T. Svoboda. Tracking by an optimal sequence of linear predictors. TPAMI, 31(4):677–692, 2009. 3