The Community for Technology Leaders
RSS Icon
Subscribe
Issue No.12 - Dec. (2012 vol.34)
pp: 2454-2466
G. Tzimiropoulos , Sch. of Comput. Sci., Univ. of Lincoln, Lincoln, UK
S. Zafeiriou , Dept. of Comput., Imperial Coll. London, London, UK
M. Pantic , Dept. of Comput., Imperial Coll. London, London, UK
ABSTRACT
We introduce the notion of subspace learning from image gradient orientations for appearance-based object recognition. As image data are typically noisy and noise is substantially different from Gaussian, traditional subspace learning from pixel intensities very often fails to estimate reliably the low-dimensional subspace of a given data population. We show that replacing pixel intensities with gradient orientations and the ℓ2 norm with a cosine-based distance measure offers, to some extend, a remedy to this problem. Within this framework, which we coin Image Gradient Orientations (IGO) subspace learning, we first formulate and study the properties of Principal Component Analysis of image gradient orientations (IGO-PCA). We then show its connection to previously proposed robust PCA techniques both theoretically and experimentally. Finally, we derive a number of other popular subspace learning techniques, namely, Linear Discriminant Analysis (LDA), Locally Linear Embedding (LLE), and Laplacian Eigenmaps (LE). Experimental results show that our algorithms significantly outperform popular methods such as Gabor features and Local Binary Patterns and achieve state-of-the-art performance for difficult problems such as illumination and occlusion-robust face recognition. In addition to this, the proposed IGO-methods require the eigendecomposition of simple covariance matrices and are as computationally efficient as their corresponding ℓ2 norm intensity-based counterparts. Matlab code for the methods presented in this paper can be found at http://ibug.doc.ic.ac.uk/resources.
INDEX TERMS
principal component analysis, covariance matrices, eigenvalues and eigenfunctions, face recognition, feature extraction, gradient methods, learning (artificial intelligence), object recognition, Matlab code, subspace learning, image gradient orientations, appearance-based object recognition, pixel intensities, data population, cosine-based distance measure, principal component analysis, IGO-PCA, linear discriminant analysis, LDA, locally linear embedding, LLE, Laplacian eigenmaps, LE, Gabor features, local binary patterns, occlusion-robust face recognition, covariance matrices, eigendecomposition, ℓ2 norm intensity-based counterparts, Correlation, Principal component analysis, Robustness, Generators, Learning systems, Face recognition, Nonlinear systems, face recognition, Image gradient orientations, robust principal component analysis, discriminant analysis, nonlinear dimensionality reduction
CITATION
G. Tzimiropoulos, S. Zafeiriou, M. Pantic, "Subspace Learning from Image Gradient Orientations", IEEE Transactions on Pattern Analysis & Machine Intelligence, vol.34, no. 12, pp. 2454-2466, Dec. 2012, doi:10.1109/TPAMI.2012.40
REFERENCES
[1] S.T. Roweis and L.K. Saul, "Nonlinear Dimensionality Reduction by Locally Linear Embedding," Science, vol. 290, no. 5500, pp. 2323-2326, 2000.
[2] M. Balasubramanian, E.L. Schwartz, J.B. Tenenbaum, V. de Silva, and J.C. Langford, "The Isomap Algorithm and Topological Stability," Science, vol. 295, no. 5552, p. 7, 2002.
[3] M. Belkin and P. Niyogi, "Laplacian Eigenmaps for Dimensionality Reduction and Data Representation," Neural Computation, vol. 15, no. 6, pp. 1373-1396, 2003.
[4] L.K. Saul and S.T. Roweis, "Think Globally, Fit Locally: Unsupervised Learning of Low Dimensional Manifolds," The J. Machine Learning Research, vol. 4, pp. 119-155, 2003.
[5] L. Chengjun, "Gabor-Based Kernel PCA with Fractional Power Polynomial Models for Face Recognition," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 26, no. 5, pp. 572-581, May 2004.
[6] J. Yang, A.F. Frangi, J. Yang, D. Zhang, and Z. Jin, "KPCA plus LDA: A Complete Kernel Fisher Discriminant Framework for Feature Extraction and Recognition," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 27, no. 2, pp. 230-244, Feb. 2005.
[7] X. He, S. Yan, Y. Hu, P. Niyogi, and H.J. Zhang, "Face Recognition Using Laplacianfaces," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 27, no. 3, pp. 328-340, Mar. 2005.
[8] H. Cevikalp, M. Neamtu, M. Wilkes, and A. Barkana, "Discriminative Common Vectors for Face Recognition," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 27, no. 1, pp. 4-13, Jan. 2005.
[9] M. Zhu and A.M. Martinez, "Subclass Discriminant Analysis," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 28, no. 8, pp. 1274-1286, Aug. 2006.
[10] L. Chengjun, "Capitalize on Dimensionality Increasing Techniques for Improving Face Recognition Grand Challenge Performance," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 28, no. 5, pp. 725-737, May 2006.
[11] D. Cai, X. He, J. Han, and H. Zhang, "Orthogonal Laplacianfaces for Face Recognition," IEEE Trans. Image Processing, vol. 15, no. 11, pp. 3608-2614, Nov. 2006.
[12] E. Kokiopoulou and Y. Saad, "Orthogonal Neighborhood Preserving Projections: A Projection-Based Dimensionality Reduction Technique," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 29, no. 12, pp. 2143-2156, Dec. 2007.
[13] G. Goudelis, S. Zafeiriou, A. Tefas, and I. Pitas, "Class-Specific Kernel-Discriminant Analysis for Face Verification," IEEE Trans. Information Forensics and Security, vol. 2, no. 3, pp. 570-587, Sept. 2007.
[14] X. Jiang, B. Mandal, and A. Kot, "Eigenfeature Regularization and Extraction in Face Recognition," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 30, no. 3, pp. 383-394, Mar. 2008.
[15] J. Wright, A. Yang, A. Ganesh, S. Sastry, and Y. Ma, "Robust Face Recognition via Sparse Representation," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 31, no. 2, pp. 210-227, Feb. 2009.
[16] G. Baudat and F. Anouar, "Generalized Discriminant Analysis Using a Kernel Approach," Neural Computation, vol. 12, pp. 2385-2404, 2000.
[17] H. Cevikalp, M. Neamtu, and M. Wilkes, "Discriminative Common Vector Method with Kernels," IEEE Trans. Neural Networks, vol. 17, no. 6, pp. 1550-1565, Nov. 2006.
[18] H. Li, T. Jiang, and K. Zhang, "Efficient and Robust Feature Extraction by Maximum Margin Criterion," IEEE Trans. Neural Networks, vol. 17, no. 1, pp. 157-165, Jan. 2006.
[19] X. He, D. Cai, S. Yan, and H.-J. Zhang, "Neighborhood Preserving Embedding," Proc. 10th IEEE Int'l Conf. Computer Vision, vol. 2, pp. 1208-1213, 2005.
[20] M. Turk and A. Pentland, "Eigenfaces for Recognition," J. Cognitive Neuroscience, vol. 3, no. 1, pp. 71-86, 1991.
[21] P.N. Belhumeur, J.P. Hespanha, and D.J. Kriegman, "Eigenfaces vs. Fisherfaces: Recognition Using Class Specific Linear Projection," IEEE Trans. Pattern Analysis and Machine Intelligences, vol. 19, no. 7, pp. 711-720, July 1997.
[22] G. Tzimiropoulos, V. Argyriou, S. Zafeiriou, and T. Stathaki, "Robust FFT-Based Scale-Invariant Image Registration with Image Gradients," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 32, no. 10, pp. 1899-1906, Oct. 2010.
[23] F.De.La Torre and M.J. Black, "A Framework for Robust Subspace Learning," Int'l J. Computer Vision, vol. 54, no. 1, pp. 117-142, 2003.
[24] H.P. Frey, P. Konig, and W. Einhauser, "The Role of First and Second-Order Stimulus Features for Human Overt Attention," Perception and Psychophysics, vol. 69, pp. 153-161, 2007.
[25] A. Papoulis and S.U. Pillai, Probability, Random Variables, and Stochastic Processes. McGraw-Hill, 2004.
[26] A.J. Fitch, A. Kadyrov, W.J. Christmas, and J. Kittler, "Orientation Correlation," Proc. British Machine Vision Conf., vol. 1, pp. 133-142, 2002.
[27] A. Ros, "A Two-Piece Property for Compact Minimal Surfaces in a Three-Sphere," Indiana Univ. Math. J., vol. 44, no. 3, pp. 841-850, 1995.
[28] N.A. Campbell, "Robust Procedures in Multivariate Analysis I: Robust Covariance Estimation," Applied Statistics, vol. 29, no. 3, pp. 231-237, 1980.
[29] C. Croux and G. Haesbroeck, "Principal Component Analysis Based on Robust Estimators of the Covariance or Correlation Matrix: Influence Functions and Efficiencies," Biometrika, vol. 87, no. 3, pp. 603-618, 2000.
[30] Q. Ke and T. Kanade, "Robust L/Sub 1/Norm Factorization in the Presence of Outliers and Missing Data by Alternative Convex Programming," Proc. IEEE Conf. Computer Vision and Pattern Recognition, vol. 1, 2005.
[31] N. Kwak, "Principal Component Analysis Based on L1-Norm Maximization," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 30, no. 9, pp. 1672-1680, 2008.
[32] V. Chandrasekaran, S. Sanghavi, P.A. Parrilo, and A.S. Willsky, "Rank-Sparsity Incoherence for Matrix Decomposition," rapid post, 2009.
[33] E.J. Candes, X. Li, Y. Ma, and J. Wright, "Robust Principal Component Analysis?" Arxiv preprint arXiv:0912.3599, 2009.
[34] M. Kirby and L. Sirovich, "Application of the Karhunen-Loeve Procedure for the Characterization of Human Faces," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 12, no. 1, pp. 103-108, Jan. 1990.
[35] A.S. Georghiades, P.N. Belhumeur, and D.J. Kriegman, "From Few to Many: Illumination Cone Models for Face Recognition under Variable Lighting and Pose," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 23, no. 6, pp. 643-660, June 2001.
[36] C. Ding, D. Zhou, X. He, and H. Zha, "R 1-PCA: Rotational Invariant l 1-Norm Principal Component Analysis for Robust Subspace Factorization," Proc. 23rd Int'l Conf. Machine Learning, pp. 281-288, 2006.
[37] R. He, B.-G. Hu, W.-S. Zheng, and X.-W. Kong, "Robust Principal Component Analysis Based on Maximum Correntropy Criterion," IEEE Trans. Image Processing, vol. 20, no. 6, pp. 1485-1494, June 2011.
[38] W.J. Krzanowski, "Between-Groups Comparison of Principal Components," J. Am. Statistical Assoc., vol. 74, pp. 703-707, 1979.
[39] A.M. Martinez and R. Benavente, "The AR Face Database," CVC technical report, 1998.
[40] S. Yan, H. Wang, J. Liu, X. Tang, and T.S. Huang, "Misalignment-Robust Face Recognition," IEEE Trans. Image Processing, vol. 19, no. 4, pp. 1087-1096, Apr. 2010.
[41] A. Wagner, J. Wright, A. Ganesh, Z. Zhou, and Y. Ma, "Towards a Practical Face Recognition System: Robust Registration and Illumination by Sparse Representation," Proc. IEEE Conf. Computer Vision and Pattern Recognition, pp. 597-604, 2009.
[42] K.C. Lee, J. Ho, and D.J. Kriegman, "Acquiring Linear Subspaces for Face Recognition under Variable Lighting," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 27, no. 5, pp. 684-698, May 2005.
[43] T. Sim, S. Baker, and M. Bsat, "The CMU Pose, Illumination, and Expression Database," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 25, no. 12 pp. 1615-1618, Dec. 2003.
[44] P.J. Phillips, H. Moon, P.J. Rauss, and S. Rizvi, "The FERET Evaluation Methodology for Face Recognition Algorithms," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 22, no. 10, pp. 1090-1104, Oct. 2000.
[45] P.J. Phillips, H. Wechsler, J. Huang, and P. Rauss, "The FERET Database and Evaluation Procedure for Face Recognition Algorithms," Image and Vision Computing, vol. 16, no. 5, pp. 295-306, 1998.
[46] L. Chengjun and H. Wechsler, "Gabor Feature Based Classification Using the Enhanced Fisher Linear Discriminant Model for Face Recognition," IEEE Trans. Image Processing, vol. 11, no. 4, pp. 467-476, Apr. 2002.
[47] L. Chengjun and H. Wechsler, "Independent Component Analysis of Gabor Features for Face Recognition," IEEE Trans. Neural Networks, vol. 14, no. 4, pp. 919-928, July 2003.
[48] T. Ahonen, A. Hadid, and M. Pietikainen, "Face Description with Local Binary Patterns: Application to Face Recognition," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 28, no. 12, pp. 2037-2041, Dec. 2006.
[49] http://www.ee.oulu.fi/mvg/pagelbp matlab , 2012.
[50] Q. McNemar, "Note on the Sampling Error of the Difference between Correlated Proportions or Percentages," Psychometrika, vol. 12, no. 2, pp. 153-157, 1947.
[51] B.A. Draper, K. Baek, M.S. Bartlett, and J.R. Beveridge, "Recognizing Faces with PCA and ICA," Computer Vision and Image Understanding, vol. 91, nos. 1/2, pp. 115-137, 2003.
[52] K.C. Lee, J. Ho, and D. Kriegman, "Acquiring Linear Subspaces for Face Recognition under Variable Lighting," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 27, no. 5, pp. 684-698, May 2005.
[53] H. Jia and A.M. Martinez, "Face Recognition with Occlusions in the Training and Testing Sets," Proc. Conf. Automatic Face and Gesture Recognition, 2008.
[54] M.J. Black and A.D. Jepson, "Eigentracking: Robust Matching and Tracking of Articulated Objects Using a View-Based Representation," Int'l J. Computer Vision, vol. 26, no. 1, pp. 63-84, 1998.
[55] T.F. Cootes, G.J. Edwards, and C.J. Taylor, "Active Appearance Models," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 23, no. 6, pp. 681-685, 2001.
[56] D.A. Ross, J. Lim, R.S. Lin, and M.H. Yang, "Incremental Learning for Robust Visual Tracking," Int'l J. Computer Vision, vol. 77, no. 1, pp. 125-141, 2008.
[57] A. Levey and M. Lindenbaum, "Sequential Karhunen-Loeve Basis Extraction and Its Application to Images," IEEE Trans. Image Processing, vol. 9, no. 8, pp. 1371-1374, Aug. 2000.
[58] G. Tzimiropoulos, S. Zafeiriou, and M. Pantic, "Principal Component Analysis of Image Gradient Orientations for Face Recognition," Proc. 2011 IEEE Int'l Conf. Automatic Face and Gesture Recognition and Workshops, pp. 553-558, 2011.
7 ms
(Ver 2.0)

Marketing Automation Platform Marketing Automation Tool