Nonnegative Matrix Factorizations Performing Object Detection and Localization

We study the problem of detecting and localizing objects in still, gray-scale images making use of the part-based representation provided by nonnegative matrix factorizations. Nonnegative matrix factorization represents an emerging example of subspace methods, which is able to extract interpretable parts from a set of template image objects and then to additively use them for describing individual objects. In this paper, we present a prototype system based on some nonnegative factorization algorithms, which differ in the additional properties added to the nonnegative representation of data, in order to investigate if any additional constraint produces better results in general object detection via nonnegative matrix factorizations.

[1]  Nanning Zheng,et al.  Non-negative matrix factorization based methods for object recognition , 2004, Pattern Recognit. Lett..

[2]  Donghui Chen,et al.  Nonnegativity constraints in numerical analysis , 2009, The Birth of Numerical Analysis.

[3]  Richard J. Mammone,et al.  Use of non-negative matrix factorization for language model adaptation in a lecture transcription task , 2001, 2001 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.01CH37221).

[4]  C. Ding,et al.  On the Equivalence of Nonnegative Matrix Factorization and K-means - Spectral Clustering , 2005 .

[5]  H. Sebastian Seung,et al.  Algorithms for Non-negative Matrix Factorization , 2000, NIPS.

[6]  Chris H. Q. Ding,et al.  Nonnegative Matrix Factorization and Probabilistic Latent Semantic Indexing: Equivalence Chi-Square Statistic, and a Hybrid Method , 2006, AAAI.

[7]  I. Jolliffe.  Principal Component Analysis , 2002 .

[8]  R. Plemmons,et al.  Optimality, computation, and interpretation of nonnegative matrix factorizations , 2004 .

[9]  Nicoletta Del Buono.  A Penalty Function for Computing Orthogonal Non-negative Matrix Factorizations , 2009, 2009 Ninth International Conference on Intelligent Systems Design and Applications.

[10]  Dan Roth,et al.  Learning to detect objects in images via a sparse, part-based representation , 2004, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[11]  Paul A. Viola,et al.  Rapid object detection using a boosted cascade of simple features , 2001, Proceedings of the 2001 IEEE Computer Society Conference on Computer Vision and Pattern Recognition. CVPR 2001.

[12]  loan Buciu.  Learning sparse non-negative features for object recognition , 2007, 2007 IEEE International Conference on Intelligent Computer Communication and Processing.

[13]  Aapo Hyvärinen,et al.  Independent Component Analysis: Fast ICA by a fixed-point algorithm that maximizes non-Gaussianity , 2001 .

[14]  I. Biederman.  Recognition-by-components: a theory of human image understanding. , 1987, Psychological review.

[15]  Chris H. Q. Ding,et al.  Orthogonal nonnegative matrix t-factorizations for clustering , 2006, KDD '06.

[16]  Chih-Jen Lin,et al.  Projected Gradient Methods for Nonnegative Matrix Factorization , 2007, Neural Computation.

[17]  V. P. Pauca,et al.  Nonnegative matrix factorization for spectral data analysis , 2006 .

[18]  Seungjin Choi,et al.  Algorithms for orthogonal nonnegative matrix factorization , 2008, 2008 IEEE International Joint Conference on Neural Networks (IEEE World Congress on Computational Intelligence).

[19]  Hyunsoo Kim,et al.  Sparse Non-negative Matrix Factorizations via Alternating Non-negativity-constrained Least Squares , 2006 .

[20]  Aapo Hyvärinen,et al.  Topographic Independent Component Analysis , 2001, Neural Computation.

[21]  Robert J. Plemmons,et al.  Nonnegative Matrices in the Mathematical Sciences , 1979, Classics in Applied Mathematics.

[22]  Ivan Bajla,et al.  Robust Object Recognition under Partial Occlusions Using NMF , 2008, Comput. Intell. Neurosci..

[23]  Jordi Vitrià,et al.  Non-negative Matrix Factorization for Face Recognition , 2002, CCIA.

[24]  Victoria Stodden,et al.  When Does Non-Negative Matrix Factorization Give a Correct Decomposition into Parts? , 2003, NIPS.

[25]  Michel Vidal-Naquet,et al.  Visual features of intermediate complexity and their use in classification , 2002, Nature Neuroscience.

[26]  Tomaso A. Poggio,et al.  Example-Based Object Detection in Images by Components , 2001, IEEE Trans. Pattern Anal. Mach. Intell..

[27]  Ziqiang Wang,et al.  Face Recognition Based on NMF and SVM , 2009, 2009 Second International Symposium on Electronic Commerce and Security.

[28]  Antonio Torralba,et al.  Object Detection and Localization Using Local and Global Features , 2006, Toward Category-Level Object Recognition.

[29]  Tai Sing Lee,et al.  Image Representation Using 2D Gabor Wavelets , 1996, IEEE Trans. Pattern Anal. Mach. Intell..

[30]  Yuan Gao,et al.  Improving molecular cancer class discovery through sparse non-negative matrix factorization , 2005 .

[31]  Golub Gene H. Et.Al.  Matrix Computations, 3rd Edition , 2007 .

[32]  I. Pitas,et al.  A new sparse image representation algorithm applied to facial expression recognition , 2004, Proceedings of the 2004 14th IEEE Signal Processing Society Workshop Machine Learning for Signal Processing, 2004..

[33]  Robin N. Strickland,et al.  Wavelet transform methods for object detection and recovery , 1997, IEEE Trans. Image Process..

[34]  Moody T. Chu,et al.  Low-Dimensional Polytope Approximation and Its Applications to Nonnegative Matrix Factorization , 2008, SIAM J. Sci. Comput..

[35]  Alex Pentland,et al.  Face recognition using eigenfaces , 1991, Proceedings. 1991 IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[36]  Bernt Schiele,et al.  Recognition without Correspondence using Multidimensional Receptive Field Histograms , 2004, International Journal of Computer Vision.

[37]  Jordi Vitrià,et al.  Evaluation of distance metrics for recognition based on non-negative matrix factorization , 2003, Pattern Recognit. Lett..

[38]  Stan Z. Li,et al.  Learning spatially localized, parts-based representation , 2001, Proceedings of the 2001 IEEE Computer Society Conference on Computer Vision and Pattern Recognition. CVPR 2001.

[39]  Patrik O. Hoyer,et al.  Non-negative Matrix Factorization with Sparseness Constraints , 2004, J. Mach. Learn. Res..

[40]  R. Plemmons,et al.  NONNEGATIVE MATRIX FACTORIZATION AND APPLICATIONS , 2005 .

[41]  H. Sebastian Seung,et al.  Learning the parts of objects by non-negative matrix factorization , 1999, Nature.

[42]  Bhavin J. Shastri,et al.  Face recognition using localized features based on non-negative sparse coding , 2006, Machine Vision and Applications.

[43]  P. Paatero,et al.  Positive matrix factorization: A non-negative factor model with optimal utilization of error estimates of data values† , 1994 .