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Designing a Boosted Classifier on Riemannian Manifolds

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Riemannian Computing in Computer Vision

Abstract

It is not trivial to build a classifier where the domain is the space of symmetric positive definite matrices such as non-singular region covariance descriptors lying on a Riemannian manifold. This chapter describes a boosted classification approach that incorporates the a priori knowledge of the geometry of the Riemannian space. The presented classifier incorporated into a rejection cascade and applied to single image human detection task. Results on INRIA and DaimlerChrysler pedestrian datasets are reported.

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References

  1. Bengio Y, Goodfellow I, Courville A (2014) Deep learning. MIT Press, Cambridge

    Google Scholar 

  2. Comaniciu D, Meer P (2002) Mean shift: a robust approach toward feature space analysis. IEEE Trans Pattern Anal Mach Intell 24:603–619

    Article  Google Scholar 

  3. Cortes C, Vapnik V (1995) Support vector networks. Mach Learn 20:273–297

    MATH  Google Scholar 

  4. Dalal N, Triggs B (2005) Histograms of oriented gradients for human detection. In: IEEE conference on computer vision and pattern recognition, pp 886–893

    Google Scholar 

  5. Dorkó G, Schmid C (2003) Selection of scale-invariant parts for object class recognition. In: International conference on computer vision, pp 634–640

    Google Scholar 

  6. Efron B (1975) The efficiency of logistic regression compared to normal discriminant analysis. J Am Stat Assoc 70(352):892–898

    Article  MATH  MathSciNet  Google Scholar 

  7. Fergus R, Perona P, Zisserman A (2003) Object class recognition by unsupervised scale-invariant learning. In: IEEE conference on computer vision and pattern recognition, pp 264–271

    Google Scholar 

  8. Fletcher PT, Joshi S (2007) Riemannian geometry for the statistical analysis of diffusion tensor data. Signal Process 87(2):250–262

    Article  MATH  Google Scholar 

  9. Förstner W, Moonen B (1999) A metric for covariance matrices. Technical report, Dept. of Geodesy and Geoinformatics, Stuttgart University

    Google Scholar 

  10. Friedman J, Hastie T, Tibshirani R (2000) Additive logistic regression: a statistical view of boosting. Ann Stat 28(2):337–407

    Article  MATH  MathSciNet  Google Scholar 

  11. Grove K, Karcher H (1973) How to conjugate C 1-close group actions. Math Z 132:11–20

    Article  MATH  MathSciNet  Google Scholar 

  12. Guo K, Ishwar P, Konrad J (2010) Action recognition using sparse representation on covariance manifolds of optical flow. In: IEEE international conference advanced video and signal based surveillance (AVSS), pp 188–195

    Google Scholar 

  13. Haykin S (1998) Neural networks: a comprehensive foundation, 2nd edn. Prentice Hall, Upper Saddle River

    Google Scholar 

  14. Moakher M (2005) A differential geometric approach to the geometric mean of symmetric positive-definite matrices. SIAM J Matrix Anal Appl 26:735–747

    Article  MATH  MathSciNet  Google Scholar 

  15. Munder S, Gavrila DM (2006) An experimental study on pedestrian classification. IEEE Trans Pattern Anal Mach Intell 28:1863–1868

    Article  Google Scholar 

  16. Papageorgiou P, Poggio T (2000) A trainable system for object detection. Int J Comput Vis 38(1):15–33

    Article  MATH  Google Scholar 

  17. Pennec X, Fillard P, Ayache N (2006) A Riemannian framework for tensor computing. Int J Comput Vis 66(1):41–66

    Article  MATH  MathSciNet  Google Scholar 

  18. Porikli F (2005) Integral histogram: a fast way to extract histograms in Cartesian spaces. In: IEEE conference on computer vision and pattern recognition, pp 829–836

    Google Scholar 

  19. Porikli F, Tuzel O, Meer P (2006) Covariance tracking using model update based on Lie algebra. In: IEEE conference on computer vision and pattern recognition, pp 728–735

    Google Scholar 

  20. Rowley H, Baluja S, Kanade T (1998) Neural network-based face detection. IEEE Trans Pattern Anal Mach Intell 20:22–38

    Article  Google Scholar 

  21. Sabzmeydani P, Mori G (2007) Detecting pedestrians by learning shapelet features. In: IEEE conference on computer vision and pattern recognition

    Book  Google Scholar 

  22. Schapire RE (2002) The boosting approach to machine learning, an overview. In: MSRI workshop on nonlinear estimation and classification

    Google Scholar 

  23. Schmah T, Hinton GE, Zemel R, Small SL, Strother S (2009) Generative versus discriminative training of RBMs for classification of fMRI images. In: Advances in neural information processing systems, 21

    Google Scholar 

  24. Sermanet P, Kavukcuoglu K, Chintala S, LeCu Y (2013) Pedestrian detection with unsupervised multi-stage feature learning. In: IEEE conference on computer vision and pattern recognition

    Book  Google Scholar 

  25. Tuzel O, Porikli F, Meer P (2006) Region covariance: a fast descriptor for detection and classification. In: European conference on computer vision, pp 589–600

    Google Scholar 

  26. Tuzel O, Porikli F, Meer P (2008) Pedestrian detection via classification on Riemannian manifolds. IEEE Trans Pattern Anal Mach Intell 30(10):1713–1727

    Article  Google Scholar 

  27. Viola P, Jones M (2001) Rapid object detection using a boosted cascade of simple features. In: IEEE conference on computer vision and pattern recognition, pp 511–518

    Google Scholar 

  28. Weber M, Welling M, Perona P (2000) Unsupervised learning of models for recognition. In: European conference on computer vision, pp 18–32

    Google Scholar 

  29. Zhang S, Kasiviswanathan S, Yuen PC, Harandi M (2015) Online dictionary learning on symmetric positive definite manifolds with vision applications. In: AAAI conference on artificial intelligence

    Google Scholar 

  30. Zhu Q, Avidan S, Yeh MC, Cheng KT (2006) Fast human detection using a cascade of histograms of oriented gradients. In: IEEE conference on computer vision and pattern recognition, pp 1491–1498

    Google Scholar 

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Correspondence to Fatih Porikli .

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Porikli, F., Tuzel, O., Meer, P. (2016). Designing a Boosted Classifier on Riemannian Manifolds. In: Turaga, P., Srivastava, A. (eds) Riemannian Computing in Computer Vision. Springer, Cham. https://doi.org/10.1007/978-3-319-22957-7_13

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  • DOI: https://doi.org/10.1007/978-3-319-22957-7_13

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-22956-0

  • Online ISBN: 978-3-319-22957-7

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