An application of a semidiscrete version of the Petitot model of the human primary visual cortex to invariant object recognition in SVM context

In this paper we propose a supervised object recognition method using new global features. The proposed technique, based on the Fourier transform evaluated on a regular hexagonal grid, allows extracting descriptors which are invariant to geometric transformations (rotations, scale invariant, translations...). The obtained descriptors are next used in order to feed an SVM classifier. We have tested our method against COIL image database and ORL face database, and compared it with other techniques based on traditional descriptors. The obtained results have shown that our approach outperforms the other techniques.

[1]  M. Golubitsky,et al.  Geometric visual hallucinations, Euclidean symmetry and the functional architecture of striate cortex. , 2001, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[2]  King-Sun Fu,et al.  Shape Discrimination Using Fourier Descriptors , 1977, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[3]  A. Barut,et al.  Theory of group representations and applications , 1977 .

[4]  R. Duits,et al.  Left-invariant parabolic evolutions on SE(2) and contour enhancement via invertible orientation scores. Part I: Linear left-invariant diffusion equations on SE(2) , 2010 .

[5]  Edwin Hewitt,et al.  Abstract Harmonic Analysis: Volume 1 , 1963 .

[6]  Jean-Paul Gauthier,et al.  Generalized Fourier Descriptors with Applications to Objects Recognition in SVM Context , 2007, Journal of Mathematical Imaging and Vision.

[7]  Robert Sabourin,et al.  “One Against One” or “One Against All”: Which One is Better for Handwriting Recognition with SVMs? , 2006 .

[8]  Jean-Paul Gauthier,et al.  Anthropomorphic Image Reconstruction via Hypoelliptic Diffusion , 2010, SIAM J. Control. Optim..

[9]  Hélène Laurent,et al.  Comparative study of global invariant descriptors for object recognition , 2008, J. Electronic Imaging.

[10]  Bruno Galerne,et al.  Random Phase Textures: Theory and Synthesis , 2011, IEEE Transactions on Image Processing.

[11]  Bill Triggs,et al.  Histograms of oriented gradients for human detection , 2005, 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05).

[12]  Faouzi Ghorbel,et al.  Robust and efficient Fourier-Mellin transform approximations for invariant grey-level image description and reconstruction , 2001 .

[13]  R. Lipsman.  Abstract harmonic analysis , 1968 .

[14]  Jean-Paul Gauthier,et al.  Image Processing in the Semidiscrete Group of Rototranslations , 2015, GSI.

[15]  G LoweDavid,et al.  Distinctive Image Features from Scale-Invariant Keypoints , 2004 .

[16]  Herbert J. Reitboeck,et al.  A Neural Network for Position Invariant Pattern Recognition Combining Spiking Neurons with the Fourier-Transform , 1996, Int. J. Neural Syst..

[17]  David G. Lowe,et al.  Distinctive Image Features from Scale-Invariant Keypoints , 2004, International Journal of Computer Vision.

[18]  Chee-Way Chong,et al.  A comparative analysis of algorithms for fast computation of Zernike moments , 2003, Pattern Recognit..

[19]  D. Hubel,et al.  Receptive fields of single neurones in the cat's striate cortex , 1959, The Journal of physiology.

[20]  Giovanna Citti,et al.  A Cortical Based Model of Perceptual Completion in the Roto-Translation Space , 2006, Journal of Mathematical Imaging and Vision.

[21]  Shlomo Dubnov,et al.  Polyspectra as measures of sound texture and timbre , 1997 .

[22]  Ralph Roskies,et al.  Fourier Descriptors for Plane Closed Curves , 1972, IEEE Transactions on Computers.

[23]  Jean-Paul Gauthier,et al.  Image reconstruction via non-isotropic diffusion in Dubins/Reed-Shepp-like control systems , 2014, 53rd IEEE Conference on Decision and Control.

[24]  J. Gauthier,et al.  Hypoelliptic diffusion and human vision: a semi-discrete new twist on the Petitot theory , 2013 .

[25]  R. Duits,et al.  Left-invariant parabolic evolutions on SE(2) and contour enhancement via invertible orientation scores. Part II: Non-linear left-invariant diffusions on invertible orientation scores , 2010 .

[26]  Ming-Kuei Hu,et al.  Visual pattern recognition by moment invariants , 1962, IRE Trans. Inf. Theory.

[27]  Andy Harter,et al.  Parameterisation of a stochastic model for human face identification , 1994, Proceedings of 1994 IEEE Workshop on Applications of Computer Vision.