E. H. Adelson and J. R. Bergen, Spatiotemporal energy models for the perception of motion, Journal of the Optical Society of America A, vol.2, issue.2, pp.284-299, 1985.
DOI : 10.1364/JOSAA.2.000284

J. Alonso and L. M. Martinez, Functional connectivity between simple cells and complex cells in cat striate cortex, Nature Neuroscience, vol.1, issue.5, pp.395-403, 1998.
DOI : 10.1038/1609

T. J. Atherton, Energy and phase orientation mechanisms: a computational model, Spatial Vision, vol.15, issue.4, pp.415-441, 2002.
DOI : 10.1163/156856802320401892

O. Ben-shahar and S. W. Zucker, Geometrical Computations Explain Projection Patterns of Long-Range Horizontal Connections in Visual Cortex, Neural Computation, vol.6, issue.4, pp.445-476, 2004.
DOI : 10.1162/neco.1989.1.1.68

P. Berkes and L. Wiskott, Slow feature analysis yields a rich repertoire of complex cell properties, Journal of Vision, vol.5, issue.6, pp.579-602, 2005.
DOI : 10.1167/5.6.9

J. S. Bridle, Probabilistic Interpretation of Feedforward Classification Network Outputs, with Relationships to Statistical Pattern Recognition, 1989.
DOI : 10.1007/978-3-642-76153-9_28

J. Canny, A computational approach to edge detection, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.8, issue.6, pp.679-698, 1986.

M. Carandini, What simple and complex cells compute, The Journal of Physiology, vol.38, issue.2, pp.463-466, 2006.
DOI : 10.1113/jphysiol.2006.118976

M. Carandini, J. B. Demb, V. Mante, D. J. Tolhurst, Y. Dan et al., Do We Know What the Early Visual System Does?, Journal of Neuroscience, vol.25, issue.46, pp.10577-10597, 2005.
DOI : 10.1523/JNEUROSCI.3726-05.2005

M. Carandini and D. Heeger, Summation and division by neurons in primate visual cortex, Science, vol.264, issue.5163, pp.1333-1336, 1994.
DOI : 10.1126/science.8191289

E. Crow and M. Siddiqui, Robust Estimation of Location, Journal of the American Statistical Association, vol.25, issue.318, pp.353-389, 1967.
DOI : 10.1214/aoms/1177704711

J. G. Daugman, Uncertainty relation for resolution in space, spatial frequency, and orientation optimized by two-dimensional visual cortical filters, Journal of the Optical Society of America A, vol.2, issue.7, pp.1160-1169, 1985.
DOI : 10.1364/JOSAA.2.001160

P. Dayan and L. F. Abbott, Theoretical neuroscience, 2001.

D. Valois, R. L. Albrecht, D. G. Thorell, and L. G. , Spatial frequency selectivity of cells in macaque visual cortex, Vision Research, vol.22, issue.5, pp.545-559, 1982.
DOI : 10.1016/0042-6989(82)90113-4

A. Dobbins, S. W. Zucker, and M. S. Cynader, Endstopped neurons in the visual cortex as a substrate for calculating curvature, Nature, vol.329, issue.6138, pp.438-441, 1987.
DOI : 10.1038/329438a0

R. C. Emerson, J. R. Bergen, and E. H. Adelson, Directionally selective complex cells and the computation of motion energy in cat visual cortex, Vision Research, vol.32, issue.2, pp.203-218, 1992.
DOI : 10.1016/0042-6989(92)90130-B

M. Felsberg and G. Sommer, The monogenic signal, IEEE Transactions on Signal Processing, vol.49, issue.12, pp.3136-3144, 2001.
DOI : 10.1109/78.969520

D. J. Fleet, H. Wagner, and D. J. Heeger, Neural encoding of binocular disparity: Energy models, position shifts and phase shifts, Vision Research, vol.36, issue.12, pp.1839-1857, 1996.
DOI : 10.1016/0042-6989(95)00313-4

W. T. Freeman and E. H. Adelson, The design and use of steerable filters, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.13, issue.9, pp.891-906, 1991.
DOI : 10.1109/34.93808

J. P. Gaska, D. A. Pollen, and P. Cavanagh, Diversity of complex cell responses to even- and odd-symmetric luminance profiles in the visual cortex of the cat, Experimental Brain Research, vol.68, issue.2, pp.249-259, 1987.
DOI : 10.1007/BF00248791

M. A. Georgeson, K. A. May, T. C. Freeman, and G. S. Hesse, From filters to features: Scale???space analysis of edge and blur coding in human vision, Journal of Vision, vol.7, issue.13, pp.1-21, 2007.
DOI : 10.1167/7.13.7

C. Gilbert and T. Wiesel, Morphology and intracortical projections of functionally characterised neurones in the cat visual cortex, Nature, vol.250, issue.5718, pp.280-120, 1979.
DOI : 10.1007/BF01173991

M. Hansard and R. Horaud, Complex cells and the representation of local image-structure (Tech. Rep. 7485), 2010.

C. Harris and M. Stephens, A Combined Corner and Edge Detector, Procedings of the Alvey Vision Conference 1988, pp.147-151, 1988.
DOI : 10.5244/C.2.23

M. J. Hawken and A. J. Parker, Spatial Properties of Neurons in the Monkey Striate Cortex, Proceedings of the Royal Society B: Biological Sciences, vol.231, issue.1263, pp.251-288, 1987.
DOI : 10.1098/rspb.1987.0044

D. J. Heeger, Abstract, Visual Neuroscience, vol.296, issue.05, pp.427-443, 1992.
DOI : 10.1007/BF00238196

D. J. Heeger, Abstract, Visual Neuroscience, vol.44, issue.02, pp.181-197, 1992.
DOI : 10.1016/0042-6989(82)90182-1

D. H. Hubel and T. N. Wiesel, Receptive fields, binocular interaction and functional architecture in the cat's visual cortex, The Journal of Physiology, vol.160, issue.1, pp.106-54, 1962.
DOI : 10.1113/jphysiol.1962.sp006837

A. Johnston, P. W. Mcowan, and H. Buxton, A Computational Model of the Analysis of Some First-Order and Second-Order Motion Patterns by Simple and Complex Cells, Proceedings of the Royal Society B: Biological Sciences, vol.250, issue.1329, pp.297-306, 1992.
DOI : 10.1098/rspb.1992.0162

J. P. Jones and L. A. Palmer, An evaluation of the two-dimensional Gabor filter model of simple receptive fields in cat striate cortex, J. Neurophysiology, issue.6, pp.58-1233, 1987.

Y. Karklin and M. S. Lewicki, Emergence of complex cell properties by learning to generalize in natural scenes, Nature, vol.9, issue.7225, pp.83-86, 2009.
DOI : 10.1016/j.conb.2004.07.007

J. Kelly and D. Van-essen, Cell structure and function in the visual cortex of the cat, The Journal of Physiology, vol.238, issue.3, pp.515-547, 1974.
DOI : 10.1113/jphysiol.1974.sp010541

T. W. Kjaer, T. J. Gawne, J. A. Hertz, and B. J. Richmond, Insensitivity of V1 complex cell responses to small shifts in the retinal image of complex patterns, J. Neurophysiology, vol.78, pp.3187-3197, 1997.

J. J. Koenderink, The structure of images, Biological Cybernetics, vol.27, issue.269, pp.363-370, 1984.
DOI : 10.1007/BF00336961

J. J. Koenderink and A. J. Van-doorn, Representation of local geometry in the visual system, Biological Cybernetics, vol.53, issue.6, pp.367-375, 1987.
DOI : 10.1007/BF00318371

J. J. Koenderink and A. J. Van-doorn, Receptive field families, Biological Cybernetics, vol.5, issue.4, pp.291-297, 1990.
DOI : 10.1007/BF00203452

J. Koenderink and A. Van-doorn, Generic neighborhood operators, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.14, issue.6, pp.597-605, 1992.
DOI : 10.1109/34.141551

I. Lampl, D. Ferster, T. Poggio, and M. Riesenhuber, Intracellular Measurements of Spatial Integration and the MAX Operation in Complex Cells of the Cat Primary Visual Cortex, Journal of Neurophysiology, vol.92, issue.5, pp.2704-2713, 2004.
DOI : 10.1152/jn.00060.2004

S. R. Lehky, T. J. Sejnowski, and R. Desimone, Selectivity and sparseness in the responses of striate complex cells, Vision Research, vol.45, issue.1, pp.57-73, 2005.
DOI : 10.1016/j.visres.2004.07.021

T. Lindeberg, Edge detection and ridge detection with automatic scale selection, Proceedings CVPR IEEE Computer Society Conference on Computer Vision and Pattern Recognition, pp.117-154, 1998.
DOI : 10.1109/CVPR.1996.517113

L. M. Martinez and J. Alonso, Complex Receptive Fields in Primary Visual Cortex, The Neuroscientist, vol.9, issue.5, pp.317-331, 2003.
DOI : 10.1177/1073858403252732

F. Mechler, D. S. Reich, and J. D. Victor, Detection and discrimination of relative spatial phase by V1 neurons, J. Neuroscience, issue.14, pp.22-6129, 2002.

F. Mechler and D. L. Ringach, On the classification of simple and complex cells, Vision Research, vol.42, issue.8, pp.1017-1013, 2002.
DOI : 10.1016/S0042-6989(02)00025-1

M. Morrone and D. Burr, Feature Detection in Human Vision: A Phase-Dependent Energy Model, Proceedings of the Royal Society B: Biological Sciences, vol.235, issue.1280, pp.221-245, 1988.
DOI : 10.1098/rspb.1988.0073

J. A. Movshon, I. D. Thompson, and D. J. Tolhurst, Receptive field organization of complex cells in the cat's striate cortex., The Journal of Physiology, vol.283, issue.1, pp.79-99, 1978.
DOI : 10.1113/jphysiol.1978.sp012489

J. A. Movshon, I. D. Thompson, and D. J. Tolhurst, Spatial summation in the receptive fields of simple cells in the cat's striate cortex., The Journal of Physiology, vol.283, issue.1, pp.53-77, 1978.
DOI : 10.1113/jphysiol.1978.sp012488

G. A. Orban, Higher Order Visual Processing in Macaque Extrastriate Cortex, Physiological Reviews, vol.88, issue.1, pp.59-89, 2008.
DOI : 10.1152/physrev.00008.2007

P. Perona, Deformable kernels for early vision, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.17, issue.5, pp.488-499, 1995.
DOI : 10.1109/34.391394

J. Petitot, The neurogeometry of pinwheels as a sub-Riemannian contact structure, Journal of Physiology-Paris, vol.97, issue.2-3, pp.265-309, 2003.
DOI : 10.1016/j.jphysparis.2003.10.010

D. A. Pollen and S. F. Ronner, Phase relationships between adjacent simple cells in the visual cortex, Science, vol.212, issue.4501, pp.212-1409, 1981.
DOI : 10.1126/science.7233231

A. D. Pollen and S. F. Ronner, Visual cortical neurons as localized spatial frequency filters, IEEE Transactions on Systems, Man, and Cybernetics, vol.13, issue.5, pp.907-916, 1983.
DOI : 10.1109/TSMC.1983.6313086

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical recipes in C Cambridge, 1992.

M. Riesenhuber and T. Poggio, Hierarchical models of object recognition in cortex, Nature Neuroscience, vol.2, issue.11, pp.1019-1025, 1999.

D. Ringach, Spatial structure & symmetry of simple-cell receptive fields in macaque primary visual cortex, J. Neurophysiology, vol.88, pp.455-463, 2002.

N. Rust, O. Schwartz, J. Movshon, and E. Simoncelli, Spatiotemporal Elements of Macaque V1 Receptive Fields, Neuron, vol.46, issue.6, pp.945-956, 2005.
DOI : 10.1016/j.neuron.2005.05.021

K. S. Sasaki and I. Ohzawa, Internal Spatial Organization of Receptive Fields of Complex Cells in the Early Visual Cortex, Journal of Neurophysiology, vol.98, issue.3, pp.1194-1212, 2007.
DOI : 10.1152/jn.00429.2007

E. P. Simoncelli, W. T. Freeman, E. H. Adelson, and D. J. Heeger, Shiftable multiscale transforms, IEEE Transactions on Information Theory, vol.38, issue.2, pp.587-607, 1992.
DOI : 10.1109/18.119725

B. C. Skottun, R. L. Valois, D. H. Grosof, J. A. Movshon, D. G. Albrecht et al., Classifying simple and complex cells on the basis of response modulation, Vision Research, vol.31, issue.7-8, pp.31-1079, 1991.
DOI : 10.1016/0042-6989(91)90033-2

H. Spitzer and S. Hochstein, Complex-cell receptive field models, Progress in Neurobiology, vol.31, issue.4, pp.285-309, 1988.
DOI : 10.1016/0301-0082(88)90016-0

J. Touryan, G. Felsen, and Y. Dan, Spatial Structure of Complex Cell Receptive Fields Measured with Natural Images, Neuron, vol.45, issue.5, pp.781-791, 2005.
DOI : 10.1016/j.neuron.2005.01.029

L. Wiskott and T. Sejnowski, Slow Feature Analysis: Unsupervised Learning of Invariances, Neural Computation, vol.13, issue.11, pp.715-770, 2002.
DOI : 10.1016/S0301-0082(96)00054-8

I. J. Wundrich, C. Von-der-malsburg, and R. P. Urtz, Image Representation by Complex Cell Responses, Neural Computation, vol.58, issue.6, pp.2563-2575, 2004.
DOI : 10.1016/S0262-8856(99)00061-X

R. A. Young and R. M. Lesperance, The Gaussian Derivative model for spatial-temporal vision: II. Cortical data, Spatial Vision, vol.14, issue.3, pp.321-389, 2001.
DOI : 10.1163/156856801753253591

R. A. Young, R. M. Lesperance, and W. W. Meyer, The Gaussian Derivative model for spatial-temporal vision: I. Cortical model, Spatial Vision, vol.14, issue.3, pp.261-319, 2001.
DOI : 10.1163/156856801753253582

A. Yu, M. Giese, and T. Poggio, Biophysiologically Plausible Implementations of the Maximum Operation, Neural Computation, vol.12, issue.4, pp.2857-2881, 2002.
DOI : 10.1162/neco.1989.1.3.334