Nonlinear Model for Complex Neurons in Biological Visual Visions

Sasan Mahmoodi, Nasim Saba

2016

Abstract

Complex cells in biological visual vision are well known to be nonlinear. In this paper, it is demonstrated that these nonlinear complex cells can be modelled under some certain conditions by a biologically inspired model which is nonlinear in nature. Our model consists of cascaded neural layers accounting for anatomical evidence in biological early visual visions. In the model proposed in this paper, the axons associated with the complex cells are considered to operate nonlinearly. We also consider the second order interaction receptive maps as directional derivatives of the complex cell's kernel along the direction of orientation tuning. Our numerical results are similar to the biologically recorded data reported in the literature.

References

  1. Adelson E, Bergen J 1985. Spaio-temporal Energy Models for the Perception of Motion. Journal of Optical Society of America A, Vol. 2, pp. 284-299.
  2. Carandini M, Ferster D 2000. Membrane Potential and Firing Rate in Cat Primary Visual Cortex. Journal of Neuroscience, Vol. 20, No. 1, pp. 470-484.
  3. DeAngelis GC, Anzai A 2004. A Modern View of the Classical Receptive Field: Linear and non-Linear Spatio-temporal Processing by V1 Neurons. In L.M. Chalupa, and J.S. Werner (eds.), The Visual Neurosciences, Vol 1, MIT Press, Cambridge, pp. 704-719.
  4. DeAngelis DC, Ohzawa I, Freeman RD 1995. Receptivefield Dynamics in the Central Visual Pathways. Trends in Neurosciences, Vol. 18, pp:451-457.
  5. Florack, L 1997. Image Structure. Series in Mathematical Imaging and Vision, Springer, Dordrecht.
  6. Koenderink JJ 1988. Scale-Time, Biological Cybernetic, Vol. 58, pp. 159-162.
  7. Hartline HK 1938. The Response of Single Optic Nerve Fibres of the Vertebrate Eye to Illumination of the Retina. American Journal of Physiology, Vol. 121, pp. 400-415.
  8. Hubel DH, Wiesel TN 2005. Brain and Visual Perception: the Story of a 25-year collaboration. Oxford University Press, Oxford.
  9. Kuffler SW 1953. Discharge Patterns and Functional Organization of Mammalian Retina. Journal of Neurophysiology, Vol. 16, No. 1, pp. 37-68.
  10. Lindeberg T 2011. Generalized Gaussian Scale-Space Axiomatic Comprising Linear Scale-Space, Affine Scale-Space and Spatio-Temporal Scale-Space. Journal of Mathematical Imaging and Vision, Vol. 40, pp: 36-81.
  11. Lindeberg T 2013. A Computational Theory of Visual Receptive Fields. Biological Cybernetics, Vol. 107, pp: 589-635.
  12. Mahmoodi, S., 2015. Linear Neural Circuitry Model for Visual Receptive Fields. Journal of Mathematical Imaging and Vision.
  13. ter Haar Romeny B 2003. Front-End Vision and MultiScale Image Analysis. Springer Dordrecht.
  14. ter Haar Romeny B, Florack L, Nielsen M 2001. Scale-time Kernels and Models, In: Scale-Space and Morphology, Proceedings of Scale-Space'01, Vancouver, Canada, LNCS, Springer, Berlin.
  15. Weickert J, Ishikawa S, Imiya A (1999) Linear Scale Space has First been proposed in Japan, Journal of Mathematical Imaging and Vision, Vol. 10, pp. 237- 252.
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Paper Citation


in Harvard Style

Mahmoodi S. and Saba N. (2016). Nonlinear Model for Complex Neurons in Biological Visual Visions . In Proceedings of the 9th International Joint Conference on Biomedical Engineering Systems and Technologies - Volume 4: BIOSIGNALS, (BIOSTEC 2016) ISBN 978-989-758-170-0, pages 162-167. DOI: 10.5220/0005692601620167


in Bibtex Style

@conference{biosignals16,
author={Sasan Mahmoodi and Nasim Saba},
title={Nonlinear Model for Complex Neurons in Biological Visual Visions},
booktitle={Proceedings of the 9th International Joint Conference on Biomedical Engineering Systems and Technologies - Volume 4: BIOSIGNALS, (BIOSTEC 2016)},
year={2016},
pages={162-167},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0005692601620167},
isbn={978-989-758-170-0},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 9th International Joint Conference on Biomedical Engineering Systems and Technologies - Volume 4: BIOSIGNALS, (BIOSTEC 2016)
TI - Nonlinear Model for Complex Neurons in Biological Visual Visions
SN - 978-989-758-170-0
AU - Mahmoodi S.
AU - Saba N.
PY - 2016
SP - 162
EP - 167
DO - 10.5220/0005692601620167