Abstract
Based on the energy model for disparity-tuned neurons, we calculate probability density functions of complex cell activity for random-dot stimuli. We investigate the effects of normalization and give analytical expressions for the disparity tuning curve and its variance. We show that while normalized and non-normalized complex cells have similar tuning curves, the variance is significantly lower for normalized complex cells, which makes disparity estimation more reliable. The results of the analytical calculations are compared to computer simulations.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Ohzawa, I., DeAngelis, G., Freeman, R.: Stereoscopic depth discrimination in the visual cortex: Neurons ideally suited as disparity detectors. Science 249, 1037–1041 (1990)
Adelson, E., Bergen, J.: Spatiotemporal energy models for the perception of motion. J. Opt. Soc. Am. A 2, 284–299 (1985)
Anzai, A., Ohzawa, I., Freeman, R.: Neural mechanisms for processing binocular information. I. Simple cells. J. Neurophysiol. 82, 891–908 (1999)
Anzai, A., Ohzawa, I., Freeman, R.: Neural mechanisms for processing binocular information. II. Complex cells. J. Neurophysiol. 82, 909–924 (1999)
Fleet, D., Heeger, D., Wagner, H.: Modeling binocular neurons in primary visual cortex. In: Jenkin, M., Harris, L. (eds.) Computational and Biological Mechanisms of Visual Coding, pp. 103–130. Cambridge University Press, Cambridge (1996)
Heeger, D.: Normalization of cell responses in cat striate cortex. Vis. Neurosci. 9, 181–197 (1992)
Carandini, M., Heeger, D., Movshon, J.A.: Linearity and normalization in simple cells of the macaque primary visual cortex. The Journal of Neuroscience 17, 8621–8644 (1997)
Wainwright, M., Schwartz, O., Simoncelli, E.: Natural image statistics and divisive normalization: Modeling nonlinearity and adaptation in cortical neurons. In: Rao, R., Olshausen, B., Lewicki, M. (eds.) Probabilistic Models of the Brain: Perception and Neural Function, MIT Press, Cambridge (2002)
Anzai, A., Ohzawa, I., Freeman, R.: Neural mechanisms for encoding binocular disparity: Receptive field position versus phase. J. Neurophysiol. 82, 874–890 (1999)
DeValois, R., DeValois, K.: Spatial Vision. Oxford University Press, Oxford (1988)
Zhu, Y., Qian, N.: Binocular receptive field models, disparity tuning, and characteristic disparity. Neural Computation 8, 1611–1641 (1996)
Tsai, J., Victor, J.: Reading a population code: a multi-scale neural model for representing binocular disparity. Vision Research 43, 445–466 (2003)
Tanabe, S., Doi, T., Umeda, K., Fujita, I.: Disparity-tuning characteristics of neuronal responses to dynamic random-dot stereograms in macaque visual area V4. J. Neurophysiol. 94, 2683–2699 (2005)
Truchard, A., Ohzawa, I., Freeman, R.: Contrast gain control in the visual cortex: Monocular versus binocular mechanisms. The Journal of Neuroscience 20, 3017–3032 (2000)
Read, J., Cumming, B.: Testing quantitative models of binocular disparity selectivity in primary visual cortex. J. Neurophysiol. 90, 2795–2817 (2003)
Prince, S., Pointon, A., Cumming, B., Parker, A.: Quantitative analysis of the responses of v1 neurons to horizontal disparity in dynamic random-dot stereograms. J. Neurophysiol. 87, 191–208 (2002)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Stürzl, W., Mallot, H.A., Knoll, A. (2007). An Analytical Model of Divisive Normalization in Disparity-Tuned Complex Cells. In: de Sá, J.M., Alexandre, L.A., Duch, W., Mandic, D. (eds) Artificial Neural Networks – ICANN 2007. ICANN 2007. Lecture Notes in Computer Science, vol 4668. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74690-4_79
Download citation
DOI: https://doi.org/10.1007/978-3-540-74690-4_79
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-74689-8
Online ISBN: 978-3-540-74690-4
eBook Packages: Computer ScienceComputer Science (R0)