Explaining adaptation in V1 neurons with a statistically optimized normalization model

M J Wainwright and E P Simoncelli

Published in Investigative Opthalmology and Visual Science Supplement (ARVO), vol.40 pp. S-573, May 1999.

This paper has been superseded by:
Natural image statistics and divisive normalization: Modeling nonlinearity and adaptation in cortical neurons
M J Wainwright, O Schwartz and E P Simoncelli.
Probabilistic Models of the Brain: Perception and Neural Function, pages 203--222. MIT Press, Feb 2002.


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  • Purpose: In previous work, we have shown that an extended divisive normalization model, in which each neuron's activity is divided by a weighted sum of the activity of neighboring neurons, can be derived from natural image statistics (Simoncelli & Schwartz, ARVO-98). Here we examine whether continuous re-optimization of normalization parameters according to recent input statistics can account for adaptation in V1 simple cells. Methods: Images are decomposed using a fixed linear basis, consisting of functions at different scales, orientations, and positions. Normalized responses are computed by dividing the squared response of each neuron by a weighted sum of squared responses at neighboring positions, orientations, and scales, plus a constant. Both the weights and additive constant are optimized to maximize the statistical independence of the normalized responses for a given image ensemble. Specifically, a generic set of weights is computed from an ensemble of natural images, and is used to compute unadapted responses. An adapted set of weights is computed from an ensemble consisting of natural images mixed with adapting stimuli. Results: The changes in response resulting from use of the adapted normalization parameters are remarkably similar to those seen in adapted V1 neurons. Adaptation to a high-contrast grating at the optimal frequency causes the contrast response function to undergo both lateral and compressive shifts, as documented in physiological experiments (Albrecht et al., 1984). In addition, adaptation to a grating of non-optimal frequency or orientation produces suppression in the corresponding flank of the tuning curve. Thus, the model distinguishes between the effects of contrast and pattern adaptation. Conclusions: A divisive normalization model, with parameters optimized for the statistics of recent visual input, can account for V1 simple cell behavior under a variety of adaptation conditions.

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