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Marcus V. C. Baldo; A vectorial model of sensory perception. Journal of Vision 2005;5(8):673. doi: https://doi.org/10.1167/5.8.673.
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© ARVO (1962-2015); The Authors (2016-present)
The decomposition of a sensory stimulus into vectorial components is quite evident in some modalities, such as the activation of the semicircular canals by rotations of the head. More abstract applications of vector spaces are found in other instances of sensory processing, such as color perception. Here I propose a vectorial model that is able to capture some significant properties of sensory perception. Its essence is the construction of a percept from the components of a stimulus vector acting on a pool of sensory detectors. A primary characteristic of this model is the intrinsically probabilistic nature of perception, in which a perceptual outcome is represented by a vector or, more generally, by a subspace of a vector space S. A sensory stimulus is initially broken down into its components, which are then further transformed yielding the generation of a normalized vector representing a sensory state in a Hilbert space. A given class of perceptual outcomes would be thus equivalent to an observable specified by an operator Â. If v is an eigenvector of Â, E is its corresponding eigenvalue and Û the projection operator onto the ray containing v, for a system in the state w the probability p(Â, E) that a sensory processing will result in the percept E is given by p(Â, E) = ≤wIÛw?≥ This equation, sometimes called the “statistical algorithm”, here relates perceptual outcomes to the probabilities of their occurrence. The model is able to assimilate some familiar results, such as the influence of attention or response bias on the probability of a perceptual outcome. Moreover, the model also offers a simpler and straightforward alternative to the mathematical description of psychometric and ROC curves obtained under psychophysical procedures.
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