Joint entropy for space and spatial frequency domains estimated from psychometric functions of achromatic discrimination.

We used psychometric functions to estimate the joint entropy for space discrimination and spatial frequency discrimination. Space discrimination was taken as discrimination of spatial extent. Seven subjects were tested. Gábor functions comprising unidimensionalsinusoidal gratings (0.4, 2, and 10 cpd...

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Main Authors: Vladímir de Aquino Silveira, Givago da Silva Souza, Bruno Duarte Gomes, Anderson Raiol Rodrigues, Luiz Carlos de Lima Silveira
Format: Article
Language:English
Published: Public Library of Science (PLoS) 2014-01-01
Series:PLoS ONE
Online Access:http://europepmc.org/articles/PMC3900586?pdf=render
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spelling doaj-c282a11f86154d6e809ffb4c323e62b12020-11-24T21:45:07ZengPublic Library of Science (PLoS)PLoS ONE1932-62032014-01-0191e8657910.1371/journal.pone.0086579Joint entropy for space and spatial frequency domains estimated from psychometric functions of achromatic discrimination.Vladímir de Aquino SilveiraGivago da Silva SouzaBruno Duarte GomesAnderson Raiol RodriguesLuiz Carlos de Lima SilveiraWe used psychometric functions to estimate the joint entropy for space discrimination and spatial frequency discrimination. Space discrimination was taken as discrimination of spatial extent. Seven subjects were tested. Gábor functions comprising unidimensionalsinusoidal gratings (0.4, 2, and 10 cpd) and bidimensionalGaussian envelopes (1°) were used as reference stimuli. The experiment comprised the comparison between reference and test stimulithat differed in grating's spatial frequency or envelope's standard deviation. We tested 21 different envelope's standard deviations around the reference standard deviation to study spatial extent discrimination and 19 different grating's spatial frequencies around the reference spatial frequency to study spatial frequency discrimination. Two series of psychometric functions were obtained for 2%, 5%, 10%, and 100% stimulus contrast. The psychometric function data points for spatial extent discrimination or spatial frequency discrimination were fitted with Gaussian functions using the least square method, and the spatial extent and spatial frequency entropies were estimated from the standard deviation of these Gaussian functions. Then, joint entropy was obtained by multiplying the square root of space extent entropy times the spatial frequency entropy. We compared our results to the theoretical minimum for unidimensional Gábor functions, 1/4π or 0.0796. At low and intermediate spatial frequencies and high contrasts, joint entropy reached levels below the theoretical minimum, suggesting non-linear interactions between two or more visual mechanisms. We concluded that non-linear interactions of visual pathways, such as the M and P pathways, could explain joint entropy values below the theoretical minimum at low and intermediate spatial frequencies and high contrasts. These non-linear interactions might be at work at intermediate and high contrasts at all spatial frequencies once there was a substantial decrease in joint entropy for these stimulus conditions when contrast was raised.http://europepmc.org/articles/PMC3900586?pdf=render
collection DOAJ
language English
format Article
sources DOAJ
author Vladímir de Aquino Silveira
Givago da Silva Souza
Bruno Duarte Gomes
Anderson Raiol Rodrigues
Luiz Carlos de Lima Silveira
spellingShingle Vladímir de Aquino Silveira
Givago da Silva Souza
Bruno Duarte Gomes
Anderson Raiol Rodrigues
Luiz Carlos de Lima Silveira
Joint entropy for space and spatial frequency domains estimated from psychometric functions of achromatic discrimination.
PLoS ONE
author_facet Vladímir de Aquino Silveira
Givago da Silva Souza
Bruno Duarte Gomes
Anderson Raiol Rodrigues
Luiz Carlos de Lima Silveira
author_sort Vladímir de Aquino Silveira
title Joint entropy for space and spatial frequency domains estimated from psychometric functions of achromatic discrimination.
title_short Joint entropy for space and spatial frequency domains estimated from psychometric functions of achromatic discrimination.
title_full Joint entropy for space and spatial frequency domains estimated from psychometric functions of achromatic discrimination.
title_fullStr Joint entropy for space and spatial frequency domains estimated from psychometric functions of achromatic discrimination.
title_full_unstemmed Joint entropy for space and spatial frequency domains estimated from psychometric functions of achromatic discrimination.
title_sort joint entropy for space and spatial frequency domains estimated from psychometric functions of achromatic discrimination.
publisher Public Library of Science (PLoS)
series PLoS ONE
issn 1932-6203
publishDate 2014-01-01
description We used psychometric functions to estimate the joint entropy for space discrimination and spatial frequency discrimination. Space discrimination was taken as discrimination of spatial extent. Seven subjects were tested. Gábor functions comprising unidimensionalsinusoidal gratings (0.4, 2, and 10 cpd) and bidimensionalGaussian envelopes (1°) were used as reference stimuli. The experiment comprised the comparison between reference and test stimulithat differed in grating's spatial frequency or envelope's standard deviation. We tested 21 different envelope's standard deviations around the reference standard deviation to study spatial extent discrimination and 19 different grating's spatial frequencies around the reference spatial frequency to study spatial frequency discrimination. Two series of psychometric functions were obtained for 2%, 5%, 10%, and 100% stimulus contrast. The psychometric function data points for spatial extent discrimination or spatial frequency discrimination were fitted with Gaussian functions using the least square method, and the spatial extent and spatial frequency entropies were estimated from the standard deviation of these Gaussian functions. Then, joint entropy was obtained by multiplying the square root of space extent entropy times the spatial frequency entropy. We compared our results to the theoretical minimum for unidimensional Gábor functions, 1/4π or 0.0796. At low and intermediate spatial frequencies and high contrasts, joint entropy reached levels below the theoretical minimum, suggesting non-linear interactions between two or more visual mechanisms. We concluded that non-linear interactions of visual pathways, such as the M and P pathways, could explain joint entropy values below the theoretical minimum at low and intermediate spatial frequencies and high contrasts. These non-linear interactions might be at work at intermediate and high contrasts at all spatial frequencies once there was a substantial decrease in joint entropy for these stimulus conditions when contrast was raised.
url http://europepmc.org/articles/PMC3900586?pdf=render
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