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Vladimir A Silveira, Givago S Souza, Anderson R Rodrigues, Bruno Duarte Gomes, Luiz Carlos L Silveira; SPACE AND SPATIAL FREQUENCY JOINT ENTROPY ESTIMATED FROM DIFFERENT ACHROMATIC AND CHROMATIC STIMULI WITH AND WITHOUT HETEROCHROMATIC FLICKER PHOTOMETRY. Invest. Ophthalmol. Vis. Sci. 2014;55(13):6244.
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© ARVO (1962-2015); The Authors (2016-present)
To estimate the joint entropy of the human vision in the domains of space and spatial frequency.
We used achromatic, chromatic, and chromatic stimuli with full equiluminance correction by HFP. Four subjects were tested in all conditions, two additional subjects were tested in the chromatic condition without HFP, and a seventh subject also performed the achromatic test. The Gábor functions comprised unidimensional horizontal sinusoidal gratings with bidimensional Gaussian envelopes. A CRS VSG ViSaGe stimulus generator was used. Achromatic stimuli: CIE1931 white x = 0.270 and y = 0.280; 44.5 cd/m2. Chromatic stimuli: 15 cd/m2; red-green stimuli; CIE1976 u’=0.131 v’=0.380 and u’=0.216, v’=0.371; CIE1976 u’=0.150 v’=0.480 and u’=0.255 v’=0.480. The reference stimuli comprised 0.4, 2, and 10 cpd gratings and 1 deg Gaussian envelope. Achromatic Michelson contrasts: 2%, 5%, 10%, and 100%. Chromatic pooled cone contrast: 17%. The procedure consisted in a two interval forced choice task with the method of constant stimuli.
The experimental data of the psychometric functions for spatial extent and spatial frequency at each contrast level, which corresponded to percent of correct responses, were fitted with Gaussian functions using the Least Square Method. For each contrast level, the spatial extent entropy and spatial frequency entropy were estimated from the standard deviations of these Gaussian functions. The joint entropy was then calculated by multiplying the square root of the spatial extent entropy by the spatial frequency entropy. The joint entropy values were compared with the theoretical minimum predicted for linear systems, 1/4π or 0.0796. For low and intermediate spatial frequencies at high contrasts, the joint entropy reached very low levels, below this minimum, suggesting that there were nonlinear interactions between two or more visual mechanisms. This phenomenon occurred similarly in all conditions (achromatic, chromatic, and crhomatic with fine equiluminance adjustment, One-Way ANOVA, Tukey Test, p>0.05) and was more pronounced for spatial frequency 0.4 cycles / degree (p<0.05).
A possible explanation for this phenomenon is the occurrence of nonlinear interactions between the K, M, and P pathways in the primary visual area or in higher levels of visual processing.
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