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) 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.
Instituto de Ciências Biológicas, Universidade Federal do Pará, Belém, Pará, Brazil.
Vladímir de Aquino
Vde A
Silveira
Instituto de Ciências Biológicas, Universidade Federal do Pará, Belém, Pará, Brazil ; Núcleo de Medicina Tropical, Universidade Federal do Pará, Belém, Pará, Brazil.
Givago da Silva
Gda S
Souza
Instituto de Ciências Biológicas, Universidade Federal do Pará, Belém, Pará, Brazil.
Bruno Duarte
BD
Gomes
Núcleo de Medicina Tropical, Universidade Federal do Pará, Belém, Pará, Brazil.
Anderson Raiol
AR
Rodrigues
Instituto de Ciências Biológicas, Universidade Federal do Pará, Belém, Pará, Brazil ; Núcleo de Medicina Tropical, Universidade Federal do Pará, Belém, Pará, Brazil.
Luiz Carlos de Lima
LC
Silveira
D000293:Adolescent; D000328:Adult; D003118:Color Perception / Q000502:physiology*; D004192:Discrimination, Psychological / Q000502:physiology*; D019277:Entropy; D007839:Functional Laterality; D006801:Humans; D009799:Ocular Physiological Phenomena; D010364:Pattern Recognition, Visual; D011594:Psychometrics; D012858:Size Perception / Q000502:physiology*; D013028:Space Perception / Q000502:physiology*; D014796:Visual Perception / Q000502:physiology; D055815:Young Adult