Estimate results for an “average subject” (ASU; see text for details).

<p>One-dimensional entropies for the domain of space (S) an d spatial frequency (F), as well as the joint entropy (J) for 0.4, 2, and 10 cycles/degree. Estimates were based on data collected from seven subjects which were tested using Gábor patterns at four different Michelson contrasts.</p

Procedure.

<p>The psychophysical measurements used a modification of the two interval forced choice task, 2IFC. A reference stimulus was compared with a test stimulus having different spatial frequency or different spatial extent. Blank fields were interleaved with reference stimulus and test stimulus. A beep indicated to the subject the moment to respond. Two forced choices were available as subject responses, either “equal stimuli” or “different stimuli”. After each trial, the spatial frequency or the spatial extent of the test stimulus was changed following the method of constant stimuli. A total of 21 different envelope's standard deviations around the reference standard deviation and 19 different grating's spatial frequencies around the reference spatial frequency were tested.</p

Statistical comparisons for the joint entropy measurements obtained from individual subjectspresented in Tables 1–3.

<p>Individual values for each subject, as well as means and standard errors of the means for the sample are plotted for different contrasts at 0.4, 2, and 10 cycles/degree (left panels, top to bottom) and for the three spatial frequencies at 5%, 10%, and 100% Michelson contrasts (right panels, top to bottom). Results for conditions with two or less measurements were not plotted (2% contrast at 0.4 and 10 cycles/degree). In all frequencies there was a trend for joint entropy to decrease when contrast was increased, but this reached the level of statistical significance only for the comparison between 5% and 100% contrasts (p<0.05; One-Way ANOVA, Tukey Multiple Comparison Test). For all contrasts, joint entropy was significantly lower at 0.4 and 2 cycles/degree when compared with 10 cycles/degree (p<0.05).</p

Spatial luminance contrast sensitivity for six of the seven subjects of this study.

<p>Both eyes were separately evaluated. Each data point represents either the right or left eye monocular contrast sensitivity at 11 different spatial frequencies (circles). Dashed curves represent the upper and lower tolerance limits estimated from control subjects (n = 62, 16–30 years old).</p

Results for all seven subjects tested, means and standard errors of the means for the sample, as well as estimate results for an “average subject” (ASU; see text for details).

<p>Subjects were tested using Gábor patterns at four different Michelson contrasts. To estimate spatial extent entropy (S²), the spatial frequency was kept constant at 0.4 cycles/degree while the spatial standard deviation was varied around 1 deg. To estimate spatial frequency entropy (F), the spatial frequency was varied around 0.4 cycles/degree while the spatial standard deviation was kept constant at 1 deg. Joint entropy (J) was obtained by multiplying the spatial frequency entropy times the square root of the spatial extent entropy to account for the use of Gábor stimuli comprising 2D Gaussian envelopes and 1D sine wave gratings (J = F x S). For some subjects and stimulus conditions it was not possible to provide a good fitting to the data points (empty cells). However, for the ASU estimates, all data points were taken in consideration.</p

ASU (“average subject”) spatial and spatial frequency joint entropy as a function of Michelson contrast for three different spatial frequencies: 0.4, 2, and 10 cycles/degree (diamonds, square, and triangles, respectively).

<p>The dashed line represents the theoretical minimum for the 1D joint entropy of a system comprising only linear interactions between its subsystems. Using standard deviation as the entropy parameter and cycles/degree as spatial frequency metrics, the joint entropy minimum corresponds to 1/4π or 0.0796, and can only be attained by the product of the joint entropies for a Gábor function and its Fourier transform <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0086579#pone.0086579-Gbor1" target="_blank">[14]</a>, <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0086579#pone.0086579-Daugman1" target="_blank">[15]</a>, <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0086579#pone.0086579-Rassias1" target="_blank">[22]</a>. For all spatial frequencies, the joint entropy was higher at low contrasts and decreased when contrast was raised. At low and intermediate spatial frequencies and high contrasts, joint entropy reached levels below the minimum, an effect particularly pronounced at 0.4 cycles/degree and high contrast. This effect is suggestive that non-linear interactions between two or more visual mechanisms occur at these ranges of contrast and spatial frequency (see text for details).</p

Psychometric functions obtained from Subject GSS for spatial frequency discrimination and spatial extent discrimination (left and right columns, respectively) at four different Michelson contrasts (100%, 10%, 5%, and 2% from top to bottom, respectively).

<p>Reference stimulus: 2 cycles/degree and 1 degree. Data points represent percent of correct responses (filled circles) or incorrect responses (empty squares). Curves are Gaussian fits to the data. The standard deviations of these Gaussian functions were used as measurement of entropy in the spatial frequency domain or spatial domain, respectively.</p

Mean psychometric functions for spatial frequency discrimination and spatial extent discrimination (left and right columns, respectively) at four different Michelson contrasts (100%, 10%, 5%, and 2% from top to bottom, respectively).

<p>Reference stimulus: 2 cycles/degree and 1 degree. Filled circles and empty squares represent means for correct responses and incorrect responses, respectively, obtained from the seven subjects. Vertical bars represent the standard errors of the means. Curves are Gaussian fits to the data. The standard deviations of these Gaussian functions were used as measurement of entropy in the spatial frequency domain or spatial domain, respectively.</p

Ganglion Cell and Displaced Amacrine Cell Density Distribution in the Retina of the Howler Monkey (<i>Alouatta caraya</i>)

<div><p>Unlike all other New World (platyrrine) monkeys, both male and female howler monkeys (<i>Alouatta sp.</i>) are obligatory trichromats. In all other platyrrines, only females can be trichromats, while males are always dichromats, as determined by multiple behavioral, electrophysiological, and genetic studies. In addition to obligatory trichromacy, <i>Alouatta</i> has an unusual fovea, with substantially higher peak cone density in the foveal pit than every other diurnal anthropoid monkey (both platyrrhines and catarrhines) and great ape yet examined, including humans. In addition to documenting the general organization of the retinal ganglion cell layer in <i>Alouatta</i>, the distribution of cones is compared to retinal ganglion cells, to explore possible relationships between their atypical trichromacy and foveal specialization. The number and distribution of retinal ganglion cells and displaced amacrine cells were determined in six flat-mounted retinas from five <i>Alouatta caraya</i>. Ganglion cell density peaked at 0.5 mm between the fovea and optic nerve head, reaching 40,700–45,200 cells/mm². Displaced amacrine cell density distribution peaked between 0.5–1.75 mm from the fovea, reaching mean values between 2,050–3,100 cells/mm². The mean number of ganglion cells was 1,133,000±79,000 cells and the mean number of displaced amacrine cells was 537,000±61,800 cells, in retinas of mean area 641±62 mm². Ganglion cell and displaced amacrine cell density distribution in the <i>Alouatta</i> retina was consistent with that observed among several species of diurnal Anthropoidea, both platyrrhines and catarrhines. The principal alteration in the <i>Alouatta</i> retina appears not to be in the number of any retinal cell class, but rather a marked gradient in cone density within the fovea, which could potentially support high chromatic acuity in a restricted central region.</p></div

Ganglion cell isodensity maps for an “average” <i>Alouatta</i> retina.

<p>Isodensity contours in cells/mm² were drawn from mean values from every retinal location that was measured and using the map of retina AC 02LM as template. (<b>A</b>) Isodensity contours for the whole retina. (<b>B</b>) Isodensity contours for the central retinal region. Conventions were the same of <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0115291#pone-0115291-g004" target="_blank">Figs. 4</a>–<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0115291#pone-0115291-g005" target="_blank">5</a>. Ganglion cell isodensity contours were elongated in the nasal direction reflecting the higher ganglion cell density in the nasal quadrant, a feature present in different degrees in all six retinas studied. The “average” retina also had a small elongation of the central isodensity contours along the dorsoventral meridian, reflecting the presence of this feature in half of the retinas (see text for details).</p