Median vs. width of to percentile interval of the models shown in Figure 3b.

<p>The red line corresponds to a static for different values of , the blue triangles correspond to the temporally adapting , the orange markers correspond to uniformly sampled (diamond) and fixational image patches with Brownian motion micro-saccades (circle) from Kienzle et al. <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002889#pcbi.1002889-Kienzle1" target="_blank">[29]</a>, the gray markers to simulated eye movement datasets from van Hateren image data <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002889#pcbi.1002889-VanHateren1" target="_blank">[31]</a>, and the black marker to the optimal extended divisive normalization model. All transforms that yield a strong redundancy reduction have models that exhibit a ratio greater than (dashed lines).</p

Radial distribution and redundancy reduction achieved by the dynamically adapting model.

<p><b>A</b>: Histogram of for natural image patches sampled with simulated eye movements: The distribution predicted by the dynamically adapting model closely matches the empirical distribution. <b>B</b>: Same as in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002889#pcbi-1002889-g001" target="_blank">Fig. 1B</a> but for simulated eye movement data. The dynamically adapting achieves an almost optimal redundancy reduction performance. <b>C</b>: Each colored line shows the distribution of a random variable from 3A transformed with a Naka-Rushton function. Different colors correspond to different values of . The dashed curve corresponds to a truncated -distribution. A mixture of the colored distributions cannot resemble the truncated -distribution since there will either be peaks on the left or the right of the dashed distribution that cannot be canceled by other mixture components.</p

Simulated eye movements and adapted contrast distributions.

<p><b>A</b>: Simulated eye movements on a image from the van Hateren database <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002889#pcbi.1002889-VanHateren1" target="_blank">[31]</a>. Local microsaccades are simulated with Brownian motion with a standard deviation of px. In this example, patches are extracted around the fixation location and whitened. <b>B</b>: Values of for the extracted patches plotted along the -axis. Vertical offset was manually introduced for visibility. Colors match the ones in <b>A</b>. The different curves are the maximum likelihood Naka-Rushton distributions estimated from the data points of the same color.</p

Dynamics of the adaptive .

<p>The scatter plot shows the values of plotted against the used to transform in the dynamic divisive normalization model. The two values are clearly correlated. This indicates that the shift of the contrast response curve, which is controlled by , tracks the ambient contrast level, which is proportional to . Single elements in the plot are colored according to the quantile the value of falls in. When the ambient contrast level changes abruptly (e.g. when a saccade is made), this value is large. If the ambient contrast level is relatively stable (e.g. during fixation), this value is small. In those situations (blue dots), and exhibit the strongest proportionality.</p

Model components of the divisive normalization and radial factorization model: Natural image patches are filtered by a set of linear oriented band-pass filters.

<p>The filter responses are normalized and their norm is rescaled in the normalization step.</p

Redundancy reduction and radial distributions for different normalization models.

<p><b>A</b>: Divisive normalization model used in this study: Natural image patches are linearly filtered. These responses are nonlinearly transformed by divisive normalization or radial factorization (see text). After linear filtering the width of the conditional distribution of two filter responses depends on the value of (conditional log-histograms as contour plots). This demonstrates the presence of variance correlations. These dependencies are decreased by divisive normalization and radial factorization. <b>B</b>: Redundancy measured by multi-information after divisive normalization, extended divisive normalization, and radial factorization: divisive normalization leaves a substantial amount of residual redundancy (error bars show standard deviation over different datasets). <b>C</b>: Distributions on the norm of the filter responses for which divisive normalization (red) and extended divisive normalization (blue) are the optimal redundancy reducing mechanisms. The radial transformation of radial factorization and its corresponding distribution (mixture of five -distributions) is shown in black. While radial factorization (inset, black curve) and extended divisive normalization (inset, blue curve) achieve good redundancy reduction, they lead to physiologically implausibly shaped contrast response curves which are mainly determined by their respective radial transformations shown in the inset. The radial transformation of divisive normalization is shown for comparison (inset, red curve).</p

Multi-information and cross-entropy rates.

<p>(A) The estimated multi-information rate decreases steadily as the scale increases (the resolution decreases). (B) The conditional cross-entropy rate increases with scale. The factor corrects for the change in variance due to block-averaging and can be different for each scale . This shows that the van Hateren dataset <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0039857#pone.0039857-vanHateren1" target="_blank">[14]</a> is generally not scale-invariant. A very similar behavior is shown by images created with an occlusion based model <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0039857#pone.0039857-Lee1" target="_blank">[17]</a>.</p

Pairwise filter statistics.

<p>The joint histogram of pairs of Gaussian derivative filter responses changes as their spatial separation increases. -spherically symmetric distributions were fitted to the filter responses for natural and synthetic data. The vertical axis shows a maximum likelihood estimate of the parameter . The horizontal axis shows the vertical offset between the position of the two filters. The plot shows that the multiscale representation enables our model to match the statistics of pairwise filter responses over much longer distances, which could be one possible explanation for the better performance in terms of the cross-entropy rate.</p

Natural image samples from different models.

<p>From left to right: Samples from a mixture of conditional Gaussians <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0039857#pone.0039857-Domke1" target="_blank">[5]</a> (5×5 neighborhoods, 5 components including means), a conditional Gaussian scale mixture <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0039857#pone.0039857-Hosseini1" target="_blank">[7]</a> (7×7 neighborhoods, 7 scales), a mixture of conditional Gaussian scale mixtures and the multiscale model. The appearance of the samples changes substantially from model to model.</p

Additional file 1: Table S1. of Effectiveness of work-related medical rehabilitation in cancer patients: study protocol of a cluster-randomized multicenter trial

World Health Organization trial registration data. (DOCX 19 kb