Connectivity structure established during training in the curve tracing task.

<p><b>A</b>, Feedforward input into the linking layer causes balanced excitation and inhibition (through the inhibitory units) preventing linking layer units to become active. The unit in the linking layer tuned to red (not shown here) provides modulatory input, thereby increasing the impact of feedforward excitation to the left unit and this extra activity can spread through horizontal connections in the linking layer. <b>B</b>, If a unit in the linking layer does not receive feedforward input, horizontal modulatory influences cannot occur, thereby preventing the spread of activity across gaps in the linking layer, which is important for the detection of connectedness.</p

Curve tracing task.

<p>We trained the model to make an eye movement to a green circular marker that was on the target curve, which was cued with a red circle. The other curve was a distractor and had to be be ignored. This task requires the grouping of the connected image elements of the target curve.</p

Connection strengths between linking units with different orientation preferences (O1–O4 denote the different orientations of contour elements) in <i>one</i> hemifield and an example association layer unit A2 with a strong connection to the motor unit in this hemisphere, after training to criterion (feedforward strength A and feedback strength B).

<p>Similar association units were established in the other hemisphere.</p

Activity in an example network trained in the curve-tracing task.

<p>A, An example stimulus with two green saccade targets and a red cue that indicates which curve is target. T1 and T2 are two pixels of the target curve and D1 and D2 are pixels of the distractor (we evaluated activity for different stimuli at the equivalent locations). <b>B</b>, Activity <i>p</i> (membrane potential) of example units of the linking layer, averaged across multiple stimulus presentations. The curve tracing task induced an increase of activity of units representing the target curve (T1 and T2) and a decrease in the activity of units representing the distractor (D1 and D2; 95% point-wise confidence bands are within line width). <b>C</b>, We normalized the difference in activity elicited by corresponding positions of the target and distractor curve in the linking layer to investigate the time-course of the response enhancement. We found that the latency of the response enhancement increased for pixels of the target curve that are farther from the red cue, in accordance with previous neurophysiological results [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004489#pcbi.1004489.ref095" target="_blank">95</a>]. <b>D</b>, Activity in the motor layer was strongest for pixels with a green cue. Note that the activity elicited by the saccade cue on the target curve (<i>S</i>_<i>T</i>) was stronger than that elicited by the saccade cue on the distractor curve (<i>S</i>_<i>D</i>). <b>E</b>, Time course of normalized response differences in the motor layer. Also here the response enhancement occurred later for pixels that were farther from the red cue. The activities in the motor layer <b>(E)</b> and the linking layer <b>(C)</b> have similar time-courses as have been reported in the frontal and visual cortex of monkeys [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004489#pcbi.1004489.ref017" target="_blank">17</a>]. Note that the propagation is quite fast due to the small network size but that it critically depends on the recurrent interaction as theoretically predicted by [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004489#pcbi.1004489.ref096" target="_blank">96</a>].</p

Generalization to longer line lengths.

<p>Although the model had been trained with lines with up to five pixels, it also generalized to longer line lengths. In this example stimulus, the model propagated enhanced activity over a target line of seven pixels (darker colors denote higher levels of activity).</p

Neuronal correlates of contour integration and curve tracing in primary visual cortex (area V1).

<p>A) Contour integration task. If monkeys have been trained to make a saccade to a pattern with a string of collinear contour elements (1, 3, 5, 7 or 9 collinear bars, left panel), the neuronal responses in V1 elicited by these elements are stronger than the responses elicited by a single line element that is not part of such a perceptual group (right panel). This influence of colinearity on V1 activity is not present before training. The purple circle in the upper panel illustrates the V1 receptive field. Re-drawn from [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004489#pcbi.1004489.ref015" target="_blank">15</a>]. <b>B)</b> Curve-tracing task. Monkeys were trained to mentally trace a target curve (T) that is connected to a fixation point (FP) because they had to make an eye movement to a larger red circle at the end of this curve. They had to ignore a distractor curve (D). After training in this task, V1 activity elicited by the target curve (red response in lower panel) became stronger than that elicited by the distractor (blue response). The green circle in the upper panel shows the V1 receptive field. Adapted from [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004489#pcbi.1004489.ref017" target="_blank">17</a>].</p

Neural network structure.

<p>The input layer contains 2D-maps of feature selective units (corresponding to representations in cortical area V1), which provide input to a “linking layer” that can establish perceptual groups. Input units activate excitatory and inhibitory units in the linking layer, and inhibitory units provide disynaptic inhibition to the excitatory units in this layer. Modulatory connections (green), which increase the excitatory impact, interconnect excitatory units with adjacent receptive fields in the same feature maps and units with overlapping receptive fields in different feature maps. Excitatory units in the linking layer can activate any unit in the association layer (e.g. in extrastriate or parietal cortex), and receive modulatory feedback connections. Units in the association layer, in turn, activate units in the motor layer (corresponding to neurons in the frontal eye field) that represent action-values and select one of a number of actions. Black connections have a fixed strength and excitatory (red), inhibitory (blue) and modulatory (green) connections undergo synaptic plasticity.</p

Stimulus and lateral connectivity in the “linking layer”.

<p><b>A</b> Example stimulus (the patterns presented to the two hemispheres are plotted above each other). Re-drawn from [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004489#pcbi.1004489.ref015" target="_blank">15</a>] <b>B</b> Lateral connectivity in the “linking layer” for one orientation and hemisphere for units selective for diagonal line elements before training. <b>C</b> Lateral connectivity after training (we observed similar patterns for the other orientations). Line thickness corresponds to connection strength (thickest line corresponds to a connection strength of 0.36). Note that due to the small amount of simulated units (one unit per spatial input location) we did not introduce jitter into the stimulus which would have resulted in multiple parallel “thick lines”.</p

Connectivity structure established during training in the curve tracing task.

<p><b>A</b>, Feedforward input into the linking layer causes balanced excitation and inhibition (through the inhibitory units) preventing linking layer units to become active. The unit in the linking layer tuned to red (not shown here) provides modulatory input, thereby increasing the impact of feedforward excitation to the left unit and this extra activity can spread through horizontal connections in the linking layer. <b>B</b>, If a unit in the linking layer does not receive feedforward input, horizontal modulatory influences cannot occur, thereby preventing the spread of activity across gaps in the linking layer, which is important for the detection of connectedness.</p

Accuracy of the model and comparison to the accuracy of monkeys.

<p>Left, performance of monkeys re-drawn from [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004489#pcbi.1004489.ref014" target="_blank">14</a>]. The five panels show the accuracy across training days with patterns of increasing contour length; 1 line (blue), 3 (purple), 5 (green), 7 (orange) or 9 colinear lines (light blue). Note that the monkeys performed at chance level for patterns with line length 1, which are indistinguishable from distractor patterns. Solid lines are cubic spline fits. <b>Right</b>, Accuracy of the model for the same stimuli, smoothed with a Gaussian (<i>σ</i> = 100 trials). The number of iterations refers to repetitions of the same contour length, i.e. the total number of iterations is five times as large because the model was exposed to five different contour lengths.</p