Figure 2:
The grouping neuron–based computation of border ownership and an example of a locally ambiguous shape. (A) The output of border ownership (BO) neurons for multiple orientations and polarity assignments are grouped together by a grouping cell, G. The grouping cell reinforces all BO neurons with polarities that support evidence of a closed object located at the grouping cell. Grouping cells receive feedforward input from BO neurons, and BO neurons receive feedback input from grouping cells. Black arrows represent polarities that support the grouping neuron; gray arrows represent polarities inconsistent with that grouping neuron. (B) BO neurons receive identical driving input (e.g., an oriented edge), but their association with a specific grouping cell ties them to a specific polarity (e.g., object left or right). BO neurons responding to the same stimulus compete with each other (dashed line), with feedback from grouping neurons driving differentiation over polarity. (C) A classical locally ambiguous shape for the assignment of border ownership. The top and bottom corners of the c shape have identical local features to the concavity missing from the middle. Each region has three edges making a nearly closed convexity and has the same number of corner features supporting the interior of an object. Each colored grouping cell has a receptive field (dashed circle) from which it receives input from BO neurons with appropriate polarities (like-colored arrows). Note that along the concavity, BO neurons of opposing polarities receive equal amounts of feedback and supply equal amounts of driving input to the grouping neurons. Only a small subset of BO and grouping neurons are drawn for illustrative purposes. (D) The same shape as in panel C with grouping performed over larger receptive fields. Note that the polarity assignment supported by the larger grouping would give an incorrect polarity to the concavity of the c shape. Without explicitly modeling the entire object, the assignment of edge polarities requires a way of quantifying the local ambiguity of decisions and moving the network toward an unambiguous assignment. (Portions of the figure were inspired by Craft et al., 2007.)

The grouping neuron–based computation of border ownership and an example of a locally ambiguous shape. (A) The output of border ownership (BO) neurons for multiple orientations and polarity assignments are grouped together by a grouping cell, G. The grouping cell reinforces all BO neurons with polarities that support evidence of a closed object located at the grouping cell. Grouping cells receive feedforward input from BO neurons, and BO neurons receive feedback input from grouping cells. Black arrows represent polarities that support the grouping neuron; gray arrows represent polarities inconsistent with that grouping neuron. (B) BO neurons receive identical driving input (e.g., an oriented edge), but their association with a specific grouping cell ties them to a specific polarity (e.g., object left or right). BO neurons responding to the same stimulus compete with each other (dashed line), with feedback from grouping neurons driving differentiation over polarity. (C) A classical locally ambiguous shape for the assignment of border ownership. The top and bottom corners of the c shape have identical local features to the concavity missing from the middle. Each region has three edges making a nearly closed convexity and has the same number of corner features supporting the interior of an object. Each colored grouping cell has a receptive field (dashed circle) from which it receives input from BO neurons with appropriate polarities (like-colored arrows). Note that along the concavity, BO neurons of opposing polarities receive equal amounts of feedback and supply equal amounts of driving input to the grouping neurons. Only a small subset of BO and grouping neurons are drawn for illustrative purposes. (D) The same shape as in panel C with grouping performed over larger receptive fields. Note that the polarity assignment supported by the larger grouping would give an incorrect polarity to the concavity of the c shape. Without explicitly modeling the entire object, the assignment of edge polarities requires a way of quantifying the local ambiguity of decisions and moving the network toward an unambiguous assignment. (Portions of the figure were inspired by Craft et al., 2007.)

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