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Active gaze control improves optic flow-based segmentation and steering.

Raudies F, Mingolla E, Neumann H - PLoS ONE (2012)

Bottom Line: To support our suggestion we derive an analytical model that shows: Tangentially fixating the outer surface of an obstacle leads to strong flow discontinuities that can be used for flow-based segmentation.Fixation of the target center while gaze and heading are locked without head-, body-, or eye-rotations gives rise to a symmetric expansion flow with its center at the point being approached, which facilitates steering toward a target.We conclude that gaze control incorporates ecological constraints to improve the robustness of steering and collision avoidance by actively generating flows appropriate to solve the task.

View Article: PubMed Central - PubMed

Affiliation: Center of Excellence for Learning in Education, Science, and Technology, Boston University, Boston, Massachusetts, United States of America. fraudies@bu.edu

ABSTRACT
An observer traversing an environment actively relocates gaze to fixate objects. Evidence suggests that gaze is frequently directed toward the center of an object considered as target but more likely toward the edges of an object that appears as an obstacle. We suggest that this difference in gaze might be motivated by specific patterns of optic flow that are generated by either fixating the center or edge of an object. To support our suggestion we derive an analytical model that shows: Tangentially fixating the outer surface of an obstacle leads to strong flow discontinuities that can be used for flow-based segmentation. Fixation of the target center while gaze and heading are locked without head-, body-, or eye-rotations gives rise to a symmetric expansion flow with its center at the point being approached, which facilitates steering toward a target. We conclude that gaze control incorporates ecological constraints to improve the robustness of steering and collision avoidance by actively generating flows appropriate to solve the task.

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Shows a neural implementation of derivative operators and a network for the computation of divergence, curl, and shear.Derivative operators  and  are applied to the flow components  and . This gives the four entries of the Jacobian matrix, see Equation (5). Sums and differences between two entries of the Jacobian matrix result in divergence, curl, and shear components (last row). The symbol ‘*’ denotes the correlation with respect to the coordinate system shown in the top, middle of the figure.
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pone-0038446-g010: Shows a neural implementation of derivative operators and a network for the computation of divergence, curl, and shear.Derivative operators and are applied to the flow components and . This gives the four entries of the Jacobian matrix, see Equation (5). Sums and differences between two entries of the Jacobian matrix result in divergence, curl, and shear components (last row). The symbol ‘*’ denotes the correlation with respect to the coordinate system shown in the top, middle of the figure.

Mentions: Partial derivatives and of the flow are approximated using biologically inspired operators with antagonistic and asymmetric center-surround [22]. These operators are similar to the motion-opponent operators used for the estimation of self-motion and relative depth [64] as well as the estimation of self-motion in combination with a monopole mapping [35]. We define these biologically inspired operators by using the difference of two Gaussian subfields. For the partial derivative in the x-component the positive Gaussian subfield that models the positive center of a cell’s receptive field has a standard deviation of two pixels in the y-component and one pixel in the x-component. This models an elliptical shape for the Gaussian kernel. The kernel’s size is 9×5 pixels. The negative Gaussian subfield or negative surround of a cell’s receptive field has a standard deviation of two pixels in the y-component and three pixels in the x-component and its modeled size is 9×13 pixels. To align correlation results from the two subfields we shift the center result by one pixel to the left and the surround result by two pixels to the right. See also the icon for x-derivatives in Figure 4. This assumes the negative subfield to be on the right and the positive subfield to be on the left. For the partial derivative in the y-component this circuit is 90° rotated in counterclockwise direction, see also the icon for y-derivatives in Figure 10. Then the decomposition into divergence, curl, and, shear components is calculated by using the Equation (5), compare also with the circuit shown in Figure 10. The x- and y-flow components are correlated with the Gaussian subfields that are subtracted in order to compute the partial x- and y-derivatives for each flow component. This results in four combinations that are shown in the middle of the circuit in Figure 10. Sums and differences of these four partial derivatives result in divergence, curl, and shear components. See bottom row in Figure 10.


Active gaze control improves optic flow-based segmentation and steering.

Raudies F, Mingolla E, Neumann H - PLoS ONE (2012)

Shows a neural implementation of derivative operators and a network for the computation of divergence, curl, and shear.Derivative operators  and  are applied to the flow components  and . This gives the four entries of the Jacobian matrix, see Equation (5). Sums and differences between two entries of the Jacobian matrix result in divergence, curl, and shear components (last row). The symbol ‘*’ denotes the correlation with respect to the coordinate system shown in the top, middle of the figure.
© Copyright Policy
Related In: Results  -  Collection

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getmorefigures.php?uid=PMC3375264&req=5

pone-0038446-g010: Shows a neural implementation of derivative operators and a network for the computation of divergence, curl, and shear.Derivative operators and are applied to the flow components and . This gives the four entries of the Jacobian matrix, see Equation (5). Sums and differences between two entries of the Jacobian matrix result in divergence, curl, and shear components (last row). The symbol ‘*’ denotes the correlation with respect to the coordinate system shown in the top, middle of the figure.
Mentions: Partial derivatives and of the flow are approximated using biologically inspired operators with antagonistic and asymmetric center-surround [22]. These operators are similar to the motion-opponent operators used for the estimation of self-motion and relative depth [64] as well as the estimation of self-motion in combination with a monopole mapping [35]. We define these biologically inspired operators by using the difference of two Gaussian subfields. For the partial derivative in the x-component the positive Gaussian subfield that models the positive center of a cell’s receptive field has a standard deviation of two pixels in the y-component and one pixel in the x-component. This models an elliptical shape for the Gaussian kernel. The kernel’s size is 9×5 pixels. The negative Gaussian subfield or negative surround of a cell’s receptive field has a standard deviation of two pixels in the y-component and three pixels in the x-component and its modeled size is 9×13 pixels. To align correlation results from the two subfields we shift the center result by one pixel to the left and the surround result by two pixels to the right. See also the icon for x-derivatives in Figure 4. This assumes the negative subfield to be on the right and the positive subfield to be on the left. For the partial derivative in the y-component this circuit is 90° rotated in counterclockwise direction, see also the icon for y-derivatives in Figure 10. Then the decomposition into divergence, curl, and, shear components is calculated by using the Equation (5), compare also with the circuit shown in Figure 10. The x- and y-flow components are correlated with the Gaussian subfields that are subtracted in order to compute the partial x- and y-derivatives for each flow component. This results in four combinations that are shown in the middle of the circuit in Figure 10. Sums and differences of these four partial derivatives result in divergence, curl, and shear components. See bottom row in Figure 10.

Bottom Line: To support our suggestion we derive an analytical model that shows: Tangentially fixating the outer surface of an obstacle leads to strong flow discontinuities that can be used for flow-based segmentation.Fixation of the target center while gaze and heading are locked without head-, body-, or eye-rotations gives rise to a symmetric expansion flow with its center at the point being approached, which facilitates steering toward a target.We conclude that gaze control incorporates ecological constraints to improve the robustness of steering and collision avoidance by actively generating flows appropriate to solve the task.

View Article: PubMed Central - PubMed

Affiliation: Center of Excellence for Learning in Education, Science, and Technology, Boston University, Boston, Massachusetts, United States of America. fraudies@bu.edu

ABSTRACT
An observer traversing an environment actively relocates gaze to fixate objects. Evidence suggests that gaze is frequently directed toward the center of an object considered as target but more likely toward the edges of an object that appears as an obstacle. We suggest that this difference in gaze might be motivated by specific patterns of optic flow that are generated by either fixating the center or edge of an object. To support our suggestion we derive an analytical model that shows: Tangentially fixating the outer surface of an obstacle leads to strong flow discontinuities that can be used for flow-based segmentation. Fixation of the target center while gaze and heading are locked without head-, body-, or eye-rotations gives rise to a symmetric expansion flow with its center at the point being approached, which facilitates steering toward a target. We conclude that gaze control incorporates ecological constraints to improve the robustness of steering and collision avoidance by actively generating flows appropriate to solve the task.

Show MeSH