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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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Response for flow divergence, curl, and shear get infinitely large if fixating tangentially.These strong responses located at objects’ edges allow for their segmentation. In all cases the camera has the translational velocity (vx, vy, vz). a) Sketch of the scenario for fixating a plane that has a tilt α >0 in the xz-plane. The lower four rows show the functions for the response of flow components depending on the declination from the center of the visual field along the horizontal axis. Divergence and Type I shear depend linearly on x, the declination along the x-axis. Curl and Type II shear are independent of x. b) For a plane parallel to the optical axis all four components are reciprocal dependent on x. For values close to zero the component’s responses approach minus infinity. In this panel we depicted div, curl, and shear components by the gray-dashed line for a specific eccentricity or horizontal distance x of the plane from the gaze direction. c) A curved surface that is cylindrical in the xz-plane and planar in the xy/yz-planes leads to the same response characteristics for divergence, curl, and shear. For x→0 or x→R all four components approach ±infinity. The difference in linear versus hyperbolic response curves for case a) versus b) and c) gives an explanation why segmentation of obstacles can be improved by fixating the edge. Such a fixation results in strong responses that could be detected by difference operators. All sketches in the first row show a top-down view of the three scenarios, respectively.
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pone-0038446-g005: Response for flow divergence, curl, and shear get infinitely large if fixating tangentially.These strong responses located at objects’ edges allow for their segmentation. In all cases the camera has the translational velocity (vx, vy, vz). a) Sketch of the scenario for fixating a plane that has a tilt α >0 in the xz-plane. The lower four rows show the functions for the response of flow components depending on the declination from the center of the visual field along the horizontal axis. Divergence and Type I shear depend linearly on x, the declination along the x-axis. Curl and Type II shear are independent of x. b) For a plane parallel to the optical axis all four components are reciprocal dependent on x. For values close to zero the component’s responses approach minus infinity. In this panel we depicted div, curl, and shear components by the gray-dashed line for a specific eccentricity or horizontal distance x of the plane from the gaze direction. c) A curved surface that is cylindrical in the xz-plane and planar in the xy/yz-planes leads to the same response characteristics for divergence, curl, and shear. For x→0 or x→R all four components approach ±infinity. The difference in linear versus hyperbolic response curves for case a) versus b) and c) gives an explanation why segmentation of obstacles can be improved by fixating the edge. Such a fixation results in strong responses that could be detected by difference operators. All sketches in the first row show a top-down view of the three scenarios, respectively.

Mentions: In order to avoid an obstacle it has to be visually segmented from the background. In addition to texture, color, and stereo cues, flow fields can provide a cue for segmentation. But what should the pattern of self-motion and gaze be to generate flow that best facilitates segmentation? Qualitative flow derivative components caused by different patterns of self-motion and gaze are shown in Figure 4a. Fixating the edge of an object, the derivative components that are present are the same regardless of the alignment between gaze and heading direction. Thus, a more qualitative analysis might be helpful. In order to approximate flow derivatives at an edge, we apply two steps; see Figure 4b. First, the edge is rotated until it is parallel to the direction of gaze. Second, the distance between optical axis and the plane that describes the edge is moved toward zero in the limit. Figure 5 and Table 1 provide qualitative values for flow derivatives. In general, directing gaze toward the center of an obstacle leads to smaller divergence, curl, and shear components than fixating the obstacle’s surface tangentially or fixating one of the obstacle’s outer or apical edges. These depictions are based on equations given in Table 2 for a general surface function Z and in Table 3 replacing the general surface function Z with a plane. Equations from Table 3 show that fixating the center of an obstacle leads to responses that are linear for varying x, the distance of the fixation point from the surface, or these responses have a constant slope for varying x (see 1st column in Figure 5). This is unlike the response curves from column two and three in Figure 5 which are hyperbolic. The singularity of these curves is reached in the limit case of tangential fixation of a planar (2nd column in Figure 5) or curved surface (3rd column in Figure 5). For tangential fixation the infinitely large values of divergence, curl, and shear could be used to first establish tangential fixation and second to segment objects from the background as they occur at this transition. This finding is also shown in Table 1 using a compact notation. Fixating the center leads to straight curves (2nd row in Table 1), and tangential fixation gives hyperbolic response curves for planar (3rd row) and curved surfaces (4th row) and thus shows the second claim from the introduction. These hyperbolic are directly linked to discontinuities in depth: “In the velocity field they [depth discontinuities] appear also as singular curves where the expansion, vorticity [curl] and shear take on infinite values”, cited from page 54 in [19].


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

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

Response for flow divergence, curl, and shear get infinitely large if fixating tangentially.These strong responses located at objects’ edges allow for their segmentation. In all cases the camera has the translational velocity (vx, vy, vz). a) Sketch of the scenario for fixating a plane that has a tilt α >0 in the xz-plane. The lower four rows show the functions for the response of flow components depending on the declination from the center of the visual field along the horizontal axis. Divergence and Type I shear depend linearly on x, the declination along the x-axis. Curl and Type II shear are independent of x. b) For a plane parallel to the optical axis all four components are reciprocal dependent on x. For values close to zero the component’s responses approach minus infinity. In this panel we depicted div, curl, and shear components by the gray-dashed line for a specific eccentricity or horizontal distance x of the plane from the gaze direction. c) A curved surface that is cylindrical in the xz-plane and planar in the xy/yz-planes leads to the same response characteristics for divergence, curl, and shear. For x→0 or x→R all four components approach ±infinity. The difference in linear versus hyperbolic response curves for case a) versus b) and c) gives an explanation why segmentation of obstacles can be improved by fixating the edge. Such a fixation results in strong responses that could be detected by difference operators. All sketches in the first row show a top-down view of the three scenarios, respectively.
© Copyright Policy
Related In: Results  -  Collection

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getmorefigures.php?uid=PMC3375264&req=5

pone-0038446-g005: Response for flow divergence, curl, and shear get infinitely large if fixating tangentially.These strong responses located at objects’ edges allow for their segmentation. In all cases the camera has the translational velocity (vx, vy, vz). a) Sketch of the scenario for fixating a plane that has a tilt α >0 in the xz-plane. The lower four rows show the functions for the response of flow components depending on the declination from the center of the visual field along the horizontal axis. Divergence and Type I shear depend linearly on x, the declination along the x-axis. Curl and Type II shear are independent of x. b) For a plane parallel to the optical axis all four components are reciprocal dependent on x. For values close to zero the component’s responses approach minus infinity. In this panel we depicted div, curl, and shear components by the gray-dashed line for a specific eccentricity or horizontal distance x of the plane from the gaze direction. c) A curved surface that is cylindrical in the xz-plane and planar in the xy/yz-planes leads to the same response characteristics for divergence, curl, and shear. For x→0 or x→R all four components approach ±infinity. The difference in linear versus hyperbolic response curves for case a) versus b) and c) gives an explanation why segmentation of obstacles can be improved by fixating the edge. Such a fixation results in strong responses that could be detected by difference operators. All sketches in the first row show a top-down view of the three scenarios, respectively.
Mentions: In order to avoid an obstacle it has to be visually segmented from the background. In addition to texture, color, and stereo cues, flow fields can provide a cue for segmentation. But what should the pattern of self-motion and gaze be to generate flow that best facilitates segmentation? Qualitative flow derivative components caused by different patterns of self-motion and gaze are shown in Figure 4a. Fixating the edge of an object, the derivative components that are present are the same regardless of the alignment between gaze and heading direction. Thus, a more qualitative analysis might be helpful. In order to approximate flow derivatives at an edge, we apply two steps; see Figure 4b. First, the edge is rotated until it is parallel to the direction of gaze. Second, the distance between optical axis and the plane that describes the edge is moved toward zero in the limit. Figure 5 and Table 1 provide qualitative values for flow derivatives. In general, directing gaze toward the center of an obstacle leads to smaller divergence, curl, and shear components than fixating the obstacle’s surface tangentially or fixating one of the obstacle’s outer or apical edges. These depictions are based on equations given in Table 2 for a general surface function Z and in Table 3 replacing the general surface function Z with a plane. Equations from Table 3 show that fixating the center of an obstacle leads to responses that are linear for varying x, the distance of the fixation point from the surface, or these responses have a constant slope for varying x (see 1st column in Figure 5). This is unlike the response curves from column two and three in Figure 5 which are hyperbolic. The singularity of these curves is reached in the limit case of tangential fixation of a planar (2nd column in Figure 5) or curved surface (3rd column in Figure 5). For tangential fixation the infinitely large values of divergence, curl, and shear could be used to first establish tangential fixation and second to segment objects from the background as they occur at this transition. This finding is also shown in Table 1 using a compact notation. Fixating the center leads to straight curves (2nd row in Table 1), and tangential fixation gives hyperbolic response curves for planar (3rd row) and curved surfaces (4th row) and thus shows the second claim from the introduction. These hyperbolic are directly linked to discontinuities in depth: “In the velocity field they [depth discontinuities] appear also as singular curves where the expansion, vorticity [curl] and shear take on infinite values”, cited from page 54 in [19].

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