Comprehensive Physiology Wiley Online Library

Artificial Intelligence: Computational Approach to Vision and Motor Control

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Abstract

The sections in this article are:

1 Founding Principles of Artificial Intelligence
2 Computational Approach to Neuroscience
3 Relation to Other Areas of Artificial Intelligence
3.1 Study of Vision
3.2 Representational Structure of Vision
3.3 Natural Constraints in Vision
3.4 From Theory to Implementation: Detection of Intensity Changes
4 Study of Motor Control
4.1 Features of Motor Control Research
4.2 Natural Constraints in Motor Control
4.3 Movement‐Planning Hierarchy
4.4 Biological Implications
5 Conclusions
Figure 1. Figure 1.

Light intensities measured by digital camera of the rectangular area outlined in the image in A are shown in B.

Figure 2. Figure 2.

Derivation of 3‐D structure from 2‐D motion. A: 3 views of 3‐D wire‐frame object that is rotating about a central vertical axis. B: projected 2‐D image and motion of object. Arrows represent projected 2‐D velocity of individual points on object.

Figure 3. Figure 3.

Ambiguity of interpreting structure from motion. A: set of dots on surface of rotating transparent cylinder are projected onto 2‐D display screen. B: bird's‐eye view of projection of dots in A. C: field of randomly moving dots that project to same 2‐D image as dots shown in B.

Figure 4. Figure 4.

Aperture problem. A: motion detector that views moving edge E through limited aperture A detects only component of motion c in direction perpendicular to edge. B: circle undergoing pure translation to the right. Arrows along contour represent perpendicular components of velocity obtained from changing image. C: contour C undergoes translation, rotation, and deformation to yield contour C' at some later time. The true motion of point p is ambiguous.

Figure 5. Figure 5.

Motion illusions. A, C, E: true velocity fields for logarithmic spiral, ellipse, and deformed circle, respectively, rotating about their centers. Short line segments along smooth contours represent direction and speed of movement of individual points on contours. B, D, F: smoothest velocity fields consistent with rotating patterns shown in A, C, E.

Figure 6. Figure 6.

Analog models of velocity field computation. A: simple resistive network that computes smoothest velocity field. Conductances g and g and currents Ii represent properties of moving contour measured directly from image. The 2‐D velocity field along contour is represented implicitly by combination of inputs and resulting voltages Vi. B: hypothetical neural implementation of circuit shown in A Synaptic‐mediated currents Ii and additional inputs Ri represent properties of moving contour. Resulting voltages Vi, sampled by dendrodendritic synapses, together with input currents represent local velocities along contour.

Figure 7. Figure 7.

Detection of intensity changes. A: 1‐D intensity profile represents light intensities measured along horizontal line of natural image. B: result of smoothing intensity profile shown in A. C: first derivative of smoothed intensity profile shown in B. D: second derivative of smoothed intensity profile shown in B. Dashed lines show relationship between significant changes in B, peaks in C, and zero‐crossings in D.

Figure 8. Figure 8.

Receptive fields of retinal ganglion cells. A: shape of spatial receptive fields of retinal ganglion cells, described quantitatively as difference of 2 Gaussian functions: a narrow positive one and broader negative one. B: on‐ and off‐center cells, which respond in opposite manner to light stimulation in central and surrounding areas of receptive fields.

Figure 9. Figure 9.

Detection of intensity changes. A: image of natural scene. B: result of filtering image shown in A with difference‐of‐Gaussians function. C: positions of zero‐crossings of filtered image shown in B.

Figure 10. Figure 10.

Use of multiple operator sizes. A: image of natural scene. B, C, D: positions of zero‐crossings that result from filtering the image shown in A with difference‐of‐Gaussian functions whose central positive region has diameter of 6, 12, and 24 image elements, respectively.

Figure 11. Figure 11.

Simple cell models. A: simple cell model proposed by Marr and Hildreth in which responses of adjacent on‐ and off‐center lateral geniculate nucleus (LGN) cells are combined through AND‐like operation. B: simple cell model proposed by Poggio in which adjacent LGN cells of same type are combined through AND‐NOT operation.

Figure 12. Figure 12.

A: “staircase” stimulus used by Richter and Ullman consisting of adjacent bars of different intensities. B: graphs represent cross section of intensity distribution across bar pattern, for range of separations between two step changes of intensity. C: asymmetric difference‐of‐Gaussians function. D: results of filtering patterns shown in B through difference‐of‐Gaussians function shown in C.

Figure 13. Figure 13.

Test of the zero‐crossing hypothesis. A: staircase stimulus of Fig. , with contrast inverted so that step changes of intensity are light at left and dark at right. B: result of filtering the profile in A with a difference‐of‐Gaussians function of intermediate size.

Figure 14. Figure 14.

Modular planning and control structure for robot arm movement. Trajectory is planned in hand coordinates, synthesizing a hybrid force‐position strategy. End‐point trajectory x(t) is transformed into joint trajectory θ(t) by solving inverse kinematics. The feedforward torques T(t) are found by solving inverse dynamics and corrected by feedback for force and position errors.

Figure 15. Figure 15.

Different planning variables and their resultant trajectories for planar two‐joint arm movement. A: straight line in joint coordinates generates complex curved end‐point trajectory. B: straight line in Cartesian coordinates requires relatively complex elbow and shoulder joint movement.

Figure 16. Figure 16.

Joint‐angle plots of shoulder angle θ1 versus elbow angle θ2 (A) and corresponding end‐point trajectories (B) for perfect straight‐line Cartesian trajectories (solid lines) versus staggered‐joint interpolation (dotted lines).

Figure 17. Figure 17.

Trajectories of unrestrained arm movement between vertical‐plane targets measured with Selspot system. End‐point trajectories are shown in AD as projected onto vertical plane, and corresponding joint‐angle plots of elbow versus shoulder angle are shown in EH.

Figure 18. Figure 18.

Simulations of vertical planar arm movements involving shoulder and elbow joints. A: ratio of elbow velocity to shoulder velocity is shown for each arm movement. Contour lines of constant joint‐rate ratio are imposed on movement plane in B. B: arm is shown in starting position in lower right quadrant of movement plane. Center represents shoulder point, and l1 and l2 are upper arm and forearm lengths. Outer circle represents workspace boundary, points of maximal reach. Simulated movements begin from starting position and approach different points on boundary along straight‐line paths.

Figure 19. Figure 19.

A: tangential velocity profiles of wrist point for 6 vertical arm movements measured with Selspot system. B: movements are normalized for time and distance to demonstrate underlying invariance in profile shape. C: hypothetical phantom arm carrying load and superimposed on actual arm allows movement speed and load conditions to be simply changed if and only if tangential velocity profile is invariant.



Figure 1.

Light intensities measured by digital camera of the rectangular area outlined in the image in A are shown in B.



Figure 2.

Derivation of 3‐D structure from 2‐D motion. A: 3 views of 3‐D wire‐frame object that is rotating about a central vertical axis. B: projected 2‐D image and motion of object. Arrows represent projected 2‐D velocity of individual points on object.



Figure 3.

Ambiguity of interpreting structure from motion. A: set of dots on surface of rotating transparent cylinder are projected onto 2‐D display screen. B: bird's‐eye view of projection of dots in A. C: field of randomly moving dots that project to same 2‐D image as dots shown in B.



Figure 4.

Aperture problem. A: motion detector that views moving edge E through limited aperture A detects only component of motion c in direction perpendicular to edge. B: circle undergoing pure translation to the right. Arrows along contour represent perpendicular components of velocity obtained from changing image. C: contour C undergoes translation, rotation, and deformation to yield contour C' at some later time. The true motion of point p is ambiguous.



Figure 5.

Motion illusions. A, C, E: true velocity fields for logarithmic spiral, ellipse, and deformed circle, respectively, rotating about their centers. Short line segments along smooth contours represent direction and speed of movement of individual points on contours. B, D, F: smoothest velocity fields consistent with rotating patterns shown in A, C, E.



Figure 6.

Analog models of velocity field computation. A: simple resistive network that computes smoothest velocity field. Conductances g and g and currents Ii represent properties of moving contour measured directly from image. The 2‐D velocity field along contour is represented implicitly by combination of inputs and resulting voltages Vi. B: hypothetical neural implementation of circuit shown in A Synaptic‐mediated currents Ii and additional inputs Ri represent properties of moving contour. Resulting voltages Vi, sampled by dendrodendritic synapses, together with input currents represent local velocities along contour.



Figure 7.

Detection of intensity changes. A: 1‐D intensity profile represents light intensities measured along horizontal line of natural image. B: result of smoothing intensity profile shown in A. C: first derivative of smoothed intensity profile shown in B. D: second derivative of smoothed intensity profile shown in B. Dashed lines show relationship between significant changes in B, peaks in C, and zero‐crossings in D.



Figure 8.

Receptive fields of retinal ganglion cells. A: shape of spatial receptive fields of retinal ganglion cells, described quantitatively as difference of 2 Gaussian functions: a narrow positive one and broader negative one. B: on‐ and off‐center cells, which respond in opposite manner to light stimulation in central and surrounding areas of receptive fields.



Figure 9.

Detection of intensity changes. A: image of natural scene. B: result of filtering image shown in A with difference‐of‐Gaussians function. C: positions of zero‐crossings of filtered image shown in B.



Figure 10.

Use of multiple operator sizes. A: image of natural scene. B, C, D: positions of zero‐crossings that result from filtering the image shown in A with difference‐of‐Gaussian functions whose central positive region has diameter of 6, 12, and 24 image elements, respectively.



Figure 11.

Simple cell models. A: simple cell model proposed by Marr and Hildreth in which responses of adjacent on‐ and off‐center lateral geniculate nucleus (LGN) cells are combined through AND‐like operation. B: simple cell model proposed by Poggio in which adjacent LGN cells of same type are combined through AND‐NOT operation.



Figure 12.

A: “staircase” stimulus used by Richter and Ullman consisting of adjacent bars of different intensities. B: graphs represent cross section of intensity distribution across bar pattern, for range of separations between two step changes of intensity. C: asymmetric difference‐of‐Gaussians function. D: results of filtering patterns shown in B through difference‐of‐Gaussians function shown in C.



Figure 13.

Test of the zero‐crossing hypothesis. A: staircase stimulus of Fig. , with contrast inverted so that step changes of intensity are light at left and dark at right. B: result of filtering the profile in A with a difference‐of‐Gaussians function of intermediate size.



Figure 14.

Modular planning and control structure for robot arm movement. Trajectory is planned in hand coordinates, synthesizing a hybrid force‐position strategy. End‐point trajectory x(t) is transformed into joint trajectory θ(t) by solving inverse kinematics. The feedforward torques T(t) are found by solving inverse dynamics and corrected by feedback for force and position errors.



Figure 15.

Different planning variables and their resultant trajectories for planar two‐joint arm movement. A: straight line in joint coordinates generates complex curved end‐point trajectory. B: straight line in Cartesian coordinates requires relatively complex elbow and shoulder joint movement.



Figure 16.

Joint‐angle plots of shoulder angle θ1 versus elbow angle θ2 (A) and corresponding end‐point trajectories (B) for perfect straight‐line Cartesian trajectories (solid lines) versus staggered‐joint interpolation (dotted lines).



Figure 17.

Trajectories of unrestrained arm movement between vertical‐plane targets measured with Selspot system. End‐point trajectories are shown in AD as projected onto vertical plane, and corresponding joint‐angle plots of elbow versus shoulder angle are shown in EH.



Figure 18.

Simulations of vertical planar arm movements involving shoulder and elbow joints. A: ratio of elbow velocity to shoulder velocity is shown for each arm movement. Contour lines of constant joint‐rate ratio are imposed on movement plane in B. B: arm is shown in starting position in lower right quadrant of movement plane. Center represents shoulder point, and l1 and l2 are upper arm and forearm lengths. Outer circle represents workspace boundary, points of maximal reach. Simulated movements begin from starting position and approach different points on boundary along straight‐line paths.



Figure 19.

A: tangential velocity profiles of wrist point for 6 vertical arm movements measured with Selspot system. B: movements are normalized for time and distance to demonstrate underlying invariance in profile shape. C: hypothetical phantom arm carrying load and superimposed on actual arm allows movement speed and load conditions to be simply changed if and only if tangential velocity profile is invariant.

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Ellen C. Hildreth, John M. Hollerbach. Artificial Intelligence: Computational Approach to Vision and Motor Control. Compr Physiol 2011, Supplement 5: Handbook of Physiology, The Nervous System, Higher Functions of the Brain: 605-642. First published in print 1987. doi: 10.1002/cphy.cp010515