Abstract

For a moving observer it is essential to foresee the locomotor course with respect to structures in the environment. Optical flows that are available to a moving observer contain powerful information for visual kinesthesis. In general, optical flows consist of separable translational and rotational components. The information examined here is contained completely in the translational component and its time derivatives. Curved paths of observation are specified by different orientations of the translational components of optical velocity and acceleration fields. Obstacles and their temporal separation from a curvilinearly moving observer are specified in the optical flow, as is the angle of collision.

© 1983 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. J. Gibson, “Ecological optics,” Vis. Res. 1, 253–262 (1961).
    [CrossRef]
  2. J. J. Gibson, P. Olum, and F. Rosenblatt, “Parallax and perspective during aircraft landings,” Am. J. Psychol. 68, 372–385 (1955).
    [CrossRef] [PubMed]
  3. J. J. Gibson, The Ecological Approach to Visual Perception (Houghton Mifflin, Boston, 1979).
  4. D. N. Lee, “The functions of vision,” in Modes of Perceiving and Processing Information, H. Pick and E. Salzmann, eds. (Erlbaum, Hillsdale, N.Y., 1978).
  5. H. C. Longuet-Higgins and K. Prazdny, “The interpretation of a moving retinal image,” Proc. R. Soc. London Ser. B 208, 385–397 (1980).
    [CrossRef]
  6. J. J. Koenderink and A. J. van Doorn, “Invariant properties of the motion parallax field due to the movement of rigid bodies relative to an observer,” Opt. Acta 22, 773–791 (1975).
    [CrossRef]
  7. J. J. Koenderink and A. J. van Doorn, “Local structure of movement parallax of the plane,” J. Opt. Soc. Am. 66, 717–723 (1976).
    [CrossRef]
  8. J. J. Koenderink and A. J. van Doorn, “Visual perception of rigidity of solid shape,” J. Math. Biol. 3, 79–85 (1976).
    [CrossRef] [PubMed]
  9. W. F. Clocksin, “Perception of surface slant and edge labels from optical flow: a computational approach,” Percept. 9, 253–269 (1980).
    [CrossRef]
  10. J. J. Koenderink and A. J. van Doorn, “Exterospecific component of the motion parallax field,” J. Opt. Soc. Am. 71, 953–956 (1981).
    [CrossRef] [PubMed]
  11. D. N. Lee, “Visual information during locomotion,” in Perception: Essays in Honor of J. J. Gibson, R. McLeod and H. Pick, eds. (Erlbaum, Hillsdale, N.Y., 1974).
  12. D. N. Lee, “A theory of visual control of braking based on information about time-to-collision,” Percept. 5, 437–459 (1976).
    [CrossRef]
  13. K. Prazdny, “Determining the instantaneous direction of motion from optical flow generated by a curvilinearly moving observer,” Comput. Graphics Image Process. 17, 238–248 (1981).
    [CrossRef]
  14. E. T. Whittaker, A Treatise on the Analytical Dynamics of Particles and Rigid Bodies (Dover, New York, 1944).
  15. We call possible locations of an observer’s eye in the environment the points of observation and a continuous curve connecting such points a path of observation.
  16. B. K. P. Horn and B. G. Schunck, “Determining optical flow,” Artif. Intell. 17, 185–203 (1981).
    [CrossRef]

1981 (3)

J. J. Koenderink and A. J. van Doorn, “Exterospecific component of the motion parallax field,” J. Opt. Soc. Am. 71, 953–956 (1981).
[CrossRef] [PubMed]

K. Prazdny, “Determining the instantaneous direction of motion from optical flow generated by a curvilinearly moving observer,” Comput. Graphics Image Process. 17, 238–248 (1981).
[CrossRef]

B. K. P. Horn and B. G. Schunck, “Determining optical flow,” Artif. Intell. 17, 185–203 (1981).
[CrossRef]

1980 (2)

W. F. Clocksin, “Perception of surface slant and edge labels from optical flow: a computational approach,” Percept. 9, 253–269 (1980).
[CrossRef]

H. C. Longuet-Higgins and K. Prazdny, “The interpretation of a moving retinal image,” Proc. R. Soc. London Ser. B 208, 385–397 (1980).
[CrossRef]

1976 (3)

D. N. Lee, “A theory of visual control of braking based on information about time-to-collision,” Percept. 5, 437–459 (1976).
[CrossRef]

J. J. Koenderink and A. J. van Doorn, “Local structure of movement parallax of the plane,” J. Opt. Soc. Am. 66, 717–723 (1976).
[CrossRef]

J. J. Koenderink and A. J. van Doorn, “Visual perception of rigidity of solid shape,” J. Math. Biol. 3, 79–85 (1976).
[CrossRef] [PubMed]

1975 (1)

J. J. Koenderink and A. J. van Doorn, “Invariant properties of the motion parallax field due to the movement of rigid bodies relative to an observer,” Opt. Acta 22, 773–791 (1975).
[CrossRef]

1961 (1)

J. J. Gibson, “Ecological optics,” Vis. Res. 1, 253–262 (1961).
[CrossRef]

1955 (1)

J. J. Gibson, P. Olum, and F. Rosenblatt, “Parallax and perspective during aircraft landings,” Am. J. Psychol. 68, 372–385 (1955).
[CrossRef] [PubMed]

Clocksin, W. F.

W. F. Clocksin, “Perception of surface slant and edge labels from optical flow: a computational approach,” Percept. 9, 253–269 (1980).
[CrossRef]

Gibson, J. J.

J. J. Gibson, “Ecological optics,” Vis. Res. 1, 253–262 (1961).
[CrossRef]

J. J. Gibson, P. Olum, and F. Rosenblatt, “Parallax and perspective during aircraft landings,” Am. J. Psychol. 68, 372–385 (1955).
[CrossRef] [PubMed]

J. J. Gibson, The Ecological Approach to Visual Perception (Houghton Mifflin, Boston, 1979).

Horn, B. K. P.

B. K. P. Horn and B. G. Schunck, “Determining optical flow,” Artif. Intell. 17, 185–203 (1981).
[CrossRef]

Koenderink, J. J.

J. J. Koenderink and A. J. van Doorn, “Exterospecific component of the motion parallax field,” J. Opt. Soc. Am. 71, 953–956 (1981).
[CrossRef] [PubMed]

J. J. Koenderink and A. J. van Doorn, “Visual perception of rigidity of solid shape,” J. Math. Biol. 3, 79–85 (1976).
[CrossRef] [PubMed]

J. J. Koenderink and A. J. van Doorn, “Local structure of movement parallax of the plane,” J. Opt. Soc. Am. 66, 717–723 (1976).
[CrossRef]

J. J. Koenderink and A. J. van Doorn, “Invariant properties of the motion parallax field due to the movement of rigid bodies relative to an observer,” Opt. Acta 22, 773–791 (1975).
[CrossRef]

Lee, D. N.

D. N. Lee, “A theory of visual control of braking based on information about time-to-collision,” Percept. 5, 437–459 (1976).
[CrossRef]

D. N. Lee, “Visual information during locomotion,” in Perception: Essays in Honor of J. J. Gibson, R. McLeod and H. Pick, eds. (Erlbaum, Hillsdale, N.Y., 1974).

D. N. Lee, “The functions of vision,” in Modes of Perceiving and Processing Information, H. Pick and E. Salzmann, eds. (Erlbaum, Hillsdale, N.Y., 1978).

Longuet-Higgins, H. C.

H. C. Longuet-Higgins and K. Prazdny, “The interpretation of a moving retinal image,” Proc. R. Soc. London Ser. B 208, 385–397 (1980).
[CrossRef]

Olum, P.

J. J. Gibson, P. Olum, and F. Rosenblatt, “Parallax and perspective during aircraft landings,” Am. J. Psychol. 68, 372–385 (1955).
[CrossRef] [PubMed]

Prazdny, K.

K. Prazdny, “Determining the instantaneous direction of motion from optical flow generated by a curvilinearly moving observer,” Comput. Graphics Image Process. 17, 238–248 (1981).
[CrossRef]

H. C. Longuet-Higgins and K. Prazdny, “The interpretation of a moving retinal image,” Proc. R. Soc. London Ser. B 208, 385–397 (1980).
[CrossRef]

Rosenblatt, F.

J. J. Gibson, P. Olum, and F. Rosenblatt, “Parallax and perspective during aircraft landings,” Am. J. Psychol. 68, 372–385 (1955).
[CrossRef] [PubMed]

Schunck, B. G.

B. K. P. Horn and B. G. Schunck, “Determining optical flow,” Artif. Intell. 17, 185–203 (1981).
[CrossRef]

van Doorn, A. J.

J. J. Koenderink and A. J. van Doorn, “Exterospecific component of the motion parallax field,” J. Opt. Soc. Am. 71, 953–956 (1981).
[CrossRef] [PubMed]

J. J. Koenderink and A. J. van Doorn, “Visual perception of rigidity of solid shape,” J. Math. Biol. 3, 79–85 (1976).
[CrossRef] [PubMed]

J. J. Koenderink and A. J. van Doorn, “Local structure of movement parallax of the plane,” J. Opt. Soc. Am. 66, 717–723 (1976).
[CrossRef]

J. J. Koenderink and A. J. van Doorn, “Invariant properties of the motion parallax field due to the movement of rigid bodies relative to an observer,” Opt. Acta 22, 773–791 (1975).
[CrossRef]

Whittaker, E. T.

E. T. Whittaker, A Treatise on the Analytical Dynamics of Particles and Rigid Bodies (Dover, New York, 1944).

Am. J. Psychol. (1)

J. J. Gibson, P. Olum, and F. Rosenblatt, “Parallax and perspective during aircraft landings,” Am. J. Psychol. 68, 372–385 (1955).
[CrossRef] [PubMed]

Artif. Intell. (1)

B. K. P. Horn and B. G. Schunck, “Determining optical flow,” Artif. Intell. 17, 185–203 (1981).
[CrossRef]

Comput. Graphics Image Process. (1)

K. Prazdny, “Determining the instantaneous direction of motion from optical flow generated by a curvilinearly moving observer,” Comput. Graphics Image Process. 17, 238–248 (1981).
[CrossRef]

J. Math. Biol. (1)

J. J. Koenderink and A. J. van Doorn, “Visual perception of rigidity of solid shape,” J. Math. Biol. 3, 79–85 (1976).
[CrossRef] [PubMed]

J. Opt. Soc. Am. (2)

Opt. Acta (1)

J. J. Koenderink and A. J. van Doorn, “Invariant properties of the motion parallax field due to the movement of rigid bodies relative to an observer,” Opt. Acta 22, 773–791 (1975).
[CrossRef]

Percept. (2)

W. F. Clocksin, “Perception of surface slant and edge labels from optical flow: a computational approach,” Percept. 9, 253–269 (1980).
[CrossRef]

D. N. Lee, “A theory of visual control of braking based on information about time-to-collision,” Percept. 5, 437–459 (1976).
[CrossRef]

Proc. R. Soc. London Ser. B (1)

H. C. Longuet-Higgins and K. Prazdny, “The interpretation of a moving retinal image,” Proc. R. Soc. London Ser. B 208, 385–397 (1980).
[CrossRef]

Vis. Res. (1)

J. J. Gibson, “Ecological optics,” Vis. Res. 1, 253–262 (1961).
[CrossRef]

Other (5)

J. J. Gibson, The Ecological Approach to Visual Perception (Houghton Mifflin, Boston, 1979).

D. N. Lee, “The functions of vision,” in Modes of Perceiving and Processing Information, H. Pick and E. Salzmann, eds. (Erlbaum, Hillsdale, N.Y., 1978).

D. N. Lee, “Visual information during locomotion,” in Perception: Essays in Honor of J. J. Gibson, R. McLeod and H. Pick, eds. (Erlbaum, Hillsdale, N.Y., 1974).

E. T. Whittaker, A Treatise on the Analytical Dynamics of Particles and Rigid Bodies (Dover, New York, 1944).

We call possible locations of an observer’s eye in the environment the points of observation and a continuous curve connecting such points a path of observation.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1

A coordinate system Oxyz moving with the observer. O is the nodal point of the observer’s eye at an instant; P is a visible detail in the environment. At a time t = 0, v = (υx, υy, υz) and ω= (ωx, ωy, ωz) denote instantaneous translatory and rotatory velocities of the observer Oxyz relative to an external, instantaneous coincident coordinate system.

Fig. 2
Fig. 2

(a) Planar projection of an optical velocity field containing translational and rotational components. The points denote positions, and lines denote velocity vectors on the projection plane PP corresponding to details on surfaces parallel to PP. The (instantaneous) angle of approach is 180°, the surface on the right is progressively disoccluding a second surface, and at the occluding edge the difference vectors of the vector pairs point toward the momentary directi0on of motion (o). (b) The rotational component of (a). This vector field is not affected by the layout of the environment; it depends only on the direction of details relative to the axis of rotation. (c) The pure translational component of (a). The momentary direction of motion (o) is the center of this radial vector field.

Fig. 3
Fig. 3

(a) Planar projection of the translational component of an optical acceleration field: (a) together with Fig. 2(c) specifies a straight path of observation (assuming that the higher-order fields also have identical orientations). (b) This acceleration field and the velocity field [Fig. 2(c)] have different orientations, which specifies that the observer’s momentary direction of motion (o) is changing; the orientation of the acceleration vector at (o) indicates the plane of the observer’s motion.

Fig. 4
Fig. 4

O, nodal point of the observer’s eye at time t = 0; Pc, collision, point on the surface of the obstacle; tx, tz = 1, 2, …, 6, equi-tx. and equi-tz, lines; y = 0, plane of motion; tx, = tz,, environmental details that will be lined up with the observer after times t = tx. = tz,.

Equations (43)

Equations on this page are rendered with MathJax. Learn more.

ρ = ( x 2 + y 2 + z 2 ) 1 / 2 ,
θ = tan 1 [ ( x 2 + y 2 ) 1 / 2 / z ] ,
φ = tan 1 ( y / x ) ,
x = ρ sin θ cos φ ,
y = ρ sin θ sin φ ,
z = ρ cos θ .
( ) ang = ( ) θ + ( ) φ .
θ ˙ = θ ,
θ = ρ 1 ( cos θ cos φ cos θ sin φ sin θ )
φ ˙ = φ ,
φ = ( ρ sin θ ) 1 ( sin φ cos φ 0 )
= v ω × r ,
θ ˙ = θ v θ ( ω × r ) ,
φ ˙ = φ v φ ( ω × r ) .
θ ˙ = ρ 1 ( υ x cos θ cos φ υ y cos θ sin φ + υ z sin θ ) + ω x sin φ ω y cos φ
φ ˙ = ( ρ sin θ ) 1 ( υ x sin φ υ y cos φ ) + cot θ ( ω x cos φ + ω y sin φ ) ω z .
( ) ang = ( T ) ang + ( R ) ang ,
( T ) ang = ρ 1 [ ( υ x cos θ cos φ υ y cos θ sin φ ) + υ z sin θ ) e θ + ( υ x sin φ υ y cos φ ) e φ / sin θ ]
( R ) ang = ( ω x sin φ ω y cos φ ) e θ + [ cot θ ( ω x cos φ + ω y sin φ ) ω z ] e φ .
θ ˙ T = ρ 1 ( υ x cos θ cos φ + υ z sin θ )
φ ˙ T = ( ρ sin θ ) 1 υ x sin φ .
ρ = z / cos θ ;
υ x = z φ ˙ T tan θ / sin φ
υ z z = ( 2 θ ˙ T + φ ˙ T sin 2 θ cot φ ) / sin 2 θ = τ z 1 .
a z z = ( τ ˙ z + 1 ) / τ z 2 ,
τ ˙ z = d d t [ sin 2 θ / ( 2 θ ˙ T + φ ˙ T sin 2 θ cot φ ) ] .
t z = υ z a z [ ± ( 2 a z z υ z 2 + 1 ) 1 / 2 1 ] .
T z = τ z ( τ ˙ z + 1 ) 1 [ 1 ± ( 2 τ ˙ z 1 ) 1 / 2 ] .
υ x = ρ φ ˙ T sin θ / sin φ ,
ρ = x ( sin θ cos φ ) 1 ;
υ x x = 2 φ ˙ T / sin 2 φ = τ x 1 .
T x = τ x ( τ ˙ x + 1 ) 1 [ 1 ± ( 2 τ ˙ x 1 ) 1 / 2 ] ,
τ ˙ x = cos 2 φ φ ¨ T sin 2 φ 2 φ ˙ T 2 .
t c = T x = T z , φ = 0 , π .
θ o ( t c ) = tan 1 [ υ x ( t c ) υ z ( t c ) ] , φ o ( t c ) = 0 .
0 = z + t 1 z 1 ! z ( 1 ) + t 2 t 2 ! z ( 2 ) + + t n z n ! z ( n )
0 = 1 + t 1 z 1 ! [ z ( 1 ) z ] + t 2 z 2 ! [ z ( 2 ) z ] + + t n z n ! [ z ( n ) z ] .
z ( 1 ) z = ψ ,
ψ = τ z 1 = ( 2 θ ˙ T + φ ˙ T sin 2 θ cot φ ) / sin 2 θ .
z ( n ) z = ( d d t + ψ ) n 1 ψ .
x ( m ) x = ( d d t + ϕ ) m 1 ϕ ,
ϕ = τ x 1 = 2 φ ˙ T / sin 2 φ .
t c = t x = t z , 0 = 1 + t 1 x 1 ! ( d d t + ϕ ) 0 ϕ + t 2 x 2 ! ( d d t + ϕ ) 1 ϕ + + t m x m ! ( d d t + ϕ ) m 1 ϕ , 0 = 1 + t 1 z 1 ! ( d d t + ψ ) 0 ψ + t 2 z 2 ! ( d d t + ψ ) 1 ψ + + t n z n ! ( d d t + ψ ) n 1 ψ , φ = 0 , π .