Abstract

We took panoramic snapshots in outdoor scenes at regular intervals in two- or three-dimensional grids covering 1 m2 or 1 m3 and determined how the root mean square pixel differences between each of the images and a reference image acquired at one of the locations in the grid develop over distance from the reference position. We then asked whether the reference position can be pinpointed from a random starting position by moving the panoramic imaging device in such a way that the image differences relative to the reference image are minimized. We find that on time scales of minutes to hours, outdoor locations are accurately defined by a clear, sharp minimum in a smooth three-dimensional (3D) volume of image differences (the 3D difference function). 3D difference functions depend on the spatial-frequency content of natural scenes and on the spatial layout of objects therein. They become steeper in the vicinity of dominant objects. Their shape and smoothness, however, are affected by changes in illumination and shadows. The difference functions generated by rotation are similar in shape to those generated by translation, but their plateau values are higher. Rotational difference functions change little with distance from the reference location. Simple gradient descent methods are surprisingly successful in recovering a goal location, even if faced with transient changes in illumination. Our results show that view-based homing with panoramic images is in principle feasible in natural environments and does not require the identification of individual landmarks. We discuss the relevance of our findings to the study of robot and insect homing.

© 2003 Optical Society of America

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    [CrossRef]
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    [CrossRef]
  28. J. Zeil, “Orientation flights of solitary wasps (Cerceris; Sphecidae; Hymenoptera): II. Similarities between orientation and return flights and the use of motion parallax,” J. Comp. Physiol., A 172, 207–222 (1993).
    [CrossRef]
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    [CrossRef]
  30. J. H. van Hateren, M. V. Srinivasan, P. B. Wait, “Pattern recognition in bees: orientation discrimination,” J. Comp. Physiol., A 167, 649–654 (1990).
  31. D. Efler, B. Ronacher, “Evidence against a retinotopic-template matching in honeybees’ pattern recognition,” Vision Res. 40, 3391–3403 (2000).
    [CrossRef]
  32. M. Dill, M. Heisenberg, “Visual pattern memory without shape recognition,” Philos. Trans. R. Soc. London, Ser. B 349, 143–152 (1995).
    [CrossRef] [PubMed]
  33. T. S. Collett, M. F. Land, “Visual spatial memory in a hoverfly,” J. Comp. Physiol. 100, 59–84 (1975).
    [CrossRef]
  34. R. Wehner, F. Räber, “Visual spatial memory in desert ants, Cataglyphis bicolor (Hymenoptera: Formicidae),” Experientia 35, 1569–1571 (1979).
    [CrossRef]
  35. M. Dill, R. Wolf, M. Heisenberg, “Visual pattern recognition in Drosophila involves retinotopic matching,” Nature (London) 365, 751–753 (1993).
    [CrossRef]
  36. M. Heisenberg, “Pattern recognition in insects,” Curr. Opin. Neurobiol. 5, 475–481 (1995).
    [CrossRef] [PubMed]
  37. B. Ronacher, U. Duft, “An image-matching mechanism describes a generalization task in honeybees,” J. Comp. Physiol., A 178, 803–812 (1996).
    [CrossRef]
  38. B. Ronacher, “How do bees learn and recognize visual patterns?” Biol. Cybern. 79, 477–485 (1998).
    [CrossRef]
  39. R. Ernst, M. Heisenberg, “The memory template in Drosophila pattern vision at the flight simulator,” Vision Res. 39, 3920–3933 (1999).
    [CrossRef]
  40. D. M. Coppola, H. R. Purves, A. N. McCoy, D. Purves, “The distribution of oriented contours in thereal world,” Proc. Natl. Acad. Sci. U.S.A. 95, 4002–4006 (1998).
    [CrossRef]
  41. A. van der Schaaf, H. van Hateren, “Modelling the power spectra of natural images: statistics and information,” Vision Res. 36, 2759–2770 (1996).
    [CrossRef] [PubMed]
  42. D. Ruderman, “Origins of scaling in natural images,” Vision Res. 23, 3385–3398 (1997).
    [CrossRef]
  43. R. Voss, J. Zeil, “Active vision in insects: an analysis of object-directed zig-zag flights in a ground-nesting wasp (Odynerus spinipes, Eumenidae),” J. Comp. Physiol., A 182, 377–387 (1998).
    [CrossRef]
  44. K. Dale, T. S. Collett, “Using artificial evolution and selection to model insect navigation,” Curr. Biol. 11, 1305–1316 (2001).
    [CrossRef] [PubMed]
  45. R. Möller, “Do insects use templates or parameters for landmark navigaion?,” J. Theor. Biol. 210, 33–45 (2001).
    [CrossRef]

2001 (2)

K. Dale, T. S. Collett, “Using artificial evolution and selection to model insect navigation,” Curr. Biol. 11, 1305–1316 (2001).
[CrossRef] [PubMed]

R. Möller, “Do insects use templates or parameters for landmark navigaion?,” J. Theor. Biol. 210, 33–45 (2001).
[CrossRef]

2000 (6)

M. O. Franz, H. A. Mallot, “Biomimetic robot navigation,” Rob. Auton. Syst. 30, 133–153 (2000).
[CrossRef]

M. Lehrer, G. Bianco, “The turn-back-and-look behaviour: bee versus robot,” Biol. Cybern. 83, 211–229 (2000).
[CrossRef] [PubMed]

P. Gaussier, C. Joulain, J. P. Banquet, S. Leprêtre, A. Revel, “The visual homing problem: an example of robotics/biology cross fertilization,” Rob. Auton. Syst. 30, 155–180 (2000).
[CrossRef]

D. Lambrinos, R. Möller, T. Labhart, R. Pfeifer, R. Wehner, “A mobile robot employing insect strategies for navigation,” Rob. Auton. Syst. 30, 39–64 (2000).
[CrossRef]

R. Möller, “Insect visual homing strategies in a robot with analog processing,” Biol. Cybern. 83, 231–243 (2000).
[CrossRef] [PubMed]

D. Efler, B. Ronacher, “Evidence against a retinotopic-template matching in honeybees’ pattern recognition,” Vision Res. 40, 3391–3403 (2000).
[CrossRef]

1999 (2)

R. Ernst, M. Heisenberg, “The memory template in Drosophila pattern vision at the flight simulator,” Vision Res. 39, 3920–3933 (1999).
[CrossRef]

M. Giurfa, E. A. Capaldi, “Vectors, routes and maps: new discoveries about navigation in insects,” Trends Neurosci. 22, 237–242 (1999).
[CrossRef] [PubMed]

1998 (4)

R. Voss, J. Zeil, “Active vision in insects: an analysis of object-directed zig-zag flights in a ground-nesting wasp (Odynerus spinipes, Eumenidae),” J. Comp. Physiol., A 182, 377–387 (1998).
[CrossRef]

M. O. Franz, B. Schölkopf, H. A. Mallot, H. H. Bülthoff, “Where did I take that snapshot? Scene-based homing by image matching,” Biol. Cybern. 79, 191–202 (1998).
[CrossRef]

D. M. Coppola, H. R. Purves, A. N. McCoy, D. Purves, “The distribution of oriented contours in thereal world,” Proc. Natl. Acad. Sci. U.S.A. 95, 4002–4006 (1998).
[CrossRef]

B. Ronacher, “How do bees learn and recognize visual patterns?” Biol. Cybern. 79, 477–485 (1998).
[CrossRef]

1997 (6)

D. Ruderman, “Origins of scaling in natural images,” Vision Res. 23, 3385–3398 (1997).
[CrossRef]

T. S. Collett, J. A. Rees, “View-based navigation in Hymenoptera: multiple strategies of landmark guidance in the approach to a feeder,” J. Comp. Physiol., A 181, 47–58 (1997).
[CrossRef]

J. S. Chahl, M. V. Srinivasan, “Reflective surfaces for panoramic imaging,” Appl. Opt. 36, 8275–8285 (1997).
[CrossRef]

M. V. Srinivasan, J. S. Chahl, S. W. Zhang, “Robot navigation by visual dead-reckoning: inspiration from insects,” Int. J. Pattern Recogn. Artif. Intell. 11, 35–47 (1997).
[CrossRef]

J. S. Chahl, M. V. Srinivasan, “Range estimation with a panoramic visual sensor,” J. Opt. Soc. Am. A 14, 2144–2151 (1997).
[CrossRef]

M. G. Nagle, M. V. Srinivasan, D. L. Wilson, “Image interpolation technique for measurement of egomotion in 6 degrees of freedom,” J. Opt. Soc. Am. A 14, 3233–3241 (1997).
[CrossRef]

1996 (6)

M. G. Nagle, M. V. Srinivasan, “Structure from motion: determining the range and orientation of surfaces by image interpolation,” J. Opt. Soc. Am. A 13, 25–34 (1996).
[CrossRef]

J. S. Chahl, M. V. Srinivasan, “Visual computation of egomotion using an image interpolation technique,” Biol. Cybern. 74, 405–411 (1996).
[CrossRef] [PubMed]

J. Zeil, A. Kelber, R. Voss, “Structure and function of learning flights in bees and wasps,” J. Exp. Biol. 199, 245–252 (1996).

T. S. Collett, J. Zeil, “Flights of learning,” Curr. Direct. Psychol. Sci. 5, 149–155 (1996).
[CrossRef]

A. van der Schaaf, H. van Hateren, “Modelling the power spectra of natural images: statistics and information,” Vision Res. 36, 2759–2770 (1996).
[CrossRef] [PubMed]

B. Ronacher, U. Duft, “An image-matching mechanism describes a generalization task in honeybees,” J. Comp. Physiol., A 178, 803–812 (1996).
[CrossRef]

1995 (2)

M. Heisenberg, “Pattern recognition in insects,” Curr. Opin. Neurobiol. 5, 475–481 (1995).
[CrossRef] [PubMed]

M. Dill, M. Heisenberg, “Visual pattern memory without shape recognition,” Philos. Trans. R. Soc. London, Ser. B 349, 143–152 (1995).
[CrossRef] [PubMed]

1994 (1)

M. V. Srinivasan, “An image interpolation technique for the computation of optic flow and egomotion,” Biol. Cybern. 71, 401–415 (1994).
[CrossRef]

1993 (5)

J. Zeil, “Orientation flights of solitary wasps (Cerceris; Sphecidae; Hymenoptera): II. Similarities between orientation and return flights and the use of motion parallax,” J. Comp. Physiol., A 172, 207–222 (1993).
[CrossRef]

J. Zeil, “Orientation flights of solitary wasps (Cerceris; Sphecidae; Hymenoptera): I. Description of flight,” J. Comp. Physiol., A 172, 189–205 (1993).
[CrossRef]

M. Lehrer, “Why do bees turn back and look?” J. Comp. Physiol., A 172, 549–563 (1993).
[CrossRef]

T. S. Collett, M. Lehrer, “Looking and learning: a spatial pattern in the orientation flight of the wasp Vespula vulgaris,” Proc. R. Soc. London, Ser. B 252, 129–134 (1993).
[CrossRef]

M. Dill, R. Wolf, M. Heisenberg, “Visual pattern recognition in Drosophila involves retinotopic matching,” Nature (London) 365, 751–753 (1993).
[CrossRef]

1992 (1)

J. Hong, X. Tan, B. Pinette, R. Weiss, E. M. Riseman, “Image-based homing,” IEEE Control Syst., special issue on robotics and automation, 12, 38–45 (1992).

1990 (1)

J. H. van Hateren, M. V. Srinivasan, P. B. Wait, “Pattern recognition in bees: orientation discrimination,” J. Comp. Physiol., A 167, 649–654 (1990).

1987 (1)

B. A. Cartwright, T. S. Collett, “Landmark maps for honeybees,” Biol. Cybern. 57, 85–93 (1987).
[CrossRef]

1983 (1)

B. A. Cartwright, T. S. Collett, “Landmark learning in bees: experiments and models,” J. Comp. Physiol. 151, 521–543 (1983).
[CrossRef]

1979 (1)

R. Wehner, F. Räber, “Visual spatial memory in desert ants, Cataglyphis bicolor (Hymenoptera: Formicidae),” Experientia 35, 1569–1571 (1979).
[CrossRef]

1975 (1)

T. S. Collett, M. F. Land, “Visual spatial memory in a hoverfly,” J. Comp. Physiol. 100, 59–84 (1975).
[CrossRef]

Banquet, J. P.

P. Gaussier, C. Joulain, J. P. Banquet, S. Leprêtre, A. Revel, “The visual homing problem: an example of robotics/biology cross fertilization,” Rob. Auton. Syst. 30, 155–180 (2000).
[CrossRef]

Beveridge, J. R.

E. M. Riseman, A. R. Hanson, J. R. Beveridge, R. Kumar, H. Sawhney, “Landmark-based navigation and the acquisition of environmental models,” in Visual Navigation, Y. Aloimonos, ed. (Erlbaum, Hillsdale, N.J., 1997), pp. 317–374.

Bianco, G.

M. Lehrer, G. Bianco, “The turn-back-and-look behaviour: bee versus robot,” Biol. Cybern. 83, 211–229 (2000).
[CrossRef] [PubMed]

Box, G. E. P.

G. E. P. Box, N. R. Draper, Evolutionary Operation (Wiley, New York, 1969).

Bülthoff, H. H.

M. O. Franz, B. Schölkopf, H. A. Mallot, H. H. Bülthoff, “Where did I take that snapshot? Scene-based homing by image matching,” Biol. Cybern. 79, 191–202 (1998).
[CrossRef]

Capaldi, E. A.

M. Giurfa, E. A. Capaldi, “Vectors, routes and maps: new discoveries about navigation in insects,” Trends Neurosci. 22, 237–242 (1999).
[CrossRef] [PubMed]

Cartwright, B. A.

B. A. Cartwright, T. S. Collett, “Landmark maps for honeybees,” Biol. Cybern. 57, 85–93 (1987).
[CrossRef]

B. A. Cartwright, T. S. Collett, “Landmark learning in bees: experiments and models,” J. Comp. Physiol. 151, 521–543 (1983).
[CrossRef]

Chahl, J. S.

J. S. Chahl, M. V. Srinivasan, “Range estimation with a panoramic visual sensor,” J. Opt. Soc. Am. A 14, 2144–2151 (1997).
[CrossRef]

M. V. Srinivasan, J. S. Chahl, S. W. Zhang, “Robot navigation by visual dead-reckoning: inspiration from insects,” Int. J. Pattern Recogn. Artif. Intell. 11, 35–47 (1997).
[CrossRef]

J. S. Chahl, M. V. Srinivasan, “Reflective surfaces for panoramic imaging,” Appl. Opt. 36, 8275–8285 (1997).
[CrossRef]

J. S. Chahl, M. V. Srinivasan, “Visual computation of egomotion using an image interpolation technique,” Biol. Cybern. 74, 405–411 (1996).
[CrossRef] [PubMed]

Collett, T. S.

K. Dale, T. S. Collett, “Using artificial evolution and selection to model insect navigation,” Curr. Biol. 11, 1305–1316 (2001).
[CrossRef] [PubMed]

T. S. Collett, J. A. Rees, “View-based navigation in Hymenoptera: multiple strategies of landmark guidance in the approach to a feeder,” J. Comp. Physiol., A 181, 47–58 (1997).
[CrossRef]

T. S. Collett, J. Zeil, “Flights of learning,” Curr. Direct. Psychol. Sci. 5, 149–155 (1996).
[CrossRef]

T. S. Collett, M. Lehrer, “Looking and learning: a spatial pattern in the orientation flight of the wasp Vespula vulgaris,” Proc. R. Soc. London, Ser. B 252, 129–134 (1993).
[CrossRef]

B. A. Cartwright, T. S. Collett, “Landmark maps for honeybees,” Biol. Cybern. 57, 85–93 (1987).
[CrossRef]

B. A. Cartwright, T. S. Collett, “Landmark learning in bees: experiments and models,” J. Comp. Physiol. 151, 521–543 (1983).
[CrossRef]

T. S. Collett, M. F. Land, “Visual spatial memory in a hoverfly,” J. Comp. Physiol. 100, 59–84 (1975).
[CrossRef]

T. S. Collett, J. Zeil, “Selection and use of landmarks by insects,” in Orientation and Communication in Arthropods, M. Lehrer, ed. (Birkhäuser Verlag, Basel, Switzerland, 1997), pp. 41–65.

T. S. Collett, J. Zeil, “Places and landmarks: an arthro-pod perspective,” in Spatial Representation in Animals, S. Healy, ed. (Oxford U. Press, Oxford, UK, 1998), pp. 18–53.

Coppola, D. M.

D. M. Coppola, H. R. Purves, A. N. McCoy, D. Purves, “The distribution of oriented contours in thereal world,” Proc. Natl. Acad. Sci. U.S.A. 95, 4002–4006 (1998).
[CrossRef]

Dale, K.

K. Dale, T. S. Collett, “Using artificial evolution and selection to model insect navigation,” Curr. Biol. 11, 1305–1316 (2001).
[CrossRef] [PubMed]

Dill, M.

M. Dill, M. Heisenberg, “Visual pattern memory without shape recognition,” Philos. Trans. R. Soc. London, Ser. B 349, 143–152 (1995).
[CrossRef] [PubMed]

M. Dill, R. Wolf, M. Heisenberg, “Visual pattern recognition in Drosophila involves retinotopic matching,” Nature (London) 365, 751–753 (1993).
[CrossRef]

Draper, N. R.

G. E. P. Box, N. R. Draper, Evolutionary Operation (Wiley, New York, 1969).

Duft, U.

B. Ronacher, U. Duft, “An image-matching mechanism describes a generalization task in honeybees,” J. Comp. Physiol., A 178, 803–812 (1996).
[CrossRef]

Eckert, M. P.

M. P. Eckert, J. Zeil, “Towards an ecology of motion vision,” in Motion Vision: Computational, Neural and Ecological Constraints, J. M. Zanker, J. Zeil, eds. (Springer-Verlag, Berlin, 2001), pp. 333–369.

Efler, D.

D. Efler, B. Ronacher, “Evidence against a retinotopic-template matching in honeybees’ pattern recognition,” Vision Res. 40, 3391–3403 (2000).
[CrossRef]

Ernst, R.

R. Ernst, M. Heisenberg, “The memory template in Drosophila pattern vision at the flight simulator,” Vision Res. 39, 3920–3933 (1999).
[CrossRef]

Franz, M. O.

M. O. Franz, H. A. Mallot, “Biomimetic robot navigation,” Rob. Auton. Syst. 30, 133–153 (2000).
[CrossRef]

M. O. Franz, B. Schölkopf, H. A. Mallot, H. H. Bülthoff, “Where did I take that snapshot? Scene-based homing by image matching,” Biol. Cybern. 79, 191–202 (1998).
[CrossRef]

Gaussier, P.

P. Gaussier, C. Joulain, J. P. Banquet, S. Leprêtre, A. Revel, “The visual homing problem: an example of robotics/biology cross fertilization,” Rob. Auton. Syst. 30, 155–180 (2000).
[CrossRef]

Giurfa, M.

M. Giurfa, E. A. Capaldi, “Vectors, routes and maps: new discoveries about navigation in insects,” Trends Neurosci. 22, 237–242 (1999).
[CrossRef] [PubMed]

Hanson, A. R.

E. M. Riseman, A. R. Hanson, J. R. Beveridge, R. Kumar, H. Sawhney, “Landmark-based navigation and the acquisition of environmental models,” in Visual Navigation, Y. Aloimonos, ed. (Erlbaum, Hillsdale, N.J., 1997), pp. 317–374.

Heisenberg, M.

R. Ernst, M. Heisenberg, “The memory template in Drosophila pattern vision at the flight simulator,” Vision Res. 39, 3920–3933 (1999).
[CrossRef]

M. Heisenberg, “Pattern recognition in insects,” Curr. Opin. Neurobiol. 5, 475–481 (1995).
[CrossRef] [PubMed]

M. Dill, M. Heisenberg, “Visual pattern memory without shape recognition,” Philos. Trans. R. Soc. London, Ser. B 349, 143–152 (1995).
[CrossRef] [PubMed]

M. Dill, R. Wolf, M. Heisenberg, “Visual pattern recognition in Drosophila involves retinotopic matching,” Nature (London) 365, 751–753 (1993).
[CrossRef]

Hong, J.

J. Hong, X. Tan, B. Pinette, R. Weiss, E. M. Riseman, “Image-based homing,” IEEE Control Syst., special issue on robotics and automation, 12, 38–45 (1992).

Joulain, C.

P. Gaussier, C. Joulain, J. P. Banquet, S. Leprêtre, A. Revel, “The visual homing problem: an example of robotics/biology cross fertilization,” Rob. Auton. Syst. 30, 155–180 (2000).
[CrossRef]

Kelber, A.

J. Zeil, A. Kelber, R. Voss, “Structure and function of learning flights in bees and wasps,” J. Exp. Biol. 199, 245–252 (1996).

Kumar, R.

E. M. Riseman, A. R. Hanson, J. R. Beveridge, R. Kumar, H. Sawhney, “Landmark-based navigation and the acquisition of environmental models,” in Visual Navigation, Y. Aloimonos, ed. (Erlbaum, Hillsdale, N.J., 1997), pp. 317–374.

Labhart, T.

D. Lambrinos, R. Möller, T. Labhart, R. Pfeifer, R. Wehner, “A mobile robot employing insect strategies for navigation,” Rob. Auton. Syst. 30, 39–64 (2000).
[CrossRef]

Lambrinos, D.

D. Lambrinos, R. Möller, T. Labhart, R. Pfeifer, R. Wehner, “A mobile robot employing insect strategies for navigation,” Rob. Auton. Syst. 30, 39–64 (2000).
[CrossRef]

Land, M. F.

T. S. Collett, M. F. Land, “Visual spatial memory in a hoverfly,” J. Comp. Physiol. 100, 59–84 (1975).
[CrossRef]

Lehrer, M.

M. Lehrer, G. Bianco, “The turn-back-and-look behaviour: bee versus robot,” Biol. Cybern. 83, 211–229 (2000).
[CrossRef] [PubMed]

T. S. Collett, M. Lehrer, “Looking and learning: a spatial pattern in the orientation flight of the wasp Vespula vulgaris,” Proc. R. Soc. London, Ser. B 252, 129–134 (1993).
[CrossRef]

M. Lehrer, “Why do bees turn back and look?” J. Comp. Physiol., A 172, 549–563 (1993).
[CrossRef]

Leprêtre, S.

P. Gaussier, C. Joulain, J. P. Banquet, S. Leprêtre, A. Revel, “The visual homing problem: an example of robotics/biology cross fertilization,” Rob. Auton. Syst. 30, 155–180 (2000).
[CrossRef]

Mallot, H. A.

M. O. Franz, H. A. Mallot, “Biomimetic robot navigation,” Rob. Auton. Syst. 30, 133–153 (2000).
[CrossRef]

M. O. Franz, B. Schölkopf, H. A. Mallot, H. H. Bülthoff, “Where did I take that snapshot? Scene-based homing by image matching,” Biol. Cybern. 79, 191–202 (1998).
[CrossRef]

McCoy, A. N.

D. M. Coppola, H. R. Purves, A. N. McCoy, D. Purves, “The distribution of oriented contours in thereal world,” Proc. Natl. Acad. Sci. U.S.A. 95, 4002–4006 (1998).
[CrossRef]

Möller, R.

R. Möller, “Do insects use templates or parameters for landmark navigaion?,” J. Theor. Biol. 210, 33–45 (2001).
[CrossRef]

R. Möller, “Insect visual homing strategies in a robot with analog processing,” Biol. Cybern. 83, 231–243 (2000).
[CrossRef] [PubMed]

D. Lambrinos, R. Möller, T. Labhart, R. Pfeifer, R. Wehner, “A mobile robot employing insect strategies for navigation,” Rob. Auton. Syst. 30, 39–64 (2000).
[CrossRef]

Nagle, M. G.

Pfeifer, R.

D. Lambrinos, R. Möller, T. Labhart, R. Pfeifer, R. Wehner, “A mobile robot employing insect strategies for navigation,” Rob. Auton. Syst. 30, 39–64 (2000).
[CrossRef]

Pinette, B.

J. Hong, X. Tan, B. Pinette, R. Weiss, E. M. Riseman, “Image-based homing,” IEEE Control Syst., special issue on robotics and automation, 12, 38–45 (1992).

Purves, D.

D. M. Coppola, H. R. Purves, A. N. McCoy, D. Purves, “The distribution of oriented contours in thereal world,” Proc. Natl. Acad. Sci. U.S.A. 95, 4002–4006 (1998).
[CrossRef]

Purves, H. R.

D. M. Coppola, H. R. Purves, A. N. McCoy, D. Purves, “The distribution of oriented contours in thereal world,” Proc. Natl. Acad. Sci. U.S.A. 95, 4002–4006 (1998).
[CrossRef]

Räber, F.

R. Wehner, F. Räber, “Visual spatial memory in desert ants, Cataglyphis bicolor (Hymenoptera: Formicidae),” Experientia 35, 1569–1571 (1979).
[CrossRef]

Rees, J. A.

T. S. Collett, J. A. Rees, “View-based navigation in Hymenoptera: multiple strategies of landmark guidance in the approach to a feeder,” J. Comp. Physiol., A 181, 47–58 (1997).
[CrossRef]

Revel, A.

P. Gaussier, C. Joulain, J. P. Banquet, S. Leprêtre, A. Revel, “The visual homing problem: an example of robotics/biology cross fertilization,” Rob. Auton. Syst. 30, 155–180 (2000).
[CrossRef]

Riseman, E. M.

J. Hong, X. Tan, B. Pinette, R. Weiss, E. M. Riseman, “Image-based homing,” IEEE Control Syst., special issue on robotics and automation, 12, 38–45 (1992).

E. M. Riseman, A. R. Hanson, J. R. Beveridge, R. Kumar, H. Sawhney, “Landmark-based navigation and the acquisition of environmental models,” in Visual Navigation, Y. Aloimonos, ed. (Erlbaum, Hillsdale, N.J., 1997), pp. 317–374.

Ronacher, B.

D. Efler, B. Ronacher, “Evidence against a retinotopic-template matching in honeybees’ pattern recognition,” Vision Res. 40, 3391–3403 (2000).
[CrossRef]

B. Ronacher, “How do bees learn and recognize visual patterns?” Biol. Cybern. 79, 477–485 (1998).
[CrossRef]

B. Ronacher, U. Duft, “An image-matching mechanism describes a generalization task in honeybees,” J. Comp. Physiol., A 178, 803–812 (1996).
[CrossRef]

Ruderman, D.

D. Ruderman, “Origins of scaling in natural images,” Vision Res. 23, 3385–3398 (1997).
[CrossRef]

Sawhney, H.

E. M. Riseman, A. R. Hanson, J. R. Beveridge, R. Kumar, H. Sawhney, “Landmark-based navigation and the acquisition of environmental models,” in Visual Navigation, Y. Aloimonos, ed. (Erlbaum, Hillsdale, N.J., 1997), pp. 317–374.

Schölkopf, B.

M. O. Franz, B. Schölkopf, H. A. Mallot, H. H. Bülthoff, “Where did I take that snapshot? Scene-based homing by image matching,” Biol. Cybern. 79, 191–202 (1998).
[CrossRef]

Srinivasan, M. V.

J. S. Chahl, M. V. Srinivasan, “Reflective surfaces for panoramic imaging,” Appl. Opt. 36, 8275–8285 (1997).
[CrossRef]

J. S. Chahl, M. V. Srinivasan, “Range estimation with a panoramic visual sensor,” J. Opt. Soc. Am. A 14, 2144–2151 (1997).
[CrossRef]

M. V. Srinivasan, J. S. Chahl, S. W. Zhang, “Robot navigation by visual dead-reckoning: inspiration from insects,” Int. J. Pattern Recogn. Artif. Intell. 11, 35–47 (1997).
[CrossRef]

M. G. Nagle, M. V. Srinivasan, D. L. Wilson, “Image interpolation technique for measurement of egomotion in 6 degrees of freedom,” J. Opt. Soc. Am. A 14, 3233–3241 (1997).
[CrossRef]

M. G. Nagle, M. V. Srinivasan, “Structure from motion: determining the range and orientation of surfaces by image interpolation,” J. Opt. Soc. Am. A 13, 25–34 (1996).
[CrossRef]

J. S. Chahl, M. V. Srinivasan, “Visual computation of egomotion using an image interpolation technique,” Biol. Cybern. 74, 405–411 (1996).
[CrossRef] [PubMed]

M. V. Srinivasan, “An image interpolation technique for the computation of optic flow and egomotion,” Biol. Cybern. 71, 401–415 (1994).
[CrossRef]

J. H. van Hateren, M. V. Srinivasan, P. B. Wait, “Pattern recognition in bees: orientation discrimination,” J. Comp. Physiol., A 167, 649–654 (1990).

Tan, X.

J. Hong, X. Tan, B. Pinette, R. Weiss, E. M. Riseman, “Image-based homing,” IEEE Control Syst., special issue on robotics and automation, 12, 38–45 (1992).

van der Schaaf, A.

A. van der Schaaf, H. van Hateren, “Modelling the power spectra of natural images: statistics and information,” Vision Res. 36, 2759–2770 (1996).
[CrossRef] [PubMed]

van Hateren, H.

A. van der Schaaf, H. van Hateren, “Modelling the power spectra of natural images: statistics and information,” Vision Res. 36, 2759–2770 (1996).
[CrossRef] [PubMed]

van Hateren, J. H.

J. H. van Hateren, M. V. Srinivasan, P. B. Wait, “Pattern recognition in bees: orientation discrimination,” J. Comp. Physiol., A 167, 649–654 (1990).

Voss, R.

R. Voss, J. Zeil, “Active vision in insects: an analysis of object-directed zig-zag flights in a ground-nesting wasp (Odynerus spinipes, Eumenidae),” J. Comp. Physiol., A 182, 377–387 (1998).
[CrossRef]

J. Zeil, A. Kelber, R. Voss, “Structure and function of learning flights in bees and wasps,” J. Exp. Biol. 199, 245–252 (1996).

Wait, P. B.

J. H. van Hateren, M. V. Srinivasan, P. B. Wait, “Pattern recognition in bees: orientation discrimination,” J. Comp. Physiol., A 167, 649–654 (1990).

Wehner, R.

D. Lambrinos, R. Möller, T. Labhart, R. Pfeifer, R. Wehner, “A mobile robot employing insect strategies for navigation,” Rob. Auton. Syst. 30, 39–64 (2000).
[CrossRef]

R. Wehner, F. Räber, “Visual spatial memory in desert ants, Cataglyphis bicolor (Hymenoptera: Formicidae),” Experientia 35, 1569–1571 (1979).
[CrossRef]

Weiss, R.

J. Hong, X. Tan, B. Pinette, R. Weiss, E. M. Riseman, “Image-based homing,” IEEE Control Syst., special issue on robotics and automation, 12, 38–45 (1992).

Wilson, D. L.

Wolf, R.

M. Dill, R. Wolf, M. Heisenberg, “Visual pattern recognition in Drosophila involves retinotopic matching,” Nature (London) 365, 751–753 (1993).
[CrossRef]

Zeil, J.

R. Voss, J. Zeil, “Active vision in insects: an analysis of object-directed zig-zag flights in a ground-nesting wasp (Odynerus spinipes, Eumenidae),” J. Comp. Physiol., A 182, 377–387 (1998).
[CrossRef]

T. S. Collett, J. Zeil, “Flights of learning,” Curr. Direct. Psychol. Sci. 5, 149–155 (1996).
[CrossRef]

J. Zeil, A. Kelber, R. Voss, “Structure and function of learning flights in bees and wasps,” J. Exp. Biol. 199, 245–252 (1996).

J. Zeil, “Orientation flights of solitary wasps (Cerceris; Sphecidae; Hymenoptera): II. Similarities between orientation and return flights and the use of motion parallax,” J. Comp. Physiol., A 172, 207–222 (1993).
[CrossRef]

J. Zeil, “Orientation flights of solitary wasps (Cerceris; Sphecidae; Hymenoptera): I. Description of flight,” J. Comp. Physiol., A 172, 189–205 (1993).
[CrossRef]

T. S. Collett, J. Zeil, “Places and landmarks: an arthro-pod perspective,” in Spatial Representation in Animals, S. Healy, ed. (Oxford U. Press, Oxford, UK, 1998), pp. 18–53.

M. P. Eckert, J. Zeil, “Towards an ecology of motion vision,” in Motion Vision: Computational, Neural and Ecological Constraints, J. M. Zanker, J. Zeil, eds. (Springer-Verlag, Berlin, 2001), pp. 333–369.

T. S. Collett, J. Zeil, “Selection and use of landmarks by insects,” in Orientation and Communication in Arthropods, M. Lehrer, ed. (Birkhäuser Verlag, Basel, Switzerland, 1997), pp. 41–65.

Zhang, S. W.

M. V. Srinivasan, J. S. Chahl, S. W. Zhang, “Robot navigation by visual dead-reckoning: inspiration from insects,” Int. J. Pattern Recogn. Artif. Intell. 11, 35–47 (1997).
[CrossRef]

Appl. Opt. (1)

Biol. Cybern. (7)

M. V. Srinivasan, “An image interpolation technique for the computation of optic flow and egomotion,” Biol. Cybern. 71, 401–415 (1994).
[CrossRef]

J. S. Chahl, M. V. Srinivasan, “Visual computation of egomotion using an image interpolation technique,” Biol. Cybern. 74, 405–411 (1996).
[CrossRef] [PubMed]

M. O. Franz, B. Schölkopf, H. A. Mallot, H. H. Bülthoff, “Where did I take that snapshot? Scene-based homing by image matching,” Biol. Cybern. 79, 191–202 (1998).
[CrossRef]

R. Möller, “Insect visual homing strategies in a robot with analog processing,” Biol. Cybern. 83, 231–243 (2000).
[CrossRef] [PubMed]

B. A. Cartwright, T. S. Collett, “Landmark maps for honeybees,” Biol. Cybern. 57, 85–93 (1987).
[CrossRef]

M. Lehrer, G. Bianco, “The turn-back-and-look behaviour: bee versus robot,” Biol. Cybern. 83, 211–229 (2000).
[CrossRef] [PubMed]

B. Ronacher, “How do bees learn and recognize visual patterns?” Biol. Cybern. 79, 477–485 (1998).
[CrossRef]

Curr. Biol. (1)

K. Dale, T. S. Collett, “Using artificial evolution and selection to model insect navigation,” Curr. Biol. 11, 1305–1316 (2001).
[CrossRef] [PubMed]

Curr. Direct. Psychol. Sci. (1)

T. S. Collett, J. Zeil, “Flights of learning,” Curr. Direct. Psychol. Sci. 5, 149–155 (1996).
[CrossRef]

Curr. Opin. Neurobiol. (1)

M. Heisenberg, “Pattern recognition in insects,” Curr. Opin. Neurobiol. 5, 475–481 (1995).
[CrossRef] [PubMed]

Experientia (1)

R. Wehner, F. Räber, “Visual spatial memory in desert ants, Cataglyphis bicolor (Hymenoptera: Formicidae),” Experientia 35, 1569–1571 (1979).
[CrossRef]

IEEE Control Syst. (1)

J. Hong, X. Tan, B. Pinette, R. Weiss, E. M. Riseman, “Image-based homing,” IEEE Control Syst., special issue on robotics and automation, 12, 38–45 (1992).

Int. J. Pattern Recogn. Artif. Intell. (1)

M. V. Srinivasan, J. S. Chahl, S. W. Zhang, “Robot navigation by visual dead-reckoning: inspiration from insects,” Int. J. Pattern Recogn. Artif. Intell. 11, 35–47 (1997).
[CrossRef]

J. Comp. Physiol. (2)

T. S. Collett, M. F. Land, “Visual spatial memory in a hoverfly,” J. Comp. Physiol. 100, 59–84 (1975).
[CrossRef]

B. A. Cartwright, T. S. Collett, “Landmark learning in bees: experiments and models,” J. Comp. Physiol. 151, 521–543 (1983).
[CrossRef]

J. Comp. Physiol., A (7)

B. Ronacher, U. Duft, “An image-matching mechanism describes a generalization task in honeybees,” J. Comp. Physiol., A 178, 803–812 (1996).
[CrossRef]

J. Zeil, “Orientation flights of solitary wasps (Cerceris; Sphecidae; Hymenoptera): II. Similarities between orientation and return flights and the use of motion parallax,” J. Comp. Physiol., A 172, 207–222 (1993).
[CrossRef]

T. S. Collett, J. A. Rees, “View-based navigation in Hymenoptera: multiple strategies of landmark guidance in the approach to a feeder,” J. Comp. Physiol., A 181, 47–58 (1997).
[CrossRef]

J. H. van Hateren, M. V. Srinivasan, P. B. Wait, “Pattern recognition in bees: orientation discrimination,” J. Comp. Physiol., A 167, 649–654 (1990).

J. Zeil, “Orientation flights of solitary wasps (Cerceris; Sphecidae; Hymenoptera): I. Description of flight,” J. Comp. Physiol., A 172, 189–205 (1993).
[CrossRef]

M. Lehrer, “Why do bees turn back and look?” J. Comp. Physiol., A 172, 549–563 (1993).
[CrossRef]

R. Voss, J. Zeil, “Active vision in insects: an analysis of object-directed zig-zag flights in a ground-nesting wasp (Odynerus spinipes, Eumenidae),” J. Comp. Physiol., A 182, 377–387 (1998).
[CrossRef]

J. Exp. Biol. (1)

J. Zeil, A. Kelber, R. Voss, “Structure and function of learning flights in bees and wasps,” J. Exp. Biol. 199, 245–252 (1996).

J. Opt. Soc. Am. A (3)

J. Theor. Biol. (1)

R. Möller, “Do insects use templates or parameters for landmark navigaion?,” J. Theor. Biol. 210, 33–45 (2001).
[CrossRef]

Nature (London) (1)

M. Dill, R. Wolf, M. Heisenberg, “Visual pattern recognition in Drosophila involves retinotopic matching,” Nature (London) 365, 751–753 (1993).
[CrossRef]

Philos. Trans. R. Soc. London, Ser. B (1)

M. Dill, M. Heisenberg, “Visual pattern memory without shape recognition,” Philos. Trans. R. Soc. London, Ser. B 349, 143–152 (1995).
[CrossRef] [PubMed]

Proc. Natl. Acad. Sci. U.S.A. (1)

D. M. Coppola, H. R. Purves, A. N. McCoy, D. Purves, “The distribution of oriented contours in thereal world,” Proc. Natl. Acad. Sci. U.S.A. 95, 4002–4006 (1998).
[CrossRef]

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

T. S. Collett, M. Lehrer, “Looking and learning: a spatial pattern in the orientation flight of the wasp Vespula vulgaris,” Proc. R. Soc. London, Ser. B 252, 129–134 (1993).
[CrossRef]

Rob. Auton. Syst. (3)

P. Gaussier, C. Joulain, J. P. Banquet, S. Leprêtre, A. Revel, “The visual homing problem: an example of robotics/biology cross fertilization,” Rob. Auton. Syst. 30, 155–180 (2000).
[CrossRef]

D. Lambrinos, R. Möller, T. Labhart, R. Pfeifer, R. Wehner, “A mobile robot employing insect strategies for navigation,” Rob. Auton. Syst. 30, 39–64 (2000).
[CrossRef]

M. O. Franz, H. A. Mallot, “Biomimetic robot navigation,” Rob. Auton. Syst. 30, 133–153 (2000).
[CrossRef]

Trends Neurosci. (1)

M. Giurfa, E. A. Capaldi, “Vectors, routes and maps: new discoveries about navigation in insects,” Trends Neurosci. 22, 237–242 (1999).
[CrossRef] [PubMed]

Vision Res. (4)

D. Efler, B. Ronacher, “Evidence against a retinotopic-template matching in honeybees’ pattern recognition,” Vision Res. 40, 3391–3403 (2000).
[CrossRef]

A. van der Schaaf, H. van Hateren, “Modelling the power spectra of natural images: statistics and information,” Vision Res. 36, 2759–2770 (1996).
[CrossRef] [PubMed]

D. Ruderman, “Origins of scaling in natural images,” Vision Res. 23, 3385–3398 (1997).
[CrossRef]

R. Ernst, M. Heisenberg, “The memory template in Drosophila pattern vision at the flight simulator,” Vision Res. 39, 3920–3933 (1999).
[CrossRef]

Other (5)

M. P. Eckert, J. Zeil, “Towards an ecology of motion vision,” in Motion Vision: Computational, Neural and Ecological Constraints, J. M. Zanker, J. Zeil, eds. (Springer-Verlag, Berlin, 2001), pp. 333–369.

G. E. P. Box, N. R. Draper, Evolutionary Operation (Wiley, New York, 1969).

E. M. Riseman, A. R. Hanson, J. R. Beveridge, R. Kumar, H. Sawhney, “Landmark-based navigation and the acquisition of environmental models,” in Visual Navigation, Y. Aloimonos, ed. (Erlbaum, Hillsdale, N.J., 1997), pp. 317–374.

T. S. Collett, J. Zeil, “Selection and use of landmarks by insects,” in Orientation and Communication in Arthropods, M. Lehrer, ed. (Birkhäuser Verlag, Basel, Switzerland, 1997), pp. 41–65.

T. S. Collett, J. Zeil, “Places and landmarks: an arthro-pod perspective,” in Spatial Representation in Animals, S. Healy, ed. (Oxford U. Press, Oxford, UK, 1998), pp. 18–53.

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