Abstract

We examine the mechanism that subserves visual contour detection and particularly its tuning for the spatial frequency of contour components. We measured the detection of contours composed of Gabor micropatterns within a field of randomly oriented distractor elements. Distractors were randomly assigned one of two spatial frequencies, and elements lying along the contour alternated between these values. We report that the degree of tolerable spatial-frequency difference between successive contour elements is inversely proportional to the orientation difference between them. Spatial-frequency tuning (half-width at half-height) for straight contours is 1.3 octaves but, for contours with a 30° difference between successive elements, drops to 0.7 octaves. Integration of curved contours operates at a narrower bandwidth. Much orientation information in natural images arises from edges, and we propose that this narrowing of tuning is related to the reduction in interscale support that accompanies increasing edge curvature.

© 1998 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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  8. S. C. Dakin, “The detection of structure in Glass patterns: psychophysics and computational models,” Vision Res. 37, 2227–2259 (1997).
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  24. J. F. Canny, “Finding edges and lines in images,” (Massachusetts Institute of Technology, Boston, Mass., 1983).
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  26. A. Hayes, “Representation by images restricted in resolution and intensity range,” Ph.D. dissertation (University of Western Australia, Perth, Australia1989).
  27. L. D. Harmon, B. Julesz, “Masking in visual recognition: effects of two dimensional filtered noise,” Science 180, 1194–1197 (1973).
    [CrossRef] [PubMed]
  28. M. C. Morrone, D. C. Burr, “Capture and transparency in coarse quantized images,” Vision Res. 37, 2609–2629 (1997).
    [CrossRef] [PubMed]
  29. S. J. M. Rainville, F. A. A. Kingdom, A. Hayes, “Is motion perception sensitive to local phase structures?” Invest. Ophthalmol. Visual Sci. 38, S215 (1997).
  30. D. G. Pelli, “The VideoToolbox software for visual psychophysics: transforming number into movies,” Spatial Vis. 10, 437–442 (1997).
    [CrossRef]
  31. W. H. McIlhagga, K. T. Mullen, “Contour integration with colour and luminance contrast,” Vision Res. 36, 1265–1279 (1996).
    [CrossRef] [PubMed]
  32. R. F. Hess, S. C. Dakin, “Absence of contour linking in peripheral vision,” Nature 390, 602–604 (1997).
    [CrossRef] [PubMed]
  33. D. W. Heeley, H. M. Buchanan-Smith, “Recognition of stimulus orientation,” Vision Res. 32, 719–743 (1990).
  34. P. H. Schiller, B. L. Finlay, S. F. Volman, “Quantitative studies of single-cell properties in monkey striate cortex: III. Spatial frequency, J. Neurophysiol. 39, 1334–1351 (1976).
    [PubMed]
  35. J. Movshon, I. D. Thompson, D. J. Tolhurst, “Spatial and temporal contrast sensitivity of neurones in area 17 and 18 of the cat’s visual cortex,” J. Physiol. (London) 283, 101–120 (1978).
  36. J. J. Kulikowski, P. O. Bishop, “Linear analysis of the responses of simple cells in the cat visual cortex,” Exp. Brain Res. 44, 386–400 (1981).
    [CrossRef] [PubMed]
  37. D. J. Tolhurst, I. D. Thompson, “On the variety of spatial frequency selectivities shown by neurons in area 17 of the cat,” Proc. R. Soc. London Ser. B 213, 183–199 (1981).
    [CrossRef]
  38. R. L. De Valois, D. G. Albrecht, L. G. Thorell, “Spatial frequency selectivity of cells in macaque visual cortex,” Vision Res. 22, 545–559 (1982).
    [CrossRef] [PubMed]
  39. D. J. Field, D. J. Tolhurst, “The structure and symmetry of simple-cell receptive-field profiles in the cat’s visual cortex,” Proc. R. Soc. London Ser. B 228, 379–400 (1986).
    [CrossRef]
  40. D. J. Field, A. Hayes, R. F. Hess, “The role of phase and contrast polarity in contour integration,” Invest. Ophthalmol. Visual Sci. 38, S999 (1997).
  41. M. W. Pettet, S. P. McKee, N. M. Grzywacz, “Smoothness constrains long-range interactions mediating contour-detection,” Invest. Ophthalmol. Visual Sci. 37, 4368 (1996).
  42. Gabor filters had 1:1 envelopes, with a wavelength equal to 1.5σ, and were in cosine phase. Their outputs were weighted by 1/f.
  43. R. J. Watt, M. J. Morgan, “A theory of the primitive spatial code in human vision,” Vision Res. 25, 1661–1674 (1985).
    [CrossRef] [PubMed]
  44. B. A. Olshausen, D. J. Field, “Emergence of simple-cell receptive field properties by learning a sparse code for naturla images,” Nature 381, 607–609 (1996).
    [CrossRef] [PubMed]
  45. A. J. Bell, T. J. Sejnowski, “The ‘independent components’ of natural scenes are edge filters,” Vision Res. 37, 3327–3338 (1997).
    [CrossRef]

1998 (1)

R. F. Hess, S. C. Dakin, D. J. Field, “The role of ‘contrast enhancement’ in the detection and appearance of visual contours,” Vision Res. 38, 783–787 (1998).
[CrossRef] [PubMed]

1997 (8)

S. C. Dakin, “The detection of structure in Glass patterns: psychophysics and computational models,” Vision Res. 37, 2227–2259 (1997).
[CrossRef] [PubMed]

M. C. Morrone, D. C. Burr, “Capture and transparency in coarse quantized images,” Vision Res. 37, 2609–2629 (1997).
[CrossRef] [PubMed]

S. J. M. Rainville, F. A. A. Kingdom, A. Hayes, “Is motion perception sensitive to local phase structures?” Invest. Ophthalmol. Visual Sci. 38, S215 (1997).

D. G. Pelli, “The VideoToolbox software for visual psychophysics: transforming number into movies,” Spatial Vis. 10, 437–442 (1997).
[CrossRef]

R. F. Hess, S. C. Dakin, “Absence of contour linking in peripheral vision,” Nature 390, 602–604 (1997).
[CrossRef] [PubMed]

D. J. Field, A. Hayes, R. F. Hess, “The role of phase and contrast polarity in contour integration,” Invest. Ophthalmol. Visual Sci. 38, S999 (1997).

A. J. Bell, T. J. Sejnowski, “The ‘independent components’ of natural scenes are edge filters,” Vision Res. 37, 3327–3338 (1997).
[CrossRef]

Z. Pizlo, M. Salach-Golyska, A. Rosenfeld, “Curve detection in a noisy image,” Vision Res. 37, 1217–1241 (1997).
[CrossRef] [PubMed]

1996 (3)

B. A. Olshausen, D. J. Field, “Emergence of simple-cell receptive field properties by learning a sparse code for naturla images,” Nature 381, 607–609 (1996).
[CrossRef] [PubMed]

M. W. Pettet, S. P. McKee, N. M. Grzywacz, “Smoothness constrains long-range interactions mediating contour-detection,” Invest. Ophthalmol. Visual Sci. 37, 4368 (1996).

W. H. McIlhagga, K. T. Mullen, “Contour integration with colour and luminance contrast,” Vision Res. 36, 1265–1279 (1996).
[CrossRef] [PubMed]

1995 (1)

R. F. Hess, D. J. Field, “Contour integration across depth,” Vision Res. 35, 1699–1711 (1995).
[CrossRef] [PubMed]

1994 (2)

U. Polat, D. Sagi, “The architecture of perceptual spatial interactions,” Vision Res. 34, 73–78 (1994).
[CrossRef] [PubMed]

I. Kovacs, B. Julesz, “Perceptual sensitivity maps within globally defined visual shapes,” Nature 370, 644–646 (1994).
[CrossRef] [PubMed]

1993 (2)

D. J. Field, A. Hayes, R. F. Hess, “Contour integration by the human visual system: evidence for a local ‘association field, ” Vision Res. 33, 173–193 (1993).
[CrossRef] [PubMed]

I. Kovacs, B. Julesz, “A closed curve is much more than an incomplete one: effect of closure in figure-ground segmentation,” Proc. Natl. Acad. Sci. USA 90, 7495–7497 (1993).
[CrossRef] [PubMed]

1991 (1)

W. H. Freeman, E. H. Adelson, “The design and use of steerable filters,” IEEE Trans. Pattern. Anal. Mach. Intell. 13, 891–906 (1991).
[CrossRef]

1990 (1)

D. W. Heeley, H. M. Buchanan-Smith, “Recognition of stimulus orientation,” Vision Res. 32, 719–743 (1990).

1989 (2)

P. Parent, S. W. Zucker, “Trace inference, curvature consistency and curve-detection,” IEEE Trans. Pattern. Anal. Mach. Intell. 11, 823–839 (1989).
[CrossRef]

S. W. Zucker, A. Dobbins, L. Iverson, “Two stages of curve detection suggest two styles of visual computation,” Neural Computation 1, 68–81 (1989).
[CrossRef]

1987 (1)

J. T. Smits, P. G. Vos, “The perception of continuous curves in dot stimuli,” Perception 16, 121–131 (1987).
[CrossRef] [PubMed]

1986 (1)

D. J. Field, D. J. Tolhurst, “The structure and symmetry of simple-cell receptive-field profiles in the cat’s visual cortex,” Proc. R. Soc. London Ser. B 228, 379–400 (1986).
[CrossRef]

1985 (2)

R. J. Watt, M. J. Morgan, “A theory of the primitive spatial code in human vision,” Vision Res. 25, 1661–1674 (1985).
[CrossRef] [PubMed]

S. W. Zucker, “Early orientation selection: tangent fields and the dimensionality of their support,” Comput. Vis. Graph. Image Process. 8, 71–77 (1985).

1982 (1)

R. L. De Valois, D. G. Albrecht, L. G. Thorell, “Spatial frequency selectivity of cells in macaque visual cortex,” Vision Res. 22, 545–559 (1982).
[CrossRef] [PubMed]

1981 (2)

J. J. Kulikowski, P. O. Bishop, “Linear analysis of the responses of simple cells in the cat visual cortex,” Exp. Brain Res. 44, 386–400 (1981).
[CrossRef] [PubMed]

D. J. Tolhurst, I. D. Thompson, “On the variety of spatial frequency selectivities shown by neurons in area 17 of the cat,” Proc. R. Soc. London Ser. B 213, 183–199 (1981).
[CrossRef]

1980 (1)

D. Marr, E. Hildreth, “Theory of edge detection,” Proc. R. Soc. London Ser. B 207, 187–217 (1980).
[CrossRef]

1979 (1)

1978 (1)

J. Movshon, I. D. Thompson, D. J. Tolhurst, “Spatial and temporal contrast sensitivity of neurones in area 17 and 18 of the cat’s visual cortex,” J. Physiol. (London) 283, 101–120 (1978).

1976 (1)

P. H. Schiller, B. L. Finlay, S. F. Volman, “Quantitative studies of single-cell properties in monkey striate cortex: III. Spatial frequency, J. Neurophysiol. 39, 1334–1351 (1976).
[PubMed]

1973 (1)

L. D. Harmon, B. Julesz, “Masking in visual recognition: effects of two dimensional filtered noise,” Science 180, 1194–1197 (1973).
[CrossRef] [PubMed]

1969 (1)

L. Glass, “Moiré effects from random dots,” Nature 243, 578–580 (1969).
[CrossRef]

Adelson, E. H.

W. H. Freeman, E. H. Adelson, “The design and use of steerable filters,” IEEE Trans. Pattern. Anal. Mach. Intell. 13, 891–906 (1991).
[CrossRef]

Albrecht, D. G.

R. L. De Valois, D. G. Albrecht, L. G. Thorell, “Spatial frequency selectivity of cells in macaque visual cortex,” Vision Res. 22, 545–559 (1982).
[CrossRef] [PubMed]

Bell, A. J.

A. J. Bell, T. J. Sejnowski, “The ‘independent components’ of natural scenes are edge filters,” Vision Res. 37, 3327–3338 (1997).
[CrossRef]

Bishop, P. O.

J. J. Kulikowski, P. O. Bishop, “Linear analysis of the responses of simple cells in the cat visual cortex,” Exp. Brain Res. 44, 386–400 (1981).
[CrossRef] [PubMed]

Buchanan-Smith, H. M.

D. W. Heeley, H. M. Buchanan-Smith, “Recognition of stimulus orientation,” Vision Res. 32, 719–743 (1990).

Burr, D. C.

M. C. Morrone, D. C. Burr, “Capture and transparency in coarse quantized images,” Vision Res. 37, 2609–2629 (1997).
[CrossRef] [PubMed]

Caelli, T.

Canny, J. F.

J. F. Canny, “Finding edges and lines in images,” (Massachusetts Institute of Technology, Boston, Mass., 1983).

Dakin, S. C.

R. F. Hess, S. C. Dakin, D. J. Field, “The role of ‘contrast enhancement’ in the detection and appearance of visual contours,” Vision Res. 38, 783–787 (1998).
[CrossRef] [PubMed]

S. C. Dakin, “The detection of structure in Glass patterns: psychophysics and computational models,” Vision Res. 37, 2227–2259 (1997).
[CrossRef] [PubMed]

R. F. Hess, S. C. Dakin, “Absence of contour linking in peripheral vision,” Nature 390, 602–604 (1997).
[CrossRef] [PubMed]

David, C.

S. W. Zucker, C. David, A. Dobbins, L. Iverson, “The organization of curve detection: coarse tangent fields and fine spline coverings,” in Proceedings of the IEEE International Conference on Computer Vision (IEEE Computer Society Press, Los Alamitos, Calif., 1988).

De Valois, R. L.

R. L. De Valois, D. G. Albrecht, L. G. Thorell, “Spatial frequency selectivity of cells in macaque visual cortex,” Vision Res. 22, 545–559 (1982).
[CrossRef] [PubMed]

Dobbins, A.

S. W. Zucker, A. Dobbins, L. Iverson, “Two stages of curve detection suggest two styles of visual computation,” Neural Computation 1, 68–81 (1989).
[CrossRef]

S. W. Zucker, C. David, A. Dobbins, L. Iverson, “The organization of curve detection: coarse tangent fields and fine spline coverings,” in Proceedings of the IEEE International Conference on Computer Vision (IEEE Computer Society Press, Los Alamitos, Calif., 1988).

Field, D. J.

R. F. Hess, S. C. Dakin, D. J. Field, “The role of ‘contrast enhancement’ in the detection and appearance of visual contours,” Vision Res. 38, 783–787 (1998).
[CrossRef] [PubMed]

D. J. Field, A. Hayes, R. F. Hess, “The role of phase and contrast polarity in contour integration,” Invest. Ophthalmol. Visual Sci. 38, S999 (1997).

B. A. Olshausen, D. J. Field, “Emergence of simple-cell receptive field properties by learning a sparse code for naturla images,” Nature 381, 607–609 (1996).
[CrossRef] [PubMed]

R. F. Hess, D. J. Field, “Contour integration across depth,” Vision Res. 35, 1699–1711 (1995).
[CrossRef] [PubMed]

D. J. Field, A. Hayes, R. F. Hess, “Contour integration by the human visual system: evidence for a local ‘association field, ” Vision Res. 33, 173–193 (1993).
[CrossRef] [PubMed]

D. J. Field, D. J. Tolhurst, “The structure and symmetry of simple-cell receptive-field profiles in the cat’s visual cortex,” Proc. R. Soc. London Ser. B 228, 379–400 (1986).
[CrossRef]

D. J. Field, “Scale-invariance and self-similar ‘wavelet’ transforms: an analysis of natural scenes and mammalian visual systems,” in Wavelets, Fractals and Fourier Transforms, M. Marge, J. C. R. Hunt, J. C. Vassilicos, eds. (Clarendon, Oxford, UK, 1993), pp. 151–193.

Finkel, L. H.

S.-C. Yen, L. H. Finkel, “Salient contour extraction by temporal binding in a cortically based network,” in Advances in Neural Information Processing Systems, D. S. Touretzky, M. C. Mozer, M. E. Hasselmo, eds. (MIT Press, Cambridge, Mass., 1996).

S.-C. Yen, L. H. Finkel, “Cortical synchronization mechanism for ‘pop-out’ of salient image contours,” in The Neurobiology of Computation, J. Bower, ed. (Kluwer Academic, Boston, Mass., 1996).

Finlay, B. L.

P. H. Schiller, B. L. Finlay, S. F. Volman, “Quantitative studies of single-cell properties in monkey striate cortex: III. Spatial frequency, J. Neurophysiol. 39, 1334–1351 (1976).
[PubMed]

Freeman, W. H.

W. H. Freeman, E. H. Adelson, “The design and use of steerable filters,” IEEE Trans. Pattern. Anal. Mach. Intell. 13, 891–906 (1991).
[CrossRef]

Gigus, Z.

Z. Gigus, J. Malik, “Detecting curvilinear structure in images,” (University of California Berkeley, Berkeley, Calif., 1991).

Glass, L.

L. Glass, “Moiré effects from random dots,” Nature 243, 578–580 (1969).
[CrossRef]

Grzywacz, N. M.

M. W. Pettet, S. P. McKee, N. M. Grzywacz, “Smoothness constrains long-range interactions mediating contour-detection,” Invest. Ophthalmol. Visual Sci. 37, 4368 (1996).

Harmon, L. D.

L. D. Harmon, B. Julesz, “Masking in visual recognition: effects of two dimensional filtered noise,” Science 180, 1194–1197 (1973).
[CrossRef] [PubMed]

Hayes, A.

D. J. Field, A. Hayes, R. F. Hess, “The role of phase and contrast polarity in contour integration,” Invest. Ophthalmol. Visual Sci. 38, S999 (1997).

S. J. M. Rainville, F. A. A. Kingdom, A. Hayes, “Is motion perception sensitive to local phase structures?” Invest. Ophthalmol. Visual Sci. 38, S215 (1997).

D. J. Field, A. Hayes, R. F. Hess, “Contour integration by the human visual system: evidence for a local ‘association field, ” Vision Res. 33, 173–193 (1993).
[CrossRef] [PubMed]

A. Hayes, “Representation by images restricted in resolution and intensity range,” Ph.D. dissertation (University of Western Australia, Perth, Australia1989).

Heeley, D. W.

D. W. Heeley, H. M. Buchanan-Smith, “Recognition of stimulus orientation,” Vision Res. 32, 719–743 (1990).

Hess, R. F.

R. F. Hess, S. C. Dakin, D. J. Field, “The role of ‘contrast enhancement’ in the detection and appearance of visual contours,” Vision Res. 38, 783–787 (1998).
[CrossRef] [PubMed]

R. F. Hess, S. C. Dakin, “Absence of contour linking in peripheral vision,” Nature 390, 602–604 (1997).
[CrossRef] [PubMed]

D. J. Field, A. Hayes, R. F. Hess, “The role of phase and contrast polarity in contour integration,” Invest. Ophthalmol. Visual Sci. 38, S999 (1997).

R. F. Hess, D. J. Field, “Contour integration across depth,” Vision Res. 35, 1699–1711 (1995).
[CrossRef] [PubMed]

D. J. Field, A. Hayes, R. F. Hess, “Contour integration by the human visual system: evidence for a local ‘association field, ” Vision Res. 33, 173–193 (1993).
[CrossRef] [PubMed]

Hildreth, E.

D. Marr, E. Hildreth, “Theory of edge detection,” Proc. R. Soc. London Ser. B 207, 187–217 (1980).
[CrossRef]

Iverson, L.

S. W. Zucker, A. Dobbins, L. Iverson, “Two stages of curve detection suggest two styles of visual computation,” Neural Computation 1, 68–81 (1989).
[CrossRef]

S. W. Zucker, C. David, A. Dobbins, L. Iverson, “The organization of curve detection: coarse tangent fields and fine spline coverings,” in Proceedings of the IEEE International Conference on Computer Vision (IEEE Computer Society Press, Los Alamitos, Calif., 1988).

Julesz, B.

I. Kovacs, B. Julesz, “Perceptual sensitivity maps within globally defined visual shapes,” Nature 370, 644–646 (1994).
[CrossRef] [PubMed]

I. Kovacs, B. Julesz, “A closed curve is much more than an incomplete one: effect of closure in figure-ground segmentation,” Proc. Natl. Acad. Sci. USA 90, 7495–7497 (1993).
[CrossRef] [PubMed]

T. Caelli, B. Julesz, “Psychophysical evidence for global feature processing in visual texture discrimination,” J. Opt. Soc. Am. 69, 675–678 (1979).
[CrossRef] [PubMed]

L. D. Harmon, B. Julesz, “Masking in visual recognition: effects of two dimensional filtered noise,” Science 180, 1194–1197 (1973).
[CrossRef] [PubMed]

Kingdom, F. A. A.

S. J. M. Rainville, F. A. A. Kingdom, A. Hayes, “Is motion perception sensitive to local phase structures?” Invest. Ophthalmol. Visual Sci. 38, S215 (1997).

Kovacs, I.

I. Kovacs, B. Julesz, “Perceptual sensitivity maps within globally defined visual shapes,” Nature 370, 644–646 (1994).
[CrossRef] [PubMed]

I. Kovacs, B. Julesz, “A closed curve is much more than an incomplete one: effect of closure in figure-ground segmentation,” Proc. Natl. Acad. Sci. USA 90, 7495–7497 (1993).
[CrossRef] [PubMed]

Kulikowski, J. J.

J. J. Kulikowski, P. O. Bishop, “Linear analysis of the responses of simple cells in the cat visual cortex,” Exp. Brain Res. 44, 386–400 (1981).
[CrossRef] [PubMed]

Lowe, D. G.

D. G. Lowe, “Organization of smooth image curves at multiple spatial scales,” in Proceedings of the IEEE International Conference on Computer Vision (IEEE Computer Society Press, Los Alamitos, Calif., 1988), pp. 119–130.

Malik, J.

Z. Gigus, J. Malik, “Detecting curvilinear structure in images,” (University of California Berkeley, Berkeley, Calif., 1991).

Marr, D.

D. Marr, E. Hildreth, “Theory of edge detection,” Proc. R. Soc. London Ser. B 207, 187–217 (1980).
[CrossRef]

D. Marr, Vision (Freeman, San Francisco, Calif., 1982).

McIlhagga, W. H.

W. H. McIlhagga, K. T. Mullen, “Contour integration with colour and luminance contrast,” Vision Res. 36, 1265–1279 (1996).
[CrossRef] [PubMed]

McKee, S. P.

M. W. Pettet, S. P. McKee, N. M. Grzywacz, “Smoothness constrains long-range interactions mediating contour-detection,” Invest. Ophthalmol. Visual Sci. 37, 4368 (1996).

Morgan, M. J.

R. J. Watt, M. J. Morgan, “A theory of the primitive spatial code in human vision,” Vision Res. 25, 1661–1674 (1985).
[CrossRef] [PubMed]

Morrone, M. C.

M. C. Morrone, D. C. Burr, “Capture and transparency in coarse quantized images,” Vision Res. 37, 2609–2629 (1997).
[CrossRef] [PubMed]

Movshon, J.

J. Movshon, I. D. Thompson, D. J. Tolhurst, “Spatial and temporal contrast sensitivity of neurones in area 17 and 18 of the cat’s visual cortex,” J. Physiol. (London) 283, 101–120 (1978).

Mullen, K. T.

W. H. McIlhagga, K. T. Mullen, “Contour integration with colour and luminance contrast,” Vision Res. 36, 1265–1279 (1996).
[CrossRef] [PubMed]

Olshausen, B. A.

B. A. Olshausen, D. J. Field, “Emergence of simple-cell receptive field properties by learning a sparse code for naturla images,” Nature 381, 607–609 (1996).
[CrossRef] [PubMed]

Parent, P.

P. Parent, S. W. Zucker, “Trace inference, curvature consistency and curve-detection,” IEEE Trans. Pattern. Anal. Mach. Intell. 11, 823–839 (1989).
[CrossRef]

Pelli, D. G.

D. G. Pelli, “The VideoToolbox software for visual psychophysics: transforming number into movies,” Spatial Vis. 10, 437–442 (1997).
[CrossRef]

Pettet, M. W.

M. W. Pettet, S. P. McKee, N. M. Grzywacz, “Smoothness constrains long-range interactions mediating contour-detection,” Invest. Ophthalmol. Visual Sci. 37, 4368 (1996).

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A. Sha’ashua, S. Ullman, “Structural saliency: the detection of globally salient structures using a locally connected network,” in Proceedings of the IEEE International Conference on Computer Vision (IEEE Computer Society Press, Los Alamitos, Calif., 1988), pp. 321–327.

S.-C. Yen, L. H. Finkel, “Salient contour extraction by temporal binding in a cortically based network,” in Advances in Neural Information Processing Systems, D. S. Touretzky, M. C. Mozer, M. E. Hasselmo, eds. (MIT Press, Cambridge, Mass., 1996).

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Gabor filters had 1:1 envelopes, with a wavelength equal to 1.5σ, and were in cosine phase. Their outputs were weighted by 1/f.

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Figures (11)

Fig. 1
Fig. 1

Two variants on the association field model that deal with variation in spatial scale of contour elements. (a) The scale-invariant model performs contour integration on orientation tokens that are abstracted from filter outputs across scale. (b) The scale-dependent model has association operations at multiple, independent spatial scales, and combination occurs after integration.

Fig. 2
Fig. 2

Examples of the stimuli used in experiment 1. The upper row shows 8 element-long paths with a 20° difference in orientation between successive elements. Elements have spatial frequencies of (a) 12.8, (b) 4.53, and (c) 1.6 c.p.d. Paths are difficult to locate in (a) because the effective separation of micropatterns, expressed in units of carrier wavelength, is very large. The first and last elements of the path in (a) are indicated (direction of arrows indicates local contour direction). The lower row shows the similar stimuli with alternate elements along the path and half of the background elements randomly deleted. No paths are visible.

Fig. 3
Fig. 3

Results from experiment 1. Circles show the contour detection performance of two subjects as a function of micropattern carrier spatial frequency. Paths were composed of eight elements and had a path angle of 20°. Performance plateaus at a spatial frequency of 6.4 c.p.d, and in all subsequent experiments we employ elements with spatial frequencies in the range indicated. Squares show path-detection performance, as a function of carrier spatial frequency, when half of the elements are removed. Both subjects are at chance, thus indicating that performance in subsequent experiments, with paths composed of alternating carrier frequency, cannot be attributable to the detection of contour structure in a single population.

Fig. 4
Fig. 4

Examples of the stimuli from experiment 2. (a)–(c) 4-element path with a path angle of 0°, (d)–(f) 8-element path with a path angle of 20°. For all textures the spatial frequency of one set is 3.2 c.p.d. and of the second set [(a),(d)] 6.4 (b),(e) 3.2, and [(c),(f)] 1.6 c.p.d. Note that the effect of mixing the frequency of elements is more disruptive to the detection of curved paths in (d) and (f) than straight paths in (a) and (c). Arrows indicate the first element of all paths.

Fig. 5
Fig. 5

Tuning of contour detection for the spatial frequency of contour components at different path angles. Data from two subjects are shown. Notice the sharpening of tuning with increasing path angle.

Fig. 6
Fig. 6

Spatial-frequency tuning for detection of contours (path angle of 20°; subject SCD) for four referent spatial frequencies. Peak performance and width of tuning curves are similar across all referent frequencies.

Fig. 7
Fig. 7

(a),(b) Stimuli from the control condition assessing the effect of bandwidth alternation in the absence of spatial-frequency change. The paths shown (20° path angle) are composed of reference patches alternating with micropatterns with envelope standard deviations equal to (a) 0.71 and (b) 1.41 times that of the reference envelope. (c) Results (triangles, upper abscissa) indicate only a small reduction of performance with bandwidth alternation compared with the equivalent spatial-frequency alternation condition (solid and dashed curves).

Fig. 8
Fig. 8

Examples of the stimuli from experiment 3. (a)–(c) Smooth paths with a path angle of 20°, (d)–(f) closed paths of 12 elements with 30° path angle. Elements in (b) and (e) are of a single spatial frequency, but one population in (a) and (d) and (c) and (f) is made up of elements with a peak spatial frequency one octave higher or lower, respectively. Arrows indicate position and orientation of the first path element.

Fig. 9
Fig. 9

Spatial-frequency tuning for smooth contours (uppermost graphs are taken from the straight path condition of Fig. 4). Tuning functions are similar to those for jagged contours.

Fig. 10
Fig. 10

Two subjects’ spatial-frequency tuning for closed versus open contours. Performance with a smooth contour and the same path angle is also shown (triangles). The two sets of data are fitted with the same tuning curve, with a constant offset subtracted for the smooth path data. Similar tuning is obtained.

Fig. 11
Fig. 11

The degree of scale support provided by edges as a function of their curvature. Edge curvature increases, from left to right in the figure. Histograms show the response of weighted Gabor filters, at the position marked by the arrows, across three octaves of scale (fine to coarse from left to right). Support is consistent across scale for near-straight edges (leftmost histogram) but drops away sharply for increasingly curved edges.

Tables (2)

Tables Icon

Table 1 Half-Width at Half-Height of the Tuning Functions Shown in Fig. 5a

Tables Icon

Table 2 Half-Width at Half-Height Measures Derived from the Tuning Functions Shown in Fig. 9a

Equations (5)

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

G(x, y)=A sinxtλ+ϕexp-x2+y22σ2,
xt=x cos θ+y sin θ,
yt=y cos θ-x sin θ.
G(x)=A+B exp-μ-log(x)σ2,
A=50,B=pcmax.

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