Abstract

Recent work has shown that salient perceptual singularities occur in visual textures even in the absence of feature gradients. In smoothly varying orientation-defined textures, these striking non-smooth percepts can be predicted from two texture curvatures, one tangential and one normal [Proc. Natl. Acad. Sci. USA103, 15704 (2006)]. We address the issue of detecting these perceptual singularities in a biologically plausible manner and present three different models to compute the tangential and normal curvatures using early cortical mechanisms. The first model relies on the response summation of similarly scaled even-symmetric simple cells at different positions by utilizing intercolumnar interactions in the primary visual cortex (V1). The second model is based on intracolumnar interactions in a two-layer mechanism of simple cells having the same orientation tuning but significantly different scales. Our third model uses a three-layer circuit in which both even-symmetric and odd-symmetric receptive fields (RFs) are used to compute all possible directional derivatives of the dominant orientation, from which the tangential and normal curvatures at each spatial position are selected using nonlinear shunting inhibition. We show experimental results of all three models, we outline an extension to oriented textures with multiple dominant orientations at each point, and we discuss how our results may be relevant to the processing of general textures.

© 2008 Optical Society of America

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  1. J. Beck, “Effect of orientation and the shape similarity on perceptual grouping,” Percept. Psychophys. 1, 300-302 (1966).
  2. R. Olson and F. Attneave, “What variables produce similarity grouping?” Am. J. Psychol. 83, 1-21 (1970).
  3. B. Julesz, “Textons, the elements of texture perception, and their interactions,” Nature 290, 91-97 (1981).
    [CrossRef]
  4. H. Nothdurft, “The role of features in preattentive vision: Comparison of orientation, motion, and color cues,” Vision Res. 33, 1937-1958 (1993).
  5. D. Sagi, “The psychophysics of texture segmentation,” in Early Vision and Beyond, T.Papathomas, C.Chubb, A.Gorea, and E.Kowler, eds. (MIT, 1995), pp. 69-78.
  6. J. Malik and P. Perona, “Preattentive texture discrimination with early vision mechanisms,” J. Opt. Soc. Am. A 7, 923-932 (1990).
  7. O. Ben-Shahar, “Visual saliency and texture segregation without feature gradient,” Proc. Natl. Acad. Sci. U.S.A. 103, 15704-15709 (2006).
  8. O. Ben-Shahar, “Saliency and segregation without feature gradient: New insights for segmentation from orientation-defined textures,” in The Fifth IEEE Computer Society Workshop on Perceptual Organization in Computer Vision (IEEE, 2006), pp. 175-182.
  9. O. Ben-Shahar and S. Zucker, “The perceptual organization of texture flows: A contextual inference approach,” IEEE Trans. Pattern Anal. Mach. Intell. 25, 401-417 (2003).
  10. M. Kass and A. Witkin, “Analyzing oriented patterns,” Comput. Vis. Graph. Image Process. 37, 362-385 (1987).
    [CrossRef]
  11. A. Rao and R. Jain, “Computerized flow field analysis: Oriented texture fields,” IEEE Trans. Pattern Anal. Mach. Intell. 17, 693-709 (1992).
  12. B. O'Neill, Elementary Differential Geometry (Academic, 1966).
  13. M. do Carmo, Differential Geometry of Curves and Surfaces (Prentice-Hall, 1976).
  14. R. Haralik, “Ridges and valleys on digital images,” Comput. Vis. Graph. Image Process. 22, 28-38 (1983).
    [CrossRef]
  15. J. Koenderink and A. van Doorn, “Local features of smooth shapes: Ridges and courses,” Proc. SPIE 2031, 2-13 (1993).
    [CrossRef]
  16. A. López and J. Serrat, “Tracing crease curves by solving a system of differential equations,” in Proceedings of the European Conference on Computer Vision, Vol. 1064 of Lecture Notes in Computer Science (Springer-Verlag, 1996), pp. 241-250.
  17. J. Rieger, “Topographical properties of generic images,” Int. J. Comput. Vis. 23, 79-92 (1997).
  18. J. Serrat, A. López, and D. Lloret, “On ridges and valleys,” in Proceedings of the 15th IEEE International Conference on Pattern Recognition (IEEE, 2000), pp. 59-66.
  19. D. Eberly, Ridges in Image and Data Analysis (Kluwer Academic, 1996).
  20. O. Ben-Shahar and S. Zucker, “Geometrical computations explain projection patterns of long range horizontal connections in visual cortex,” Neural Comput. 16, 445-476 (2004).
  21. A. Dobbins, S. Zucker, and M. Cynader, “Endstopped neurons in the visual cortex as a substrate for calculating curvature,” Nature 329, 438-441 (1987).
    [CrossRef]
  22. M. Versavel, G. Orban, and L. Lagae, “Responses of visual cortical neurons to curved stimuli and chevrons,” Vision Res. 30, 235-248 (1990).
  23. J. Bergen and M. Landy, “Computational modeling of visual texture segregation,” in Computational Models of Visual Processing, M.Landy and J.Movshon, eds. (MIT, 1991), pp. 253-271.
  24. D. Hubel and T. Wiesel, “Functional architecture of macaque monkey visual cortex,” in Proc. R. Soc. London, Ser. B 198, 1-59 (1977).
  25. W. Bosking, Y. Zhang, B. Schofield, and D. Fitzpatrick, “Orientation selectivity and the arrangement of horizontal connections in the tree shrew striate cortex,” J. Neurosci. 17, 2112-2127 (1997).
  26. M. Concetta Morrone and D. Burr, “Feature detection in human vision: A phase-dependent energy model,” Proc. R. Soc. London, Ser. B 235, 221-245 (1988).
  27. V. Torre and T. Poggio, “A synaptic mechanism possibly underlying directional selectivity to motion,” Proc. R. Soc. London, Ser. B 202, 409-416 (1978).
  28. C. Koch, T. Poggio, and V. Torre, “Nonlinear interactions in a dendritic tree: Localization, timing, and role in information processing,” Proc. Natl. Acad. Sci. U.S.A. 80, 2799-2802 (1983).
  29. H. Barlow and W. Levick, “The mechanism of directionally selective units in rabbit's retina,” J. Physiol. (London) 178, 477-504 (1965).
  30. L. Borg-Graham, C. Monier, and Y. Frégnac, “Visual input evokes transient and strong shunting inhibition in visual cortical neurons,” Nature 393, 369-373 (1998).
    [CrossRef]
  31. Y. Frégnac, C. Monier, F. Chavane, P. Baudot, and L. Graham, “Shunting inhibition, a silent step in visual cortical computation,” J. Physiol. (Paris) 97, 441-451 (2003).
  32. M. Riesenhuber and T. Poggio, “Hierarchical models of object recognition in cortex,” Nat. Neurosci. 2, 1019-1025 (1999).
    [CrossRef]
  33. I. Lampl, D. Ferster, T. Poggio, and M. Riesenhuber, “Intracellular measurements of spatial integration and the MAX operator in complex cells of the cat primary visual cortex,” J. Neurophysiol. 92, 2704-2713 (2004).
  34. A. Yu, M. Gisse, and T. Poggio, “Biophysiologically plausible implementations of the maximum operation,” Neural Comput. 14, 2857-2881 (2002).
    [CrossRef]
  35. S. Wolfson and M. Landy, “Discrimination of oriention-defined texture edges,” Vision Res. 35, 2863-2877 (1995).
    [CrossRef]
  36. C. Gilbert, “Horizontal integration and cortical dynamics,” Neuron 9, 1-13 (1992).
    [CrossRef]
  37. R. Malach, Y. Amir, M. Harel, and A. Grinvald, “Relationship between intrinsic connections and functional architecture revealed by optical imaging and in vivo targeted biocytin injections in primate striate cortex,” Proc. Natl. Acad. Sci. U.S.A. 90, 10469-10473 (1993).
    [CrossRef]
  38. K. Rockland and J. Lund, “Widespread periodic intrinsic connections in the tree shrew visual cortex,” Science 215, 1532-1534 (1982).
  39. S. Dakin, C. Williams, and R. Hess, “The interaction of first- and second-order cues to orientation,” Vision Res. 39, 2867-2884 (1999).
    [CrossRef]
  40. H. Nothdurft, “Orientation sensitivity and texture segmentation in patterns with different line orientation,” Vision Res. 25, 551-560 (1985).
    [CrossRef]
  41. H. Nothdurft, “Texture segmentation and pop-out from orientation contrast,” Vision Res. 31, 1073-1078 (1991).
    [CrossRef]
  42. M. Landy and J. Bergen, “Texture segregation and orientation gradient,” Vision Res. 31, 679-691 (1991).
    [CrossRef]
  43. I. Motoyoshi and S. Nishida, “Visual response saturation to orientation constrast in the perception of texture boundary,” J. Opt. Soc. Am. A 18, 2209-2219 (2001).
  44. O. Ben-Shahar and S. Zucker, “Sensitivity to curvatures in orientation-based texture segmentation,” Vision Res. 44, 257-277 (2004).
  45. C. Baker and I. Mareschal, “Processing of second-order stimuli in the visual cortex,” Prog. Brain Res. 134, 171-191 (2001).
  46. A. Mussap and D. Levi, “Orientation-based texture segmentation in strabismic amblyopia,” Vision Res. 39, 411-418 (1999).
  47. N. Prins and F. Kingdom, “Detection and discrimination of texture modulations defined by orientation, spatial frequency, and contrast,” J. Opt. Soc. Am. A 20, 401-410 (2003).
  48. A. Johnson, N. Prins, F. Kingdom, and C. Baker, “Ecologically valid combinations of first- and second-order surface markings facilitate texture discrimination,” Vision Res. 47, 2281-2290 (2007).
  49. M. S. Landy and N. Graham, “Visual perception of texture,” in The Visual Neurosciences, L.M.Chalupa and J.S.Werner, eds. (MIT, 2004), pp. 1106-1118.
  50. H. Wilson and F. Wilkinson, “Detection of global structure in glass patterns: Implications for form vision,” Vision Res. 38, 2933-2947 (1998).
    [CrossRef]
  51. I. Mareschal and C. Baker, “A cortical locus for the processing of contrast-defined contours,” Nat. Neurosci. 1, 150-154 (1998).
    [CrossRef]
  52. F. Kingdom, N. Prins, and A. Hayes, “Mechanism independence for texture-modulations detection is consistent with filter-rectify-filter mechanism,” Visual Neurosci. 20, 65-76 (2003).
  53. W. Richards, J. Keonderink, and D. Hoffman, “Inferring 3D shapes from 2D silhouettes,” J. Opt. Soc. Am. A 4, 1168-1175 (1987).
  54. L. Strother and M. Kubovy, “On the surprising salience of curvature in grouping by proximity,” J. Exp. Psychol. 32, 226-234 (2006).
  55. H. Wilson and W. Richards, “Mechanisms of contour curvature discrimination,” J. Opt. Soc. Am. A 6, 106-115 (1989).
  56. H. Nothdurft, J. Gallant, and D. Van Essen, “Response profiles to texture border patterns in area V1,” Visual Neurosci. 17, 421-436 (2000).
  57. R. Oliveira, L. da Fondtoura Costa, and A. Roque, “A possible mechanism of curvature coding in early vision,” Neurocomputing 65-66, 117-124 (2005).
  58. A. Angelucci and J. Bullier, “Reaching beyond the classical receptive field of V1 neurons: Horizontal or feedback axons?” J. Physiol. (Paris) 97, 141-154 (2003).
  59. G. Kanizsa, Organization in Vision: Essays on Gestalt Perception (Praeger, 1979).
  60. K. Stevens, “The visual interpretation of surface contours,” Artif. Intell. 17, 47-73 (1981).
    [CrossRef]
  61. J. Todd and F. Reichel, “Visual perception of smoothly curved surfaces from double-projected contour patterns,” J. Exp. Psychol. 16, 665-674 (1990).
  62. B. Carbal and L. Leedom, “Imaging vector fields using line integral convolution,” in Proceedings of SIGGRAPH (ACMSIGGRAPH, 1993), pp. 263-270.
  63. A. Sha'ashua and S. Ullman, “Structural saliency: The detection of globally salient structures using a locally connected network,” in Proceedings of the Second IEEE International Conference on Computer Vision (IEEE, 1988), pp. 321-327.
  64. D. Field, A. Hayes, and R. Hess, “Contour integration in the human visual system: Evidence for a local 'association' field,” Vision Res. 33, 173-193 (1993).
    [CrossRef]
  65. K. Schmidt, R. Goebel, S. Löwel, and W. Singer, “The perceptual grouping criterion of colinearity is reflected by anisotropies in the primary visual cortex,” Eur. J. Neurosci. 9, 1083-1089 (1997).
  66. N. Fisher, Statistical Analysis of Circular Data (Cambridge U. Press, 1993).

2007 (1)

A. Johnson, N. Prins, F. Kingdom, and C. Baker, “Ecologically valid combinations of first- and second-order surface markings facilitate texture discrimination,” Vision Res. 47, 2281-2290 (2007).

2006 (3)

L. Strother and M. Kubovy, “On the surprising salience of curvature in grouping by proximity,” J. Exp. Psychol. 32, 226-234 (2006).

O. Ben-Shahar, “Visual saliency and texture segregation without feature gradient,” Proc. Natl. Acad. Sci. U.S.A. 103, 15704-15709 (2006).

O. Ben-Shahar, “Saliency and segregation without feature gradient: New insights for segmentation from orientation-defined textures,” in The Fifth IEEE Computer Society Workshop on Perceptual Organization in Computer Vision (IEEE, 2006), pp. 175-182.

2005 (1)

R. Oliveira, L. da Fondtoura Costa, and A. Roque, “A possible mechanism of curvature coding in early vision,” Neurocomputing 65-66, 117-124 (2005).

2004 (4)

O. Ben-Shahar and S. Zucker, “Sensitivity to curvatures in orientation-based texture segmentation,” Vision Res. 44, 257-277 (2004).

M. S. Landy and N. Graham, “Visual perception of texture,” in The Visual Neurosciences, L.M.Chalupa and J.S.Werner, eds. (MIT, 2004), pp. 1106-1118.

O. Ben-Shahar and S. Zucker, “Geometrical computations explain projection patterns of long range horizontal connections in visual cortex,” Neural Comput. 16, 445-476 (2004).

I. Lampl, D. Ferster, T. Poggio, and M. Riesenhuber, “Intracellular measurements of spatial integration and the MAX operator in complex cells of the cat primary visual cortex,” J. Neurophysiol. 92, 2704-2713 (2004).

2003 (5)

Y. Frégnac, C. Monier, F. Chavane, P. Baudot, and L. Graham, “Shunting inhibition, a silent step in visual cortical computation,” J. Physiol. (Paris) 97, 441-451 (2003).

O. Ben-Shahar and S. Zucker, “The perceptual organization of texture flows: A contextual inference approach,” IEEE Trans. Pattern Anal. Mach. Intell. 25, 401-417 (2003).

F. Kingdom, N. Prins, and A. Hayes, “Mechanism independence for texture-modulations detection is consistent with filter-rectify-filter mechanism,” Visual Neurosci. 20, 65-76 (2003).

N. Prins and F. Kingdom, “Detection and discrimination of texture modulations defined by orientation, spatial frequency, and contrast,” J. Opt. Soc. Am. A 20, 401-410 (2003).

A. Angelucci and J. Bullier, “Reaching beyond the classical receptive field of V1 neurons: Horizontal or feedback axons?” J. Physiol. (Paris) 97, 141-154 (2003).

2002 (1)

A. Yu, M. Gisse, and T. Poggio, “Biophysiologically plausible implementations of the maximum operation,” Neural Comput. 14, 2857-2881 (2002).
[CrossRef]

2001 (2)

C. Baker and I. Mareschal, “Processing of second-order stimuli in the visual cortex,” Prog. Brain Res. 134, 171-191 (2001).

I. Motoyoshi and S. Nishida, “Visual response saturation to orientation constrast in the perception of texture boundary,” J. Opt. Soc. Am. A 18, 2209-2219 (2001).

2000 (2)

H. Nothdurft, J. Gallant, and D. Van Essen, “Response profiles to texture border patterns in area V1,” Visual Neurosci. 17, 421-436 (2000).

J. Serrat, A. López, and D. Lloret, “On ridges and valleys,” in Proceedings of the 15th IEEE International Conference on Pattern Recognition (IEEE, 2000), pp. 59-66.

1999 (3)

S. Dakin, C. Williams, and R. Hess, “The interaction of first- and second-order cues to orientation,” Vision Res. 39, 2867-2884 (1999).
[CrossRef]

M. Riesenhuber and T. Poggio, “Hierarchical models of object recognition in cortex,” Nat. Neurosci. 2, 1019-1025 (1999).
[CrossRef]

A. Mussap and D. Levi, “Orientation-based texture segmentation in strabismic amblyopia,” Vision Res. 39, 411-418 (1999).

1998 (3)

L. Borg-Graham, C. Monier, and Y. Frégnac, “Visual input evokes transient and strong shunting inhibition in visual cortical neurons,” Nature 393, 369-373 (1998).
[CrossRef]

H. Wilson and F. Wilkinson, “Detection of global structure in glass patterns: Implications for form vision,” Vision Res. 38, 2933-2947 (1998).
[CrossRef]

I. Mareschal and C. Baker, “A cortical locus for the processing of contrast-defined contours,” Nat. Neurosci. 1, 150-154 (1998).
[CrossRef]

1997 (3)

K. Schmidt, R. Goebel, S. Löwel, and W. Singer, “The perceptual grouping criterion of colinearity is reflected by anisotropies in the primary visual cortex,” Eur. J. Neurosci. 9, 1083-1089 (1997).

W. Bosking, Y. Zhang, B. Schofield, and D. Fitzpatrick, “Orientation selectivity and the arrangement of horizontal connections in the tree shrew striate cortex,” J. Neurosci. 17, 2112-2127 (1997).

J. Rieger, “Topographical properties of generic images,” Int. J. Comput. Vis. 23, 79-92 (1997).

1996 (2)

D. Eberly, Ridges in Image and Data Analysis (Kluwer Academic, 1996).

A. López and J. Serrat, “Tracing crease curves by solving a system of differential equations,” in Proceedings of the European Conference on Computer Vision, Vol. 1064 of Lecture Notes in Computer Science (Springer-Verlag, 1996), pp. 241-250.

1995 (2)

S. Wolfson and M. Landy, “Discrimination of oriention-defined texture edges,” Vision Res. 35, 2863-2877 (1995).
[CrossRef]

D. Sagi, “The psychophysics of texture segmentation,” in Early Vision and Beyond, T.Papathomas, C.Chubb, A.Gorea, and E.Kowler, eds. (MIT, 1995), pp. 69-78.

1993 (6)

B. Carbal and L. Leedom, “Imaging vector fields using line integral convolution,” in Proceedings of SIGGRAPH (ACMSIGGRAPH, 1993), pp. 263-270.

H. Nothdurft, “The role of features in preattentive vision: Comparison of orientation, motion, and color cues,” Vision Res. 33, 1937-1958 (1993).

N. Fisher, Statistical Analysis of Circular Data (Cambridge U. Press, 1993).

D. Field, A. Hayes, and R. Hess, “Contour integration in the human visual system: Evidence for a local 'association' field,” Vision Res. 33, 173-193 (1993).
[CrossRef]

R. Malach, Y. Amir, M. Harel, and A. Grinvald, “Relationship between intrinsic connections and functional architecture revealed by optical imaging and in vivo targeted biocytin injections in primate striate cortex,” Proc. Natl. Acad. Sci. U.S.A. 90, 10469-10473 (1993).
[CrossRef]

J. Koenderink and A. van Doorn, “Local features of smooth shapes: Ridges and courses,” Proc. SPIE 2031, 2-13 (1993).
[CrossRef]

1992 (2)

A. Rao and R. Jain, “Computerized flow field analysis: Oriented texture fields,” IEEE Trans. Pattern Anal. Mach. Intell. 17, 693-709 (1992).

C. Gilbert, “Horizontal integration and cortical dynamics,” Neuron 9, 1-13 (1992).
[CrossRef]

1991 (3)

J. Bergen and M. Landy, “Computational modeling of visual texture segregation,” in Computational Models of Visual Processing, M.Landy and J.Movshon, eds. (MIT, 1991), pp. 253-271.

H. Nothdurft, “Texture segmentation and pop-out from orientation contrast,” Vision Res. 31, 1073-1078 (1991).
[CrossRef]

M. Landy and J. Bergen, “Texture segregation and orientation gradient,” Vision Res. 31, 679-691 (1991).
[CrossRef]

1990 (3)

J. Todd and F. Reichel, “Visual perception of smoothly curved surfaces from double-projected contour patterns,” J. Exp. Psychol. 16, 665-674 (1990).

J. Malik and P. Perona, “Preattentive texture discrimination with early vision mechanisms,” J. Opt. Soc. Am. A 7, 923-932 (1990).

M. Versavel, G. Orban, and L. Lagae, “Responses of visual cortical neurons to curved stimuli and chevrons,” Vision Res. 30, 235-248 (1990).

1989 (1)

1988 (2)

A. Sha'ashua and S. Ullman, “Structural saliency: The detection of globally salient structures using a locally connected network,” in Proceedings of the Second IEEE International Conference on Computer Vision (IEEE, 1988), pp. 321-327.

M. Concetta Morrone and D. Burr, “Feature detection in human vision: A phase-dependent energy model,” Proc. R. Soc. London, Ser. B 235, 221-245 (1988).

1987 (3)

A. Dobbins, S. Zucker, and M. Cynader, “Endstopped neurons in the visual cortex as a substrate for calculating curvature,” Nature 329, 438-441 (1987).
[CrossRef]

M. Kass and A. Witkin, “Analyzing oriented patterns,” Comput. Vis. Graph. Image Process. 37, 362-385 (1987).
[CrossRef]

W. Richards, J. Keonderink, and D. Hoffman, “Inferring 3D shapes from 2D silhouettes,” J. Opt. Soc. Am. A 4, 1168-1175 (1987).

1985 (1)

H. Nothdurft, “Orientation sensitivity and texture segmentation in patterns with different line orientation,” Vision Res. 25, 551-560 (1985).
[CrossRef]

1983 (2)

C. Koch, T. Poggio, and V. Torre, “Nonlinear interactions in a dendritic tree: Localization, timing, and role in information processing,” Proc. Natl. Acad. Sci. U.S.A. 80, 2799-2802 (1983).

R. Haralik, “Ridges and valleys on digital images,” Comput. Vis. Graph. Image Process. 22, 28-38 (1983).
[CrossRef]

1982 (1)

K. Rockland and J. Lund, “Widespread periodic intrinsic connections in the tree shrew visual cortex,” Science 215, 1532-1534 (1982).

1981 (2)

K. Stevens, “The visual interpretation of surface contours,” Artif. Intell. 17, 47-73 (1981).
[CrossRef]

B. Julesz, “Textons, the elements of texture perception, and their interactions,” Nature 290, 91-97 (1981).
[CrossRef]

1979 (1)

G. Kanizsa, Organization in Vision: Essays on Gestalt Perception (Praeger, 1979).

1978 (1)

V. Torre and T. Poggio, “A synaptic mechanism possibly underlying directional selectivity to motion,” Proc. R. Soc. London, Ser. B 202, 409-416 (1978).

1977 (1)

D. Hubel and T. Wiesel, “Functional architecture of macaque monkey visual cortex,” in Proc. R. Soc. London, Ser. B 198, 1-59 (1977).

1976 (1)

M. do Carmo, Differential Geometry of Curves and Surfaces (Prentice-Hall, 1976).

1970 (1)

R. Olson and F. Attneave, “What variables produce similarity grouping?” Am. J. Psychol. 83, 1-21 (1970).

1966 (2)

J. Beck, “Effect of orientation and the shape similarity on perceptual grouping,” Percept. Psychophys. 1, 300-302 (1966).

B. O'Neill, Elementary Differential Geometry (Academic, 1966).

1965 (1)

H. Barlow and W. Levick, “The mechanism of directionally selective units in rabbit's retina,” J. Physiol. (London) 178, 477-504 (1965).

Amir, Y.

R. Malach, Y. Amir, M. Harel, and A. Grinvald, “Relationship between intrinsic connections and functional architecture revealed by optical imaging and in vivo targeted biocytin injections in primate striate cortex,” Proc. Natl. Acad. Sci. U.S.A. 90, 10469-10473 (1993).
[CrossRef]

Angelucci, A.

A. Angelucci and J. Bullier, “Reaching beyond the classical receptive field of V1 neurons: Horizontal or feedback axons?” J. Physiol. (Paris) 97, 141-154 (2003).

Attneave, F.

R. Olson and F. Attneave, “What variables produce similarity grouping?” Am. J. Psychol. 83, 1-21 (1970).

Baker, C.

A. Johnson, N. Prins, F. Kingdom, and C. Baker, “Ecologically valid combinations of first- and second-order surface markings facilitate texture discrimination,” Vision Res. 47, 2281-2290 (2007).

C. Baker and I. Mareschal, “Processing of second-order stimuli in the visual cortex,” Prog. Brain Res. 134, 171-191 (2001).

I. Mareschal and C. Baker, “A cortical locus for the processing of contrast-defined contours,” Nat. Neurosci. 1, 150-154 (1998).
[CrossRef]

Barlow, H.

H. Barlow and W. Levick, “The mechanism of directionally selective units in rabbit's retina,” J. Physiol. (London) 178, 477-504 (1965).

Baudot, P.

Y. Frégnac, C. Monier, F. Chavane, P. Baudot, and L. Graham, “Shunting inhibition, a silent step in visual cortical computation,” J. Physiol. (Paris) 97, 441-451 (2003).

Beck, J.

J. Beck, “Effect of orientation and the shape similarity on perceptual grouping,” Percept. Psychophys. 1, 300-302 (1966).

Ben-Shahar, O.

O. Ben-Shahar, “Saliency and segregation without feature gradient: New insights for segmentation from orientation-defined textures,” in The Fifth IEEE Computer Society Workshop on Perceptual Organization in Computer Vision (IEEE, 2006), pp. 175-182.

O. Ben-Shahar, “Visual saliency and texture segregation without feature gradient,” Proc. Natl. Acad. Sci. U.S.A. 103, 15704-15709 (2006).

O. Ben-Shahar and S. Zucker, “Geometrical computations explain projection patterns of long range horizontal connections in visual cortex,” Neural Comput. 16, 445-476 (2004).

O. Ben-Shahar and S. Zucker, “Sensitivity to curvatures in orientation-based texture segmentation,” Vision Res. 44, 257-277 (2004).

O. Ben-Shahar and S. Zucker, “The perceptual organization of texture flows: A contextual inference approach,” IEEE Trans. Pattern Anal. Mach. Intell. 25, 401-417 (2003).

Bergen, J.

J. Bergen and M. Landy, “Computational modeling of visual texture segregation,” in Computational Models of Visual Processing, M.Landy and J.Movshon, eds. (MIT, 1991), pp. 253-271.

M. Landy and J. Bergen, “Texture segregation and orientation gradient,” Vision Res. 31, 679-691 (1991).
[CrossRef]

Borg-Graham, L.

L. Borg-Graham, C. Monier, and Y. Frégnac, “Visual input evokes transient and strong shunting inhibition in visual cortical neurons,” Nature 393, 369-373 (1998).
[CrossRef]

Bosking, W.

W. Bosking, Y. Zhang, B. Schofield, and D. Fitzpatrick, “Orientation selectivity and the arrangement of horizontal connections in the tree shrew striate cortex,” J. Neurosci. 17, 2112-2127 (1997).

Bullier, J.

A. Angelucci and J. Bullier, “Reaching beyond the classical receptive field of V1 neurons: Horizontal or feedback axons?” J. Physiol. (Paris) 97, 141-154 (2003).

Burr, D.

M. Concetta Morrone and D. Burr, “Feature detection in human vision: A phase-dependent energy model,” Proc. R. Soc. London, Ser. B 235, 221-245 (1988).

Carbal, B.

B. Carbal and L. Leedom, “Imaging vector fields using line integral convolution,” in Proceedings of SIGGRAPH (ACMSIGGRAPH, 1993), pp. 263-270.

Chavane, F.

Y. Frégnac, C. Monier, F. Chavane, P. Baudot, and L. Graham, “Shunting inhibition, a silent step in visual cortical computation,” J. Physiol. (Paris) 97, 441-451 (2003).

Concetta Morrone, M.

M. Concetta Morrone and D. Burr, “Feature detection in human vision: A phase-dependent energy model,” Proc. R. Soc. London, Ser. B 235, 221-245 (1988).

Cynader, M.

A. Dobbins, S. Zucker, and M. Cynader, “Endstopped neurons in the visual cortex as a substrate for calculating curvature,” Nature 329, 438-441 (1987).
[CrossRef]

da Fondtoura Costa, L.

R. Oliveira, L. da Fondtoura Costa, and A. Roque, “A possible mechanism of curvature coding in early vision,” Neurocomputing 65-66, 117-124 (2005).

Dakin, S.

S. Dakin, C. Williams, and R. Hess, “The interaction of first- and second-order cues to orientation,” Vision Res. 39, 2867-2884 (1999).
[CrossRef]

do Carmo, M.

M. do Carmo, Differential Geometry of Curves and Surfaces (Prentice-Hall, 1976).

Dobbins, A.

A. Dobbins, S. Zucker, and M. Cynader, “Endstopped neurons in the visual cortex as a substrate for calculating curvature,” Nature 329, 438-441 (1987).
[CrossRef]

Eberly, D.

D. Eberly, Ridges in Image and Data Analysis (Kluwer Academic, 1996).

Ferster, D.

I. Lampl, D. Ferster, T. Poggio, and M. Riesenhuber, “Intracellular measurements of spatial integration and the MAX operator in complex cells of the cat primary visual cortex,” J. Neurophysiol. 92, 2704-2713 (2004).

Field, D.

D. Field, A. Hayes, and R. Hess, “Contour integration in the human visual system: Evidence for a local 'association' field,” Vision Res. 33, 173-193 (1993).
[CrossRef]

Fisher, N.

N. Fisher, Statistical Analysis of Circular Data (Cambridge U. Press, 1993).

Fitzpatrick, D.

W. Bosking, Y. Zhang, B. Schofield, and D. Fitzpatrick, “Orientation selectivity and the arrangement of horizontal connections in the tree shrew striate cortex,” J. Neurosci. 17, 2112-2127 (1997).

Frégnac, Y.

Y. Frégnac, C. Monier, F. Chavane, P. Baudot, and L. Graham, “Shunting inhibition, a silent step in visual cortical computation,” J. Physiol. (Paris) 97, 441-451 (2003).

L. Borg-Graham, C. Monier, and Y. Frégnac, “Visual input evokes transient and strong shunting inhibition in visual cortical neurons,” Nature 393, 369-373 (1998).
[CrossRef]

Gallant, J.

H. Nothdurft, J. Gallant, and D. Van Essen, “Response profiles to texture border patterns in area V1,” Visual Neurosci. 17, 421-436 (2000).

Gilbert, C.

C. Gilbert, “Horizontal integration and cortical dynamics,” Neuron 9, 1-13 (1992).
[CrossRef]

Gisse, M.

A. Yu, M. Gisse, and T. Poggio, “Biophysiologically plausible implementations of the maximum operation,” Neural Comput. 14, 2857-2881 (2002).
[CrossRef]

Goebel, R.

K. Schmidt, R. Goebel, S. Löwel, and W. Singer, “The perceptual grouping criterion of colinearity is reflected by anisotropies in the primary visual cortex,” Eur. J. Neurosci. 9, 1083-1089 (1997).

Graham, L.

Y. Frégnac, C. Monier, F. Chavane, P. Baudot, and L. Graham, “Shunting inhibition, a silent step in visual cortical computation,” J. Physiol. (Paris) 97, 441-451 (2003).

Graham, N.

M. S. Landy and N. Graham, “Visual perception of texture,” in The Visual Neurosciences, L.M.Chalupa and J.S.Werner, eds. (MIT, 2004), pp. 1106-1118.

Grinvald, A.

R. Malach, Y. Amir, M. Harel, and A. Grinvald, “Relationship between intrinsic connections and functional architecture revealed by optical imaging and in vivo targeted biocytin injections in primate striate cortex,” Proc. Natl. Acad. Sci. U.S.A. 90, 10469-10473 (1993).
[CrossRef]

Haralik, R.

R. Haralik, “Ridges and valleys on digital images,” Comput. Vis. Graph. Image Process. 22, 28-38 (1983).
[CrossRef]

Harel, M.

R. Malach, Y. Amir, M. Harel, and A. Grinvald, “Relationship between intrinsic connections and functional architecture revealed by optical imaging and in vivo targeted biocytin injections in primate striate cortex,” Proc. Natl. Acad. Sci. U.S.A. 90, 10469-10473 (1993).
[CrossRef]

Hayes, A.

F. Kingdom, N. Prins, and A. Hayes, “Mechanism independence for texture-modulations detection is consistent with filter-rectify-filter mechanism,” Visual Neurosci. 20, 65-76 (2003).

D. Field, A. Hayes, and R. Hess, “Contour integration in the human visual system: Evidence for a local 'association' field,” Vision Res. 33, 173-193 (1993).
[CrossRef]

Hess, R.

S. Dakin, C. Williams, and R. Hess, “The interaction of first- and second-order cues to orientation,” Vision Res. 39, 2867-2884 (1999).
[CrossRef]

D. Field, A. Hayes, and R. Hess, “Contour integration in the human visual system: Evidence for a local 'association' field,” Vision Res. 33, 173-193 (1993).
[CrossRef]

Hoffman, D.

Hubel, D.

D. Hubel and T. Wiesel, “Functional architecture of macaque monkey visual cortex,” in Proc. R. Soc. London, Ser. B 198, 1-59 (1977).

Jain, R.

A. Rao and R. Jain, “Computerized flow field analysis: Oriented texture fields,” IEEE Trans. Pattern Anal. Mach. Intell. 17, 693-709 (1992).

Johnson, A.

A. Johnson, N. Prins, F. Kingdom, and C. Baker, “Ecologically valid combinations of first- and second-order surface markings facilitate texture discrimination,” Vision Res. 47, 2281-2290 (2007).

Julesz, B.

B. Julesz, “Textons, the elements of texture perception, and their interactions,” Nature 290, 91-97 (1981).
[CrossRef]

Kanizsa, G.

G. Kanizsa, Organization in Vision: Essays on Gestalt Perception (Praeger, 1979).

Kass, M.

M. Kass and A. Witkin, “Analyzing oriented patterns,” Comput. Vis. Graph. Image Process. 37, 362-385 (1987).
[CrossRef]

Keonderink, J.

Kingdom, F.

A. Johnson, N. Prins, F. Kingdom, and C. Baker, “Ecologically valid combinations of first- and second-order surface markings facilitate texture discrimination,” Vision Res. 47, 2281-2290 (2007).

F. Kingdom, N. Prins, and A. Hayes, “Mechanism independence for texture-modulations detection is consistent with filter-rectify-filter mechanism,” Visual Neurosci. 20, 65-76 (2003).

N. Prins and F. Kingdom, “Detection and discrimination of texture modulations defined by orientation, spatial frequency, and contrast,” J. Opt. Soc. Am. A 20, 401-410 (2003).

Koch, C.

C. Koch, T. Poggio, and V. Torre, “Nonlinear interactions in a dendritic tree: Localization, timing, and role in information processing,” Proc. Natl. Acad. Sci. U.S.A. 80, 2799-2802 (1983).

Koenderink, J.

J. Koenderink and A. van Doorn, “Local features of smooth shapes: Ridges and courses,” Proc. SPIE 2031, 2-13 (1993).
[CrossRef]

Kubovy, M.

L. Strother and M. Kubovy, “On the surprising salience of curvature in grouping by proximity,” J. Exp. Psychol. 32, 226-234 (2006).

Lagae, L.

M. Versavel, G. Orban, and L. Lagae, “Responses of visual cortical neurons to curved stimuli and chevrons,” Vision Res. 30, 235-248 (1990).

Lampl, I.

I. Lampl, D. Ferster, T. Poggio, and M. Riesenhuber, “Intracellular measurements of spatial integration and the MAX operator in complex cells of the cat primary visual cortex,” J. Neurophysiol. 92, 2704-2713 (2004).

Landy, M.

S. Wolfson and M. Landy, “Discrimination of oriention-defined texture edges,” Vision Res. 35, 2863-2877 (1995).
[CrossRef]

M. Landy and J. Bergen, “Texture segregation and orientation gradient,” Vision Res. 31, 679-691 (1991).
[CrossRef]

J. Bergen and M. Landy, “Computational modeling of visual texture segregation,” in Computational Models of Visual Processing, M.Landy and J.Movshon, eds. (MIT, 1991), pp. 253-271.

Landy, M. S.

M. S. Landy and N. Graham, “Visual perception of texture,” in The Visual Neurosciences, L.M.Chalupa and J.S.Werner, eds. (MIT, 2004), pp. 1106-1118.

Leedom, L.

B. Carbal and L. Leedom, “Imaging vector fields using line integral convolution,” in Proceedings of SIGGRAPH (ACMSIGGRAPH, 1993), pp. 263-270.

Levi, D.

A. Mussap and D. Levi, “Orientation-based texture segmentation in strabismic amblyopia,” Vision Res. 39, 411-418 (1999).

Levick, W.

H. Barlow and W. Levick, “The mechanism of directionally selective units in rabbit's retina,” J. Physiol. (London) 178, 477-504 (1965).

Lloret, D.

J. Serrat, A. López, and D. Lloret, “On ridges and valleys,” in Proceedings of the 15th IEEE International Conference on Pattern Recognition (IEEE, 2000), pp. 59-66.

López, A.

J. Serrat, A. López, and D. Lloret, “On ridges and valleys,” in Proceedings of the 15th IEEE International Conference on Pattern Recognition (IEEE, 2000), pp. 59-66.

A. López and J. Serrat, “Tracing crease curves by solving a system of differential equations,” in Proceedings of the European Conference on Computer Vision, Vol. 1064 of Lecture Notes in Computer Science (Springer-Verlag, 1996), pp. 241-250.

Löwel, S.

K. Schmidt, R. Goebel, S. Löwel, and W. Singer, “The perceptual grouping criterion of colinearity is reflected by anisotropies in the primary visual cortex,” Eur. J. Neurosci. 9, 1083-1089 (1997).

Lund, J.

K. Rockland and J. Lund, “Widespread periodic intrinsic connections in the tree shrew visual cortex,” Science 215, 1532-1534 (1982).

Malach, R.

R. Malach, Y. Amir, M. Harel, and A. Grinvald, “Relationship between intrinsic connections and functional architecture revealed by optical imaging and in vivo targeted biocytin injections in primate striate cortex,” Proc. Natl. Acad. Sci. U.S.A. 90, 10469-10473 (1993).
[CrossRef]

Malik, J.

Mareschal, I.

C. Baker and I. Mareschal, “Processing of second-order stimuli in the visual cortex,” Prog. Brain Res. 134, 171-191 (2001).

I. Mareschal and C. Baker, “A cortical locus for the processing of contrast-defined contours,” Nat. Neurosci. 1, 150-154 (1998).
[CrossRef]

Monier, C.

Y. Frégnac, C. Monier, F. Chavane, P. Baudot, and L. Graham, “Shunting inhibition, a silent step in visual cortical computation,” J. Physiol. (Paris) 97, 441-451 (2003).

L. Borg-Graham, C. Monier, and Y. Frégnac, “Visual input evokes transient and strong shunting inhibition in visual cortical neurons,” Nature 393, 369-373 (1998).
[CrossRef]

Motoyoshi, I.

Mussap, A.

A. Mussap and D. Levi, “Orientation-based texture segmentation in strabismic amblyopia,” Vision Res. 39, 411-418 (1999).

Nishida, S.

Nothdurft, H.

H. Nothdurft, J. Gallant, and D. Van Essen, “Response profiles to texture border patterns in area V1,” Visual Neurosci. 17, 421-436 (2000).

H. Nothdurft, “The role of features in preattentive vision: Comparison of orientation, motion, and color cues,” Vision Res. 33, 1937-1958 (1993).

H. Nothdurft, “Texture segmentation and pop-out from orientation contrast,” Vision Res. 31, 1073-1078 (1991).
[CrossRef]

H. Nothdurft, “Orientation sensitivity and texture segmentation in patterns with different line orientation,” Vision Res. 25, 551-560 (1985).
[CrossRef]

Oliveira, R.

R. Oliveira, L. da Fondtoura Costa, and A. Roque, “A possible mechanism of curvature coding in early vision,” Neurocomputing 65-66, 117-124 (2005).

Olson, R.

R. Olson and F. Attneave, “What variables produce similarity grouping?” Am. J. Psychol. 83, 1-21 (1970).

O'Neill, B.

B. O'Neill, Elementary Differential Geometry (Academic, 1966).

Orban, G.

M. Versavel, G. Orban, and L. Lagae, “Responses of visual cortical neurons to curved stimuli and chevrons,” Vision Res. 30, 235-248 (1990).

Perona, P.

Poggio, T.

I. Lampl, D. Ferster, T. Poggio, and M. Riesenhuber, “Intracellular measurements of spatial integration and the MAX operator in complex cells of the cat primary visual cortex,” J. Neurophysiol. 92, 2704-2713 (2004).

A. Yu, M. Gisse, and T. Poggio, “Biophysiologically plausible implementations of the maximum operation,” Neural Comput. 14, 2857-2881 (2002).
[CrossRef]

M. Riesenhuber and T. Poggio, “Hierarchical models of object recognition in cortex,” Nat. Neurosci. 2, 1019-1025 (1999).
[CrossRef]

C. Koch, T. Poggio, and V. Torre, “Nonlinear interactions in a dendritic tree: Localization, timing, and role in information processing,” Proc. Natl. Acad. Sci. U.S.A. 80, 2799-2802 (1983).

V. Torre and T. Poggio, “A synaptic mechanism possibly underlying directional selectivity to motion,” Proc. R. Soc. London, Ser. B 202, 409-416 (1978).

Prins, N.

A. Johnson, N. Prins, F. Kingdom, and C. Baker, “Ecologically valid combinations of first- and second-order surface markings facilitate texture discrimination,” Vision Res. 47, 2281-2290 (2007).

F. Kingdom, N. Prins, and A. Hayes, “Mechanism independence for texture-modulations detection is consistent with filter-rectify-filter mechanism,” Visual Neurosci. 20, 65-76 (2003).

N. Prins and F. Kingdom, “Detection and discrimination of texture modulations defined by orientation, spatial frequency, and contrast,” J. Opt. Soc. Am. A 20, 401-410 (2003).

Rao, A.

A. Rao and R. Jain, “Computerized flow field analysis: Oriented texture fields,” IEEE Trans. Pattern Anal. Mach. Intell. 17, 693-709 (1992).

Reichel, F.

J. Todd and F. Reichel, “Visual perception of smoothly curved surfaces from double-projected contour patterns,” J. Exp. Psychol. 16, 665-674 (1990).

Richards, W.

Rieger, J.

J. Rieger, “Topographical properties of generic images,” Int. J. Comput. Vis. 23, 79-92 (1997).

Riesenhuber, M.

I. Lampl, D. Ferster, T. Poggio, and M. Riesenhuber, “Intracellular measurements of spatial integration and the MAX operator in complex cells of the cat primary visual cortex,” J. Neurophysiol. 92, 2704-2713 (2004).

M. Riesenhuber and T. Poggio, “Hierarchical models of object recognition in cortex,” Nat. Neurosci. 2, 1019-1025 (1999).
[CrossRef]

Rockland, K.

K. Rockland and J. Lund, “Widespread periodic intrinsic connections in the tree shrew visual cortex,” Science 215, 1532-1534 (1982).

Roque, A.

R. Oliveira, L. da Fondtoura Costa, and A. Roque, “A possible mechanism of curvature coding in early vision,” Neurocomputing 65-66, 117-124 (2005).

Sagi, D.

D. Sagi, “The psychophysics of texture segmentation,” in Early Vision and Beyond, T.Papathomas, C.Chubb, A.Gorea, and E.Kowler, eds. (MIT, 1995), pp. 69-78.

Schmidt, K.

K. Schmidt, R. Goebel, S. Löwel, and W. Singer, “The perceptual grouping criterion of colinearity is reflected by anisotropies in the primary visual cortex,” Eur. J. Neurosci. 9, 1083-1089 (1997).

Schofield, B.

W. Bosking, Y. Zhang, B. Schofield, and D. Fitzpatrick, “Orientation selectivity and the arrangement of horizontal connections in the tree shrew striate cortex,” J. Neurosci. 17, 2112-2127 (1997).

Serrat, J.

J. Serrat, A. López, and D. Lloret, “On ridges and valleys,” in Proceedings of the 15th IEEE International Conference on Pattern Recognition (IEEE, 2000), pp. 59-66.

A. López and J. Serrat, “Tracing crease curves by solving a system of differential equations,” in Proceedings of the European Conference on Computer Vision, Vol. 1064 of Lecture Notes in Computer Science (Springer-Verlag, 1996), pp. 241-250.

Sha'ashua, A.

A. Sha'ashua and S. Ullman, “Structural saliency: The detection of globally salient structures using a locally connected network,” in Proceedings of the Second IEEE International Conference on Computer Vision (IEEE, 1988), pp. 321-327.

Singer, W.

K. Schmidt, R. Goebel, S. Löwel, and W. Singer, “The perceptual grouping criterion of colinearity is reflected by anisotropies in the primary visual cortex,” Eur. J. Neurosci. 9, 1083-1089 (1997).

Stevens, K.

K. Stevens, “The visual interpretation of surface contours,” Artif. Intell. 17, 47-73 (1981).
[CrossRef]

Strother, L.

L. Strother and M. Kubovy, “On the surprising salience of curvature in grouping by proximity,” J. Exp. Psychol. 32, 226-234 (2006).

Todd, J.

J. Todd and F. Reichel, “Visual perception of smoothly curved surfaces from double-projected contour patterns,” J. Exp. Psychol. 16, 665-674 (1990).

Torre, V.

C. Koch, T. Poggio, and V. Torre, “Nonlinear interactions in a dendritic tree: Localization, timing, and role in information processing,” Proc. Natl. Acad. Sci. U.S.A. 80, 2799-2802 (1983).

V. Torre and T. Poggio, “A synaptic mechanism possibly underlying directional selectivity to motion,” Proc. R. Soc. London, Ser. B 202, 409-416 (1978).

Ullman, S.

A. Sha'ashua and S. Ullman, “Structural saliency: The detection of globally salient structures using a locally connected network,” in Proceedings of the Second IEEE International Conference on Computer Vision (IEEE, 1988), pp. 321-327.

van Doorn, A.

J. Koenderink and A. van Doorn, “Local features of smooth shapes: Ridges and courses,” Proc. SPIE 2031, 2-13 (1993).
[CrossRef]

Van Essen, D.

H. Nothdurft, J. Gallant, and D. Van Essen, “Response profiles to texture border patterns in area V1,” Visual Neurosci. 17, 421-436 (2000).

Versavel, M.

M. Versavel, G. Orban, and L. Lagae, “Responses of visual cortical neurons to curved stimuli and chevrons,” Vision Res. 30, 235-248 (1990).

Wiesel, T.

D. Hubel and T. Wiesel, “Functional architecture of macaque monkey visual cortex,” in Proc. R. Soc. London, Ser. B 198, 1-59 (1977).

Wilkinson, F.

H. Wilson and F. Wilkinson, “Detection of global structure in glass patterns: Implications for form vision,” Vision Res. 38, 2933-2947 (1998).
[CrossRef]

Williams, C.

S. Dakin, C. Williams, and R. Hess, “The interaction of first- and second-order cues to orientation,” Vision Res. 39, 2867-2884 (1999).
[CrossRef]

Wilson, H.

H. Wilson and F. Wilkinson, “Detection of global structure in glass patterns: Implications for form vision,” Vision Res. 38, 2933-2947 (1998).
[CrossRef]

H. Wilson and W. Richards, “Mechanisms of contour curvature discrimination,” J. Opt. Soc. Am. A 6, 106-115 (1989).

Witkin, A.

M. Kass and A. Witkin, “Analyzing oriented patterns,” Comput. Vis. Graph. Image Process. 37, 362-385 (1987).
[CrossRef]

Wolfson, S.

S. Wolfson and M. Landy, “Discrimination of oriention-defined texture edges,” Vision Res. 35, 2863-2877 (1995).
[CrossRef]

Yu, A.

A. Yu, M. Gisse, and T. Poggio, “Biophysiologically plausible implementations of the maximum operation,” Neural Comput. 14, 2857-2881 (2002).
[CrossRef]

Zhang, Y.

W. Bosking, Y. Zhang, B. Schofield, and D. Fitzpatrick, “Orientation selectivity and the arrangement of horizontal connections in the tree shrew striate cortex,” J. Neurosci. 17, 2112-2127 (1997).

Zucker, S.

O. Ben-Shahar and S. Zucker, “Geometrical computations explain projection patterns of long range horizontal connections in visual cortex,” Neural Comput. 16, 445-476 (2004).

O. Ben-Shahar and S. Zucker, “Sensitivity to curvatures in orientation-based texture segmentation,” Vision Res. 44, 257-277 (2004).

O. Ben-Shahar and S. Zucker, “The perceptual organization of texture flows: A contextual inference approach,” IEEE Trans. Pattern Anal. Mach. Intell. 25, 401-417 (2003).

A. Dobbins, S. Zucker, and M. Cynader, “Endstopped neurons in the visual cortex as a substrate for calculating curvature,” Nature 329, 438-441 (1987).
[CrossRef]

Am. J. Psychol. (1)

R. Olson and F. Attneave, “What variables produce similarity grouping?” Am. J. Psychol. 83, 1-21 (1970).

Artif. Intell. (1)

K. Stevens, “The visual interpretation of surface contours,” Artif. Intell. 17, 47-73 (1981).
[CrossRef]

Comput. Vis. Graph. Image Process. (2)

M. Kass and A. Witkin, “Analyzing oriented patterns,” Comput. Vis. Graph. Image Process. 37, 362-385 (1987).
[CrossRef]

R. Haralik, “Ridges and valleys on digital images,” Comput. Vis. Graph. Image Process. 22, 28-38 (1983).
[CrossRef]

Eur. J. Neurosci. (1)

K. Schmidt, R. Goebel, S. Löwel, and W. Singer, “The perceptual grouping criterion of colinearity is reflected by anisotropies in the primary visual cortex,” Eur. J. Neurosci. 9, 1083-1089 (1997).

IEEE Trans. Pattern Anal. Mach. Intell. (2)

A. Rao and R. Jain, “Computerized flow field analysis: Oriented texture fields,” IEEE Trans. Pattern Anal. Mach. Intell. 17, 693-709 (1992).

O. Ben-Shahar and S. Zucker, “The perceptual organization of texture flows: A contextual inference approach,” IEEE Trans. Pattern Anal. Mach. Intell. 25, 401-417 (2003).

Int. J. Comput. Vis. (1)

J. Rieger, “Topographical properties of generic images,” Int. J. Comput. Vis. 23, 79-92 (1997).

J. Exp. Psychol. (2)

J. Todd and F. Reichel, “Visual perception of smoothly curved surfaces from double-projected contour patterns,” J. Exp. Psychol. 16, 665-674 (1990).

L. Strother and M. Kubovy, “On the surprising salience of curvature in grouping by proximity,” J. Exp. Psychol. 32, 226-234 (2006).

J. Neurophysiol. (1)

I. Lampl, D. Ferster, T. Poggio, and M. Riesenhuber, “Intracellular measurements of spatial integration and the MAX operator in complex cells of the cat primary visual cortex,” J. Neurophysiol. 92, 2704-2713 (2004).

J. Neurosci. (1)

W. Bosking, Y. Zhang, B. Schofield, and D. Fitzpatrick, “Orientation selectivity and the arrangement of horizontal connections in the tree shrew striate cortex,” J. Neurosci. 17, 2112-2127 (1997).

J. Opt. Soc. Am. A (5)

J. Physiol. (London) (1)

H. Barlow and W. Levick, “The mechanism of directionally selective units in rabbit's retina,” J. Physiol. (London) 178, 477-504 (1965).

J. Physiol. (Paris) (2)

Y. Frégnac, C. Monier, F. Chavane, P. Baudot, and L. Graham, “Shunting inhibition, a silent step in visual cortical computation,” J. Physiol. (Paris) 97, 441-451 (2003).

A. Angelucci and J. Bullier, “Reaching beyond the classical receptive field of V1 neurons: Horizontal or feedback axons?” J. Physiol. (Paris) 97, 141-154 (2003).

Nat. Neurosci. (2)

I. Mareschal and C. Baker, “A cortical locus for the processing of contrast-defined contours,” Nat. Neurosci. 1, 150-154 (1998).
[CrossRef]

M. Riesenhuber and T. Poggio, “Hierarchical models of object recognition in cortex,” Nat. Neurosci. 2, 1019-1025 (1999).
[CrossRef]

Nature (3)

L. Borg-Graham, C. Monier, and Y. Frégnac, “Visual input evokes transient and strong shunting inhibition in visual cortical neurons,” Nature 393, 369-373 (1998).
[CrossRef]

B. Julesz, “Textons, the elements of texture perception, and their interactions,” Nature 290, 91-97 (1981).
[CrossRef]

A. Dobbins, S. Zucker, and M. Cynader, “Endstopped neurons in the visual cortex as a substrate for calculating curvature,” Nature 329, 438-441 (1987).
[CrossRef]

Neural Comput. (2)

O. Ben-Shahar and S. Zucker, “Geometrical computations explain projection patterns of long range horizontal connections in visual cortex,” Neural Comput. 16, 445-476 (2004).

A. Yu, M. Gisse, and T. Poggio, “Biophysiologically plausible implementations of the maximum operation,” Neural Comput. 14, 2857-2881 (2002).
[CrossRef]

Neurocomputing (1)

R. Oliveira, L. da Fondtoura Costa, and A. Roque, “A possible mechanism of curvature coding in early vision,” Neurocomputing 65-66, 117-124 (2005).

Neuron (1)

C. Gilbert, “Horizontal integration and cortical dynamics,” Neuron 9, 1-13 (1992).
[CrossRef]

Percept. Psychophys. (1)

J. Beck, “Effect of orientation and the shape similarity on perceptual grouping,” Percept. Psychophys. 1, 300-302 (1966).

Proc. Natl. Acad. Sci. U.S.A. (3)

R. Malach, Y. Amir, M. Harel, and A. Grinvald, “Relationship between intrinsic connections and functional architecture revealed by optical imaging and in vivo targeted biocytin injections in primate striate cortex,” Proc. Natl. Acad. Sci. U.S.A. 90, 10469-10473 (1993).
[CrossRef]

C. Koch, T. Poggio, and V. Torre, “Nonlinear interactions in a dendritic tree: Localization, timing, and role in information processing,” Proc. Natl. Acad. Sci. U.S.A. 80, 2799-2802 (1983).

O. Ben-Shahar, “Visual saliency and texture segregation without feature gradient,” Proc. Natl. Acad. Sci. U.S.A. 103, 15704-15709 (2006).

Proc. R. Soc. London, Ser. B (3)

M. Concetta Morrone and D. Burr, “Feature detection in human vision: A phase-dependent energy model,” Proc. R. Soc. London, Ser. B 235, 221-245 (1988).

V. Torre and T. Poggio, “A synaptic mechanism possibly underlying directional selectivity to motion,” Proc. R. Soc. London, Ser. B 202, 409-416 (1978).

D. Hubel and T. Wiesel, “Functional architecture of macaque monkey visual cortex,” in Proc. R. Soc. London, Ser. B 198, 1-59 (1977).

Proc. SPIE (1)

J. Koenderink and A. van Doorn, “Local features of smooth shapes: Ridges and courses,” Proc. SPIE 2031, 2-13 (1993).
[CrossRef]

Prog. Brain Res. (1)

C. Baker and I. Mareschal, “Processing of second-order stimuli in the visual cortex,” Prog. Brain Res. 134, 171-191 (2001).

Science (1)

K. Rockland and J. Lund, “Widespread periodic intrinsic connections in the tree shrew visual cortex,” Science 215, 1532-1534 (1982).

Vision Res. (12)

S. Dakin, C. Williams, and R. Hess, “The interaction of first- and second-order cues to orientation,” Vision Res. 39, 2867-2884 (1999).
[CrossRef]

H. Nothdurft, “Orientation sensitivity and texture segmentation in patterns with different line orientation,” Vision Res. 25, 551-560 (1985).
[CrossRef]

H. Nothdurft, “Texture segmentation and pop-out from orientation contrast,” Vision Res. 31, 1073-1078 (1991).
[CrossRef]

M. Landy and J. Bergen, “Texture segregation and orientation gradient,” Vision Res. 31, 679-691 (1991).
[CrossRef]

H. Nothdurft, “The role of features in preattentive vision: Comparison of orientation, motion, and color cues,” Vision Res. 33, 1937-1958 (1993).

S. Wolfson and M. Landy, “Discrimination of oriention-defined texture edges,” Vision Res. 35, 2863-2877 (1995).
[CrossRef]

M. Versavel, G. Orban, and L. Lagae, “Responses of visual cortical neurons to curved stimuli and chevrons,” Vision Res. 30, 235-248 (1990).

A. Mussap and D. Levi, “Orientation-based texture segmentation in strabismic amblyopia,” Vision Res. 39, 411-418 (1999).

O. Ben-Shahar and S. Zucker, “Sensitivity to curvatures in orientation-based texture segmentation,” Vision Res. 44, 257-277 (2004).

D. Field, A. Hayes, and R. Hess, “Contour integration in the human visual system: Evidence for a local 'association' field,” Vision Res. 33, 173-193 (1993).
[CrossRef]

A. Johnson, N. Prins, F. Kingdom, and C. Baker, “Ecologically valid combinations of first- and second-order surface markings facilitate texture discrimination,” Vision Res. 47, 2281-2290 (2007).

H. Wilson and F. Wilkinson, “Detection of global structure in glass patterns: Implications for form vision,” Vision Res. 38, 2933-2947 (1998).
[CrossRef]

Visual Neurosci. (2)

F. Kingdom, N. Prins, and A. Hayes, “Mechanism independence for texture-modulations detection is consistent with filter-rectify-filter mechanism,” Visual Neurosci. 20, 65-76 (2003).

H. Nothdurft, J. Gallant, and D. Van Essen, “Response profiles to texture border patterns in area V1,” Visual Neurosci. 17, 421-436 (2000).

Other (13)

B. Carbal and L. Leedom, “Imaging vector fields using line integral convolution,” in Proceedings of SIGGRAPH (ACMSIGGRAPH, 1993), pp. 263-270.

A. Sha'ashua and S. Ullman, “Structural saliency: The detection of globally salient structures using a locally connected network,” in Proceedings of the Second IEEE International Conference on Computer Vision (IEEE, 1988), pp. 321-327.

M. S. Landy and N. Graham, “Visual perception of texture,” in The Visual Neurosciences, L.M.Chalupa and J.S.Werner, eds. (MIT, 2004), pp. 1106-1118.

N. Fisher, Statistical Analysis of Circular Data (Cambridge U. Press, 1993).

G. Kanizsa, Organization in Vision: Essays on Gestalt Perception (Praeger, 1979).

J. Bergen and M. Landy, “Computational modeling of visual texture segregation,” in Computational Models of Visual Processing, M.Landy and J.Movshon, eds. (MIT, 1991), pp. 253-271.

J. Serrat, A. López, and D. Lloret, “On ridges and valleys,” in Proceedings of the 15th IEEE International Conference on Pattern Recognition (IEEE, 2000), pp. 59-66.

D. Eberly, Ridges in Image and Data Analysis (Kluwer Academic, 1996).

A. López and J. Serrat, “Tracing crease curves by solving a system of differential equations,” in Proceedings of the European Conference on Computer Vision, Vol. 1064 of Lecture Notes in Computer Science (Springer-Verlag, 1996), pp. 241-250.

O. Ben-Shahar, “Saliency and segregation without feature gradient: New insights for segmentation from orientation-defined textures,” in The Fifth IEEE Computer Society Workshop on Perceptual Organization in Computer Vision (IEEE, 2006), pp. 175-182.

B. O'Neill, Elementary Differential Geometry (Academic, 1966).

M. do Carmo, Differential Geometry of Curves and Surfaces (Prentice-Hall, 1976).

D. Sagi, “The psychophysics of texture segmentation,” in Early Vision and Beyond, T.Papathomas, C.Chubb, A.Gorea, and E.Kowler, eds. (MIT, 1995), pp. 69-78.

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