1932
0
  1. Home
  2. A-Z Publications
  3. Annual Review of Vision Science
  4. Volume 4, 2018
  5. Article

Annual Review of Vision Science

Volume 4, 2018

Geometry of Pictorial Relief

Abstract

Pictorial relief is a quality of visual awareness that happens when one looks into (as opposed to at) a picture. It has no physical counterpart of a geometrical nature. It takes account of cues, mentally identified in the tonal gradients of the physical picture—pigments distributed over a planar substrate. Among generally recognized qualities of relief are color, pattern, texture, shape, and depth. This review focuses on geometrical properties, the spatial variation of depth. To be aware of an extended quality like relief implies a “depth” dimension, a nonphysical spatial entity that may smoothly vary in a surface-like manner. The conceptual understanding is in terms of formal geometry. The review centers on pertinent facts and formal models. The facts are necessarily so-called brute facts (i.e., they cannot be explained scientifically). This review is a foray into the speculative and experimental phenomenology of the visual field.

Keyword(s): depth, pictorial space, relief, visual field
Loading

Article metrics loading...

/content/journals/10.1146/annurev-vision-091517-034250
2018-09-15
2024-04-16
Loading full text...

Full text loading...

/deliver/fulltext/vision/4/1/annurev-vision-091517-034250.html?itemId=/content/journals/10.1146/annurev-vision-091517-034250&mimeType=html&fmt=ahah

Literature Cited

  1. Adelson EH, Pentland AP 1996. The perception of shading and reflectance. Perception as Bayesian Inference D Knill, W Richards 409–23 New York: Cambridge Univ. Press
     [Google Scholar]
  2. Alberti LB 1972 (1435). Della Pittura [On Painting] London: Penguin Class.
     [Google Scholar]
  3. Ames A Jr. 1925. Depth in pictorial art. Art Bull 8:5–24
     [Google Scholar]
  4. Barrow I 1916 (1670). The Geometrical Lectures of Isaac Barrow transl. JM Child Chicago: Open Court Publ. Co.
  5. Belhumeur PN, Kriegman DJ, Yuille AL 1999. The bas-relief ambiguity. Int. J. Comput. Vis. 35:33–44
     [Google Scholar]
  6. Biederman I 1987. Recognition-by-components: a theory of human image understanding. Psychol. Rev. 94:115–47
     [Google Scholar]
  7. Biederman I 1988. Surface versus edge-base determinants of visual recognition. Cogn. Psychol. 20:38–64
     [Google Scholar]
  8. Bridgman PW 1927. The Logic of Modern Physics New York: MacMillan Co.
  9. Bülthoff HH, Mallot HA 1988. Integration of depth modules: stereo and shading. J. Opt. Soc. Am. A 5:1749–58
     [Google Scholar]
  10. Chevrier J, Delorme A 1983. Depth perception in Pandora's box and size illusion: evolution with age. Perception 12:177–85
     [Google Scholar]
  11. Claparède E 1904. Stereoscopie monoculaire paradoxale. Ann. Ocul. 132:465
     [Google Scholar]
  12. Clowes MB 1971. On seeing things. Artif. Intel. 2:79–112
     [Google Scholar]
  13. Cornelis EVK, van Doorn AJ, de Ridder H 2003. Mirror-reflecting a picture of an object: What happens to the shape percept. ? Percept. Psychophys. 65:1110–25
     [Google Scholar]
  14. Cornelis EVK, van Doorn AJ, Wagemans J 2009. The effects of mirror reflections and planar rotations of pictures on the shape percept of the depicted object. Perception 38:1439–66
     [Google Scholar]
  15. Cornilleau-Pérès V, Wexler M, Droulez J, Marin E, Miège C, Bourdoncle B 2002. Visual perception of planar orientation: dominance of static depth cues over motion cues. Vis. Res. 42:1403–12
     [Google Scholar]
  16. Crane W 1900. Line and Form London: G. Bell & Sons
  17. da Vinci L 1540. Libro di Pittura Vatican City: Bibl. Apostol. Vaticana
  18. De Haan E, Erens RGF, Noest AJ 1995. Shape from shaded random surfaces. Vis. Res. 35:2985–3001
     [Google Scholar]
  19. DeCarlo D, Finkelstein A, Rusinkiewicz S, Santella A 2003. Suggestive contours for conveying shape. ACM Trans. Graph. 22:848–55
     [Google Scholar]
  20. Denis M 1890. Définition du neo-traditionnisme. Art Crit 65:540–43
     [Google Scholar]
  21. Eddington AS 1928. The Nature of the Physical World Cambridge, UK: Univ. Press
  22. Emerson E 1863. On the perception of relief. Br. J. Photogr. 10:10–11
     [Google Scholar]
  23. Enright JT 1987. Perspective vergence: oculomotor responses to line drawings. Vis. Res. 27:1513–26
     [Google Scholar]
  24. Erens RGF, Kappers AML, Koenderink JJ 1993. Perception of local shape from shading. Percept. Psychophys. 54:145–56
     [Google Scholar]
  25. Gauss CF 1827. Disquisitiones generales circa superficies curvas. Comment. Soc. R. Sci. Gottingensis Recentioris 6:3–50
     [Google Scholar]
  26. Gibson JJ 1950. The Perception of the Visual World Boston, MA: Houghton-Mifflin
  27. Gombrich EH 1961. Art and Illusion: A Study in the Psychology of Pictorial Representation Princeton, NJ: Princeton Univ. Press
  28. Gregory RL 1968. Perceptual illusions and brain models. Proc. R. Soc. B 171:279–96
     [Google Scholar]
  29. Hilbert D, Cohn-Vossen S 1952. Geometry and the Imagination transl. P Nemenyi New York: Chelsea
  30. Hildebrand Av 1893. Das Problem der Form in der Bildenden Kunst Strassburg, Ger.: Heitz & Mündel
  31. Higashiyama A, Shimono K 2012. Apparent depth of pictures reflected by a mirror: the plastic effect. Atten. Percept. Psychophys. 74:71522–32
     [Google Scholar]
  32. Hoffman DD, Richards WA 1984. Parts of recognition. Cognition 18:65–96
     [Google Scholar]
  33. Hoffman DD, Singh M, Prakash C 2015. The interface theory of visual perception. Psychon. Bull. Rev. 22:1480–506
     [Google Scholar]
  34. Johnston A, Passmore PJ 1994. Independent encoding of surface orientation and surface curvature. Vis. Res. 34:3005–12
     [Google Scholar]
  35. Kennedy JM, Silver J 1974. The surrogate functions of lines in visual perception: evidence from antipodal rock and cave artwork sources. Perception 3:313–22
     [Google Scholar]
  36. Koenderink JJ 2011. Gestalts and pictorial worlds. Gestalt Theory 33:289–324
     [Google Scholar]
  37. Koenderink JJ 2013. .…to see or not to see. Perception 42:379–84
     [Google Scholar]
  38. Koenderink JJ 2014.a Q…. Perception 43:1015–17
     [Google Scholar]
  39. Koenderink JJ 2014.b The all seeing eye. Perception 43:1–6
     [Google Scholar]
  40. Koenderink JJ 2015.a Ontology of the mirror world. Gestalt Theory 37:2119–40
     [Google Scholar]
  41. Koenderink JJ 2015.b PPP. Perception 44:473–76
     [Google Scholar]
  42. Koenderink JJ 2015.c Seeing with the ears. Perception 44:610–12
     [Google Scholar]
  43. Koenderink JJ 2015.d Visual art and visual perception. Perception 44:1–4
     [Google Scholar]
  44. Koenderink JJ, van Doorn AJ 1992. Surface shape and curvature scales. Image Vis. Comput. 10:557–65
     [Google Scholar]
  45. Koenderink JJ, van Doorn AJ 1995. Relief: pictorial and otherwise. Image Vis. Comput. 13:321–34
     [Google Scholar]
  46. Koenderink JJ, van Doorn AJ 2012. Gauge fields in pictorial space. SIAM J. Imaging Sci. 5:1213–33
     [Google Scholar]
  47. Koenderink JJ, van Doorn AJ, Christou C, Lappin JS 1996.a Perturbation study of shading in pictures. Perception 25:1009–26
     [Google Scholar]
  48. Koenderink JJ, van Doorn AJ, Christou C, Lappin JS 1996.b Shape constancy in pictorial relief. Perception 25:155–64
     [Google Scholar]
  49. Koenderink JJ, van Doorn AJ, Kappers AML 1992. Surface perception in pictures. Percept. Psychophys. 52:487–96
     [Google Scholar]
  50. Koenderink JJ, van Doorn AJ, Kappers AML 1994. On so-called paradoxical monocular stereoscopy. Perception 23:583–94
     [Google Scholar]
  51. Koenderink JJ, van Doorn AJ, Kappers AML 1995. Depth relief. Perception 24:115–26
     [Google Scholar]
  52. Koenderink JJ, van Doorn AJ, Kappers AML 1996.c Pictorial surface attitude and local depth comparisons. Percept. Psychophys. 58:163–73
     [Google Scholar]
  53. Koenderink JJ, van Doorn AJ, Kappers AML 2006. Pictorial relief. Seeing Spatial Form MRM Jenkin, LR Harris 11–36 New York: Oxford Univ. Press
     [Google Scholar]
  54. Koenderink JJ, van Doorn AJ, Kappers AML, Todd JT 1997. The visual contour in depth. Percept. Psychophys. 59:828–38
     [Google Scholar]
  55. Koenderink JJ, van Doorn AJ, Kappers AML, Todd JT 2001. Ambiguity and the ‘mental eye’ in pictorial relief. Perception 30:431–48
     [Google Scholar]
  56. Koenderink JJ, van Doorn AJ, Kappers AML, Todd JT 2004. Pointing out of the picture. Perception 33:513–30
     [Google Scholar]
  57. Koenderink JJ, van Doorn AJ, Pinna B, Pepperell R 2016.a Facing the spectator. i-Perception 7:1–29
     [Google Scholar]
  58. Koenderink JJ, van Doorn AJ, Pont S 2012.a Shading, a view from the inside. Seeing Perceiv 25:303–38
     [Google Scholar]
  59. Koenderink JJ, van Doorn AJ, Wagemans J 2011. Depth. i-Perception 2:541–64
     [Google Scholar]
  60. Koenderink JJ, van Doorn AJ, Wagemans J 2012.b Picasso in the mind's eye of the beholder: three-dimensional filling-in of ambiguous line drawings. Cognition 125:394–412
     [Google Scholar]
  61. Koenderink JJ, van Doorn AJ, Wagemans J 2013. SFS? Not likely. ! i-Perception 4:299–302
     [Google Scholar]
  62. Koenderink JJ, van Doorn AJ, Wagemans J 2014. Local shape of pictorial relief. i-Perception 5:188–204
     [Google Scholar]
  63. Koenderink JJ, van Doorn AJ, Wagemans J 2015.a Local solid shape. i-Perception 6:1–15
     [Google Scholar]
  64. Koenderink JJ, van Doorn AJ, Wagemans J 2015.b Part and whole in pictorial relief. i-Perception 6:1–21
     [Google Scholar]
  65. Koenderink JJ, van Doorn AJ, Wagemans J, Pinna B 2016.b Shading and the landmarks of relief. Art Percept 4:295–326
     [Google Scholar]
  66. Langer SK 1953. Feeling and Form: A Theory of Art New York: Charles Scribner's Sons
  67. Lipschitz R 1864. De explicatione per series trigonometricas instituenda functionum unius variabilis arbitrariarum, et praecipue earum, quae per variabilis spatium finitum valorum maximorum et minimorum numerum habent infinitum, disquisitio. J. Reine Angew. Math. 63:296–308
     [Google Scholar]
  68. Maxwell JC 1870. L. On hills and dales. Lond. Edinb. Dublin Philos. Mag. J. Sci. 40:421–25
     [Google Scholar]
  69. Meinong A 1899. Über Gegenstände höherer Ordnung und deren Verhältnis zur inneren Wahrnehmung. Z. Psychol. Physiol. Sinnesorgane 21:182–272
     [Google Scholar]
  70. Phillips F, Todd JT, Koenderink JJ, Kappers AML 2003. Perceptual representation of visible surfaces. Percept. Psychophys. 65:747–62
     [Google Scholar]
  71. Pizlo Z 2001. Perception viewed as an inverse problem. Vis. Res. 41:3145–61
     [Google Scholar]
  72. Pollack P 1955. A note on monocular depth perception. Am. J. Psychol. 68:315–18
     [Google Scholar]
  73. Reichel FD, Todd JT, Yilmaz E 1995. Visual discrimination of local surface depth and orientation. Percept. Psychophys. 57:1233–40
     [Google Scholar]
  74. Richards W, Bobick A 1988. Playing Twenty Questions with nature. Computational Processes in Human Vision: An Interdisciplinary Perspective ZW Pylyshyn 3–26 Norwood, NJ: Ablex Publ. Corp.
     [Google Scholar]
  75. Rogers B, Graham M 1982. Similarities between motion parallax and stereopsis in human depth perception. Vis. Res. 22:261–70
     [Google Scholar]
  76. Rogers LR 1969. Sculpture: The Appreciation of the Arts/2 London: Oxford Univ. Press
  77. Rothe R 1915. Zum problem des Talwegs. Sitzungsberichte Berliner Math. Gesellschaft 14:51–69
     [Google Scholar]
  78. Sachs H 1990. Isotrope Geometrie des Raumes Braunschweig, Ger.: Vieweg
  79. Saunders JA, Backus BT 2006. Perception of surface slant from oriented textures. J. Vis. 6:93
     [Google Scholar]
  80. Schlosberg H 1941. Stereoscopic depth from single pictures. Am. J. Psychol. 54:601–5
     [Google Scholar]
  81. Schrödinger E 1958. Mind and Matter (Tarner Lectures, 1956) Cambridge, UK: Univ. Press
     [Google Scholar]
  82. Schwartz AH 1971. Stereoscopic perception with single pictures. Opt. Spectra 9:25–27
     [Google Scholar]
  83. Spelke ES, Lee SA 2012. Core systems of geometry in animal minds. Philos. Trans. R. Soc. B 367:2784–93
     [Google Scholar]
  84. Spivak M 1975. A Comprehensive Introduction to Differential Geometry Boston, MA: Publish or Perish
  85. Stevens KA 1983. Surface tilt (the direction of slant): a neglected psychophysical variable. Percept. Psychophys. 33:241–50
     [Google Scholar]
  86. Stevens KA 1990. Constructing the perception of surfaces from multiple cues. Mind Lang 5:253–66
     [Google Scholar]
  87. Stevens KA, Brookes A 1987. Probing depth in monocular images. Biol. Cybernet. 56:355–66
     [Google Scholar]
  88. Stevens SS 1957. On the psychophysical law. Psychol. Rev. 64:153–81
     [Google Scholar]
  89. Strubecker K 1942. Differentialgeometrie des isotropen Raumes III: Flächentheorie. Math. Z. 48:369–427
     [Google Scholar]
  90. Teller DY 1984. Linking propositions. Vis. Res. 24:1233–46
     [Google Scholar]
  91. Todd JT, Koenderink JJ, van Doorn AJ, Kappers AML 1996. Effect of changing viewing conditions on the perceived structure of smoothly curved surfaces. J. Exp. Psychol. Hum. Percept. Perform. 22:695–706
     [Google Scholar]
  92. Todd JT, Reichel FD 1989. Ordinal structure in the visual perception and cognition of smoothly curved surfaces. Psychol. Rev. 96:643–57
     [Google Scholar]
  93. Todd JT, Thaler L, Dijkstra TMH 2005. The effects of field of view on the perception of 3D slant from texture. Vis. Res. 45:1501–17
     [Google Scholar]
  94. Todd JT, Thaler L, Dijkstra TMH, Koenderink JJ, Kappers AML 2007. The effects of viewing angle, camera angle, and sign of surface curvature on the perception of three-dimensional shape from texture. J. Vis. 7:129
     [Google Scholar]
  95. Topper DR 1983. Art in the realist ontology of J.J. Gibson. Synthese 54:71–83
     [Google Scholar]
  96. Tyler CW 1975. Spatial organization of binocular disparity sensitivity. Vis. Res. 15:583–90
     [Google Scholar]
  97. Vallortigara G, Zanforlin G, Pasti G 1990. Geometric modules in animal's spatial representation: a test with chicks (Gallus gallus domesticus). J. Comp. Psychol. 104:248–54
     [Google Scholar]
  98. van Doorn AJ, Koenderink JJ, Wagemans J 2011. Light fields and shape from shading. J. Vis. 11:321
     [Google Scholar]
  99. Vico G 1725. Scienza Nuova Naples, Italy: Muziana
  100. Vishwanath D 2014. Towards a new theory of stereopsis. Psychol. Rev. 121:151–78
     [Google Scholar]
  101. Vishwanath D, Girshick AR, Banks MS 2005. Why pictures look right when viewed from the wrong place. Nat. Neurosci. 8:1401–10
     [Google Scholar]
  102. von Foerster H 1992. Ethics and second order cybernetics. Cybern. Hum. Knowing 1:9–20
     [Google Scholar]
  103. von Rohr M 1904. Linsensystem zur einaugigen Betrachten einer in der Brennebene befindlichen Photographie Kaiserliches Patentamt Patentschrift Nr.151312 Klasse 42h
  104. von Uexküll J 1909. Umwelt und Innenwelt der Tiere Berlin: Verlag von Julius Springer
  105. Wagemans J, van Doorn AJ, Koenderink JJ 2010. The shading cue in context. i-Perception 1:159–78
     [Google Scholar]
  106. Wijntjes MWA 2017. Ways of viewing pictorial plasticity. i-Perception 8:1–10
     [Google Scholar]
  107. Yuille A, Kersten D 2006. Vision as Bayesian inference: analysis by synthesis. ? TRENDS Cogn. Sci. 10:301–8
     [Google Scholar]
  108. Zeiss C 1907. Instrument zum beidäugigen Betrachten von Gemälden u.ggl. Kaiserliches Patentamt Patentschrift Nr.194480 Klasse 42h Gruppe 34
/content/journals/10.1146/annurev-vision-091517-034250
Loading
Geometry of Pictorial Relief
Annual Review of Vision Science 4, 451 (2018); https://doi.org/10.1146/annurev-vision-091517-034250
/content/journals/10.1146/annurev-vision-091517-034250
/content/journals/10.1146/annurev-vision-091517-034250
Loading

Data & Media loading...

  • Article Type: Review Article

Most Cited Most Cited RSS feed

This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error