Abstract
Any computation of metric surface structure from horizontal disparities depends on the viewing geometry, and analysing this dependence allows us to narrow down the choice of viable schemes. For example, all depth-based or slant-based schemes (i.e. nearly all existing models) are found to be unrealistically sensitive to natural errors in vergence. Curvature-based schemes avoid these problems and require only moderate, more robust view-dependent corrections to yield local object shape, without any depth coding. This fits the fact that humans are strikingly insensitive to global depth but accurate in discriminating surface curvature. The latter also excludes coding only affine structure. In view of new adaptation results, our goal becomes to directly extract retinotopic fields of metric surface curvatures (i.e. avoiding intermediate disparity curvature).
To find a robust neural realisation, we combine new exact analysis with basic neural and psychophysical constraints. Systematic, step-by-step ‘design’ leads to neural operators which employ a novel family of ‘dynamic’ receptive fields (RFs), tuned to specific (bi-)local disparity structure. The required RF family is dictated by the non-Euclidean geometry that we identify as inherent in cyclopean vision. The dynamic RF-subfield patterns are controlled via gain modulation by binocular vergence and version, and parameterised by a cell-specific tuning to slant. Our full characterisation of the neural operators invites a range of new neurophysiological tests. Regarding shape perception, the model inverts widely accepted interpretations: It predicts the various types of errors that have often been mistaken for evidence against metric shape extraction.
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References
Anstis SM, Howard IP, Rogers B (1978) A Craik-Cornsweet illusion for visual depth. Vision Res 18:213–217
Aslin RN, Battaglia PW, Jacobs RA (2004) Depth-dependent contrast gain-control. Vision Res 44:685–693
Ben-Shahar O, Huggins PS, Izo T, Zucker SW (2003) Cortical connections and early visual function: intra- and inter-columnar processing. J Physiol 97:191–208
Berends EM, Liu B, Schor CM (2005) Stereo-slant adaptation is high-level, and does not involve disparity-coding. J Vision 5:71–80
van den Berg AV, van Ee R, Noest AJ (2005) Mixed visual reference frames: perceiving nonretino-centric visual quantities in a retino-centric frame. In: Rogowitz BE, Pappas TN, Daly SJ (eds) Human vision and electronic imaging X; Proceedings of SPIE vol 5666 pp 449–461
Bingham GP, Crowell JA, Todd JT (2004) Distortions of distance and shape are not produced by a single continuous transformation of reach space. Percept Psychophys 66:152–169
Burke WL (1985) Applied differential geometry. Cambridge University Press, Cambridge
Cumming BG (2002) An unexpected specialization for horizontal disparity in primate primary visual cortex. Nature 418:633–636
DeAngelis GC (2000) Seeing in three dimensions: the neurophysiology of stereopsis. Trends Cogn Sci 4:80–90
Domini F, Adams W, Banks MS (2001) 3D after-effects are due to shape and not disparity adaptation. Vision Res 41:2733–2739
Duke PA, Wilcox LM (2003) Adaptation to vertical disparity induced depth: implications for disparity processing. Vision Res 43:135–147
Erkelens CJ, Collewijn H (1985) Motion perception during dichoptic viewing of moving random-dot stereograms. Vision Res 25:583–588
Erkelens CJ, van Ee R (1998) A computational model of depth perception based on headcentric disparity. Vision Res 38:2999–3018
Gårding J, Porrill J, Mayhew JEW, Frisby JP (1995) Stereopsis, vertical disparity and relief transformations. Vision Res 35:703–722
Gillam B, Flagg T, Finlay D (1984) Evidence for disparity change as the primary stimulus for stereoscopic processing. Percept Psychophys 36:559–564
Glennerster A, McKee SP, Birch MD (2002) Evidence for surface-based processing of binocular disparity. Curr Biol 12:825–828
Gonzalez F, Perez R (1998) Modulation of cell responses to horizontal disparities by ocular vergence in the visual cortex of the awake macaca mulatta monkey. Neurosci Lett 245: 101–104
Grossberg S, Swaminathan G (2004) A laminar cortical model for 3D perception of slanted and curved surfaces and of 2D images: development, attention, and bistability. Vision Res 44:1147–1187
von Helmholtz H (1867) Handbuch der physiologischen Optik. Vos, Hamburg
Hinkle DA, Connor CE (2002) Three-dimensional orientation tuning in macaque area V4. Nat Neurosci 5:665–670
Howard IP, Rogers BJ (2002) Seeing in depth, vol 2: Depth perception. Porteous, Toronto
Janssen P, Vogels R, Orban G (1999) Macaque inferior temporal neurons are selective for disparity-defined three-dimensional shapes. Proc Natl Acad Sci USA 96:8217–8222
Janssen P, Vogels R, Orban GA (2000) Three-dimensional shape coding in inferior temporal cortex. Neuron 27:385–397
Janssen P, Vogels R, Orban GA (2001) Macaque inferior temporal neurons are selective for three-dimensional boundaries and surfaces. J Neurosci 21:9419–9429
Johnston EB (1991) Systematic distortions of shape from stereopsis. Vision Res 31:1351–1360
Knapen T, van Ee R (2006) Slant perception, and its voluntary control, do not govern the slant aftereffect: multiple slant signals adapt independently. Vision Res, DOI:10.106/j.visres2006.03.027.
Koenderink JJ (1990) Solid shape. MIT Press, Cambridge
Koenderink JJ (1992) Fundamentals of bicentric perspective. Lecture notes in computer science, vol 653. Springer, Berlin Heidelberg New York, pp 233–251
Koenderink JJ (2003) Monocentric optical space. Lecture notes in computer science, vol 2756. Springer, Berlin Heidelberg New York, pp 689–696
Koenderink JJ, van Doorn AJ (1976) Geometry of binocular vision and a model for stereopsis. Biol Cybern 21:29–35
Koenderink JJ, van Doorn AJ (1987) Representation of local geometry in the visual system. Biol Cybern 35:367–375
Koenderink JJ, van Doorn AJ (1991) Affine structure from motion. J Opt Soc Am A 8:377–385
Koenderink JJ, van Doorn AJ (2002) Image processing done right. Lecture notes in computer science, vol 2350. Springer, Berlin Heidelberg New York, pp 158–172
Koenderink JJ, Richards W (1988) Two-dimensional curvature operators. J Opt Soc Am A 5:1136–1141
Köhler W, Emery DA (1947) Figural after-effects in the third dimension of visual space. Am J Psychol 60:159–201
Lee B (1999) Aftereffects and the representation of stereoscopic surfaces. Perception 28:1155–1169
Lunn PD, Morgan MJ (1997) Discrimination of the spatial derivatives of horizontal binocular disparity. J Opt Soc Am A 14:360–371
Mayhew JEW (1982) The interpretation of stereo-disparity information: the computation of surface orientation and depth. Perception 11:387–403
Mayhew JEW, Longuet-Higgins HC (1982) A computational model of binocular depth perception. Nature 297:376–378
Nguyenkim JD, DeAngelis GC (2003) Disparity-based coding of three-dimensional surface orientation by macaque middle temporal neurons. J Neurosci 23:7117–7128
Nienborg H, Bridge H, Parker AJ, Cumming BG (2004) Receptive field size in V1 neurons limits acuity for perceiving disparity modulation. J Neurosci 24:2065–2076
Nishida S, Motoyoshi I, Andersen RA, Shimojo S (2003) Gaze modulation of visual aftereffects. Vision Res 43:639–649
Noest AJ (1994) Neural processing of overlapping shapes. In: Toet et al (eds) Shape in picture. NATO ASI series, vol 126, pp 383–392
Noest AJ, van Ee R, van den Berg, AV (2003) Disentangling retinal and head-centric disparity-coding involved in perception of metric depth from stereo. Perception 32(suppl):13–14
Ohzawa I (1998) Mechanisms of stereoscopic vision: the disparity energy model. Curr Opin Neurobiol 8:509–515
Petrov Y, Glennerster A (2004) The role of a local reference in stereoscopic detection of depth relief. Vision Res 44:367–376
Pianta MJ, Gillam BJ (2003) Monocular gap stereopsis: manipulation of the outer edge disparity and the shape of the gap. Vision Res 43:1937–1950
Pottmann H, Opitz K (1994) Curvature analysis and visualization for functions defined on Euclidean spaces or surfaces. Comput Aided Geom Des 11:655–674
Rogers BJ, Cagenello R (1989) Disparity curvature and the perception of three-dimensional surfaces. Nature 339:135–137
Rosenbluth D, Allman JM (2002) The effect of gaze angle and fixation distance on the responses of neurons in V1, V2, and V4. Neuron 33:143–149
Ryan C, Gillam B (1993) A proximity-contingent stereoscopic depth aftereffect: evidence for adaptation to disparity gradients. Perception 22:403–418
Sachs H (1987) Ebene isotrope Geometrie. Vieweg, Braunschweig
Steinman RM, Cushman WB, Martins AJ (1982) The precision of gaze. Hum Neurobiol 1:97–109
Strubecker K (1942) Differentialgeometrie des isotropen Raumes III Flächentheorie. Math Zeitschrift 48:369–427
Todd JT, Norman JF (2003) The visual perception of 3D shape from multiple cues: are observers capable of perceiving metric structure? Percept Psychophys 65:31–47
Trotter Y, Celebrini S, Stricanne B, Thorpe S, Imbert M (1992) Modulation of neural stereoscopic processing in primate area V1 by the viewing distance. Science 257:1279–1281
Trotter Y, Celebrini S, Stricanne B, Thorpe S, Imbert M (1996) Neural processing of stereopsis as a function of viewing distance in primate visual cortical area V1. J Neurophysiol 76:2872–2885
Trotter Y, Celebrini S (1999) Gaze direction controls response gain in primary visual-cortex neurons. Nature 398:239–242
van Ee R, Erkelens CJ (1996) Stability of binocular depth perception with moving head and eyes. Vision Res 36:3827–3842
van Ee R (2001) Perceptual learning without feedback and the stability of stereoscopic slant estimation. Perception 30:95–114
Wilson HR, Richards WA (1989) Mechanisms of contour curvature discrimination. J Opt Soc Am A 6:106–115
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Noest, A.J., van Ee, R. & van den Berg, A.V. Direct extraction of curvature-based metric shape from stereo by view-modulated receptive fields. Biol Cybern 95, 455–486 (2006). https://doi.org/10.1007/s00422-006-0101-9
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DOI: https://doi.org/10.1007/s00422-006-0101-9