New results in stereopsis and Listing's law.
GeoGebra’s dynamic geometry
Asymmetric retinal correspondence
Horizontal, vertical, and torsional disparities
Iso-disparity conic sections
Listing’s Law
Stereopsis
The asymmetric eye
Vertical horopters
Journal
Scientific reports
ISSN: 2045-2322
Titre abrégé: Sci Rep
Pays: England
ID NLM: 101563288
Informations de publication
Date de publication:
28 Sep 2024
28 Sep 2024
Historique:
received:
09
04
2024
accepted:
05
09
2024
medline:
29
9
2024
pubmed:
29
9
2024
entrez:
28
9
2024
Statut:
epublish
Résumé
Human eyes' optical components are misaligned. This study presents comprehensive geometric constructions in the binocular system, with the eye model incorporating the fovea that is displaced from the posterior pole and the lens that is tilted away from the eye's optical axis. It extends their previously considered horizontal misalignment with the vertical components. When the eyes' binocular posture changes, 3D spatial coordinates of the retinal disparity (iso-disparity curves), the subjective vertical horopter, and the eye's torsional orientation transformations are visualized in GeoGebra's simulations. The consequences and functional roles of vertical misalignment of the eye's optical components are explained in the following findings: (1) The classic Helmholtz theory, which states that the subjective vertical retinal meridian inclination to the retinal horizon explains the backward tilt of the perceived vertical horopter, is less relevant when the eye's optical components are misaligned. Instead, the lens vertical tilt provides the retinal vertical criterion that explains the experimentally measured vertical horopter inclination. (2) Listing's law, which originally restricts single-eye torsional positions and has imprecise binocular extensions, is formulated for binocular fixations using Euler's rotation theorem. It, however, replaces Listing's plane, which is defined for eyes looking at infinity, with the eyes muscles' natural tonus resting position corresponding to the abathic distance fixation of empirical straight frontal horopter. This new meaning of Listing's plane provides neurophysiological significance that has remained elusive.
Identifiants
pubmed: 39341867
doi: 10.1038/s41598-024-72239-9
pii: 10.1038/s41598-024-72239-9
doi:
Types de publication
Journal Article
Langues
eng
Sous-ensembles de citation
IM
Pagination
22474Informations de copyright
© 2024. The Author(s).
Références
Chang, Y., Wu, H. M. & Lin, Y. F. The axial misalignment between ocular lens and cornea observed by MRI (I) at fixed accommodative state. Vis. Res. 33, 71–84. https://doi.org/10.1016/j.visres.2006.09.018 (2007).
doi: 10.1016/j.visres.2006.09.018
de Castro, A., Rosale, P. & Marcos, S. Tilt and decentration of intraocular lenses in vivo from Purkinje and Scheimpflug imaging: validation study. J. Cataract Refract. Surg. 33, 418–429 (2007).
doi: 10.1016/j.jcrs.2006.10.054
pubmed: 17321392
Schaeffel, F. & Kaymak, H. New techniques to measure lens tilt, decentration and longitudinal chromatic aberration in Phakic and Pseudophakic eyes. Nova Acta Leopoldina 111, 127–136. https://doi.org/10.1167/iovs.07-1022 (2010).
doi: 10.1167/iovs.07-1022
Aguirre, G. K. A model of the entrance pupil of the human eye. Sci. Rep. 9(1), 9360. https://doi.org/10.1038/s41598-019-45827-3 (2019).
doi: 10.1038/s41598-019-45827-3
pubmed: 31249360
pmcid: 6597540
Wang, L. et al. Evaluation of crystalline lens and intraocular lens tilt using a swept-source optical coherence tomography biometer. J. Cataract Refract Surg. 45, 35–40. https://doi.org/10.1167/iovs.07-1022 (2019).
doi: 10.1167/iovs.07-1022
pubmed: 30309775
Tabernero, J. et al. Mechanism of compensation of aberrations in the human eye. Prog. Brain Res. 24, 3274–3283 (2007).
Charman, W. N. & Atchison, D. A. Decentred optical axes and aberrations along principal visual field meridians. Vis. Res. 49, 1869–1876. https://doi.org/10.1016/j.visres.2009.04.024.36 (2009).
doi: 10.1016/j.visres.2009.04.024.36
pubmed: 19426752
Artal, P. Optics of the eyes and its impact in vision. Adv. Opt. Photon. 6, 340–367. https://doi.org/10.1364/AOP.6.000340 (2014).
doi: 10.1364/AOP.6.000340
Liu, T. & Thibos, L. N. Variation of axial and oblique astigmatism with accommodation across the visual field. J. Vis. 17(3), 1–23. https://doi.org/10.1167/17.3.24 (2017).
doi: 10.1167/17.3.24
Wheatstone, C. On some remarkable and hitherto unobserved phenomena of binocular vision. Philos. Trans. R. Soc. 128, 371–394 (1838).
doi: 10.1098/rstl.1838.0019
Julesz, B. Foundation of Cyclopean Perception (University of Chicago Press, 1971).
Turski, J. Binocular system with asymmetric eyes. J. Opt. Soc. Am. A 35, 1180–1191. https://doi.org/10.1364/JOSAA.35.001180 (2018).
doi: 10.1364/JOSAA.35.001180
Turski, J. A geometric theory integrating human binocular vision with eye movement. Front. Neurosci. 14(555965), 1–17. https://doi.org/10.3389/fnins.2020.555965 (2020).
doi: 10.3389/fnins.2020.555965
Turski, J. Riemannian geometries of visual space: Variable curvature and horizon. Math. Methods Appl. Sci. 46, 9298–9324. https://doi.org/10.1002/mma.9054 (2023).
doi: 10.1002/mma.9054
Holladay, J. T. Quality of Vision: Essential Optics for the Cataract and Refractive Surgeon (SLACK Inc., 2007).
Ebenholtz, S. M. Oculomotor Systems and Perception (Cambridge University Press, 2001).
Shipley, T. & Rawlings, S. The nonius horopter-I history and theory. Vis. Res. 10, 1225–1262. https://doi.org/10.1016/0042-6989(70)90039-8 (1970).
doi: 10.1016/0042-6989(70)90039-8
pubmed: 4927973
Nelson, J. I. The plasticity of correspondence: After-effects, illusions and horopter shifts in depth perception. J. Theor. Biol. 66, 203–266 (1977).
doi: 10.1016/0022-5193(77)90170-9
pubmed: 886865
Howard, I. P. & Rogers, B. J. Perceiving in Depth Vol. 2 (Oxford University Press, 2012).
Barry, S. R. Beyond the critical period. acquiring stereopsis in adulthood. In Plasticity in Sensory Systems 175–195. (Cambridge University Press, 2013). https://doi.org/10.1017/CBO9781139136907.010.
Pollard, S. B., Mayhew, J. E. W. & Frisby, J. P. A stereo correspondence algorithm using a disparity gradient limit. Perception 14, 449–470 (1985).
doi: 10.1068/p140449
pubmed: 3834387
Blake, A., & Zisserman, A. Visual Reconstruction (MIT Press, 1987).
Blakemore, C. A new kind of stereoscopic vision. Vis. Res. 10, 1181–1200 (1970).
doi: 10.1016/0042-6989(70)90036-2
pubmed: 5508965
Koenderink, J. J. & van Doom, A. J. Geometry of binocular vision and a model for stereopsis. Biol. Cybern. 21, 29–35 (1976).
doi: 10.1007/BF00326670
pubmed: 1244864
Tyler, C. W. & Sutter, E. E. Depth from spatial frequency difference: An old kind of stereopsis?. Vis. Res. 19, 859–865 (1979).
doi: 10.1016/0042-6989(79)90019-1
pubmed: 516457
Rogers, B. J. & Cagenello, R. Orientation and curvature disparities in the perception of three-dimensional surfaces. Invest. Ophthalmol. Vis. Sci. 30, 262 (1989).
Gårding, J., & Lindeberg, T. Direct estimation of local surface shape in a fixating binocular vision system. In Computer Vision - ECCV ’94, Lecture Notes in Computer Science Vol 800 175–195 (Springer, 1994). https://doi.org/10.1007/3-540-57956-740 .
Lappin, J. S. What is binocular disparity?. Front. Psychol. 5, 1–6. https://doi.org/10.3389/fpsyg.2014.00870 (2014).
doi: 10.3389/fpsyg.2014.00870
Helmholtz, H. L. F. Physiological Optics (Optical Society of America, 1867/1925).
Guyton, D. L. Ocular torsion: Sensorimotor principles. Am. Orthop. J. 37, 13–21. https://doi.org/10.1080/0065955X.1987.11981728 (1987).
doi: 10.1080/0065955X.1987.11981728
Amigo, G. A vertical horopter. Opt. Acta 21, 277–292 (1974).
doi: 10.1080/713818889
Tyler, C.W. The horopter and binocular fusion. In Binocular Vision, Vision and Visual Dysfunction Vol. 9 19–37 (Macmillan, 1991).
Harrold, A. L. & Grove, P. M. Binocular correspondence and the range of fusible horizontal disparities in the central visual field. J. Vis. 15, 1–17. https://doi.org/10.1167/15.8.12 (2015).
doi: 10.1167/15.8.12
Daddaoua, N., Dicke, P. W. & Their, P. Eye position information is used to compensate the consequences of ocular torsion on v1 receptive fields. Nat. Commun.[SPACE] https://doi.org/10.1038/ncomms4047 (2014).
doi: 10.1038/ncomms4047
pubmed: 24407156
Tweed, D., Cadera, W. & Vilis, T. Computing three-dimensional eye position quaternions and eye velocity from search coil signals. Vis. Res. 30, 97–110 (1990).
doi: 10.1016/0042-6989(90)90130-D
pubmed: 2321369
Tweed, D. & Vilis, T. Geometric relation of eye position and velocity vectors during saccades. Vis. Res. 30, 111–127 (1990).
doi: 10.1016/0042-6989(90)90131-4
pubmed: 2321357
Haslwanter, T. Mathematics of three-dimensional eye rotations. Vis. Res. 35, 1727–1739 (1995).
doi: 10.1016/0042-6989(94)00257-M
pubmed: 7660581
Novelia, A. & O’Reilly, M. O. On the dynamics of the eye: Geodesics on a configuration manifold, motions of the gaze direction and Helmholtz’s theorem. Nonlinear Dyn. 80, 1303–1327. https://doi.org/10.1007/s11071-015-1945-0 (2015).
doi: 10.1007/s11071-015-1945-0
Mok, D. et al. Rotation of listing’s plane during vergence. Vis. Res. 32, 2055–2064 (1992).
doi: 10.1016/0042-6989(92)90067-S
pubmed: 1304083
Minken, A. H. & van Gisbergen, J. A. M. A three-dimensional analysis of vergence movements at various levels of elevation. Exp. Brain Res. 101, 331–345. https://doi.org/10.1007/BF00228754 (1994).
doi: 10.1007/BF00228754
pubmed: 7843320
Van Rijn, L. J. & Van der Berg, A. V. Binocular eye orientation during fixations: Listing’s law extended to include eye vergence. Vis. Res. 33, 691–708 (1993).
doi: 10.1016/0042-6989(93)90189-4
pubmed: 8351841
Tweed, D. Visual-motor optimization in binocular control. Vis. Res. 37, 1939–1951 (1997).
doi: 10.1016/S0042-6989(97)00002-3
pubmed: 9274779
Hess, B. J. M. & Thomassen, J. S. Kinematics of visually-guided eye movements. PLoS ONE 9(e95234), 1–16. https://doi.org/10.1371/journal.pone.0095234 (2014).
doi: 10.1371/journal.pone.0095234
Siderov, J. R. S. & Bedell, H. E. Stereopsis, cyclovergence and the backward tilt of the vertical horopter. Vis. Res. 39, 1347–1357 (1999).
doi: 10.1016/S0042-6989(98)00252-1
pubmed: 10343847
Nakayama, K. Geometric and physiological aspects of depth perception. Proc. SPIE 120, 2–9. https://doi.org/10.1117/12.955728 (1977).
doi: 10.1117/12.955728
Cogan, A. I. The relationship between the apparent vertical and the vertical horopter. Vis. Res. 19, 655–665. https://doi.org/10.1016/0042-7756989(79)90241-4 (1979).
doi: 10.1016/0042-7756989(79)90241-4
pubmed: 547475
Cooper, E. A., Burge, J. & Banks, M. S. The vertical horopter is not adaptable, but it may be adaptive. J. Vis. 11(3), 778. https://doi.org/10.1167/11.3.20 (2011).
doi: 10.1167/11.3.20
Ogle, K. N. An analytical treatment of the longitudinal horopter; its measurement and application to related phenomena, especially to the relative size and shape of the ocular images. J. Opt. Soc. Am. 22, 665–728. https://doi.org/10.1364/JOSA.22.000665 (1932).
doi: 10.1364/JOSA.22.000665
Turski, J. On binocular vision: The geometric horopter and cyclopean eye. Vis. Res. 119, 73–81. https://doi.org/10.1016/j.visres.2015.11.001 (2016).
doi: 10.1016/j.visres.2015.11.001
pubmed: 26548811
Luneburg, R. K. Mathematical Analysis of Binocular Vision (Princeton University Press, 1947).
Blank, A. A. The geometry of vision. Br. J. Physiol. Opt. 14, 1–30 (1957).
Pinã, E. Rotations with Rodrigues’ vector. Eur. J. Phys. 32, 171–1178 (2011).
doi: 10.1088/0143-0807/32/5/005
Gray, J. J. Olinde Rodrigues’ paper of 1840 on transformation groups. Arch. Hist. Exact Sci. 21, 375–384 (1980).
doi: 10.1007/BF00595376
Martinez-Trujillo, J. C. Noncommutativity of eye rotations and the half-angle rule. Neuron 47, 171–173. https://doi.org/10.1016/j.neuron.2005.07.004 (2005).
doi: 10.1016/j.neuron.2005.07.004
pubmed: 16039558
Cannata, G. & Maggiali, M. Models for the design of bioinspired robot eyes. IEEE Trans. Robot. 24, 27–44. https://doi.org/10.1109/TRO.2007.906270 (2008).
doi: 10.1109/TRO.2007.906270