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A Neurogeometric Stereo Model for Individuation of 3D Perceptual Units

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Geometric Science of Information (GSI 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14071))

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Abstract

We present a neurogeometric model for stereo vision and individuation of 3D perceptual units. We first model the space of position and orientation of 3D curves in the visual scene as a sub-Riemannian structure. Horizontal curves in this setting express good continuation principles in 3D. Starting from the equation of neural activity we apply harmonic analysis techniques in the sub-Riemannian structure to solve the correspondence problem and find 3D percepts.

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References

  1. Alibhai, S., Zucker, S.W.: Contour-based correspondence for stereo. In: Vernon, D. (ed.) ECCV 2000. LNCS, vol. 1842, pp. 314–330. Springer, Heidelberg (2000). https://doi.org/10.1007/3-540-45054-8_21

    Chapter  Google Scholar 

  2. Anzai, A., Ohzawa, I., Freeman, R.: Neural mechanisms for processing binocular information i. simple cells. J. Neurophysiol. 82(2), 891–908 (1999)

    Article  Google Scholar 

  3. Barbieri, D., Citti, G., Cocci, G., Sarti, A.: A cortical-inspired geometry for contour perception and motion integration. J. Math. Imaging Vis. 49(3), 511–529 (2014)

    Article  MATH  Google Scholar 

  4. Bolelli, M.V., Citti, G., Sarti, A., Zucker, S.W.: Good continuation in 3D: the neurogeometry of stereo vision. arXiv preprint arXiv:2301.04542 (2023)

  5. Boscain, U., Duits, R., Rossi, F., Sachkov, Y.: Curve cuspless reconstruction via sub-riemannian geometry. ESAIM: Control, Optimisat, Calculus Variations 20, 748–770 (2014)

    Google Scholar 

  6. Bressloff, P.C., Cowan, J.D.: The functional geometry of local and horizontal connections in a model of V1. J. Physiol. Paris 97(2), 221–236 (2003)

    Article  Google Scholar 

  7. Bridge, H., Cumming, B.: Responses of macaque V1 neurons to binocular orientation differences. J. Neurosci. 21(18), 7293–7302 (2001)

    Article  Google Scholar 

  8. Citti, G., Sarti, A.: A cortical based model of perceptual completion in the roto-translation space. J. Math. Imaging Vis. 24(3), 307–326 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  9. Deas, L.M., Wilcox, L.M.: Perceptual grouping via binocular disparity: The impact of stereoscopic good continuation. J. Vis. 15(11), 11 (2015)

    Article  Google Scholar 

  10. Duits, R., Bekkers, E.J., Mashtakov, A.: Fourier transform on the homogeneous space of 3D positions and orientations for exact solutions to linear pdes. Entropy 21(1), 38 (2019)

    Article  Google Scholar 

  11. Duits, R., Dela Haije, T., Creusen, E., Ghosh, A.: Morphological and linear scale spaces for fiber enhancement in dw-mri. J. Mathematical Imaging Vis. 46, 326–368 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  12. Duits, R., Franken, E.: Left-invariant diffusions on the space of positions and orientations and their application to crossing-preserving smoothing of HARDI images. IJCV (2011)

    Google Scholar 

  13. Faugeras, O.: Three-dimensional computer vision: a geometric viewpoint. MIT press (1993)

    Google Scholar 

  14. Field, D.J., Hayes, A., Hess, R.F.: Contour integration by the human visual system: Evidence for a local “association field." Vision Res. 33(2), 173–193 (1993)

    Google Scholar 

  15. Hess, R.F., Hayes, A., Kingdom, F.A.A.: Integrating contours within and through depth. Vision. Res. 37(6), 691–696 (1997)

    Article  Google Scholar 

  16. Hoffman, W.C.: The visual cortex is a contact bundle. Appl. Math. Comput. 32(2), 137–167 (1989)

    MathSciNet  MATH  Google Scholar 

  17. Kellman, P.J., Garrigan, P., Shipley, T.F., Yin, C., Machado, L.: 3-d interpolation in object perception: Evidence from an objective performance paradigm. J. Exp. Psychol. Hum. Percept. Perform. 31(3), 558–583 (2005)

    Article  Google Scholar 

  18. Khuu, S.K., Honson, V., Kim, J.: The perception of three-dimensional contours and the effect of luminance polarity and color change on their detection. J. Vis. (2016)

    Google Scholar 

  19. Koenderink, J.J., van Doorn, A.J.: Representation of local geometry in the visual system. Biol. Cybern. 55(6), 367–375 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  20. Li, G., Zucker, S.W.: Contextual inference in contour-based stereo correspondence. IJCV 69(1), 59–75 (2006)

    Article  Google Scholar 

  21. Mumford, D.: Elastica and computer vision. In: Algebraic geometry and its applications, pp. 491–506. Springer (1994). https://doi.org/10.1007/978-1-4612-2628-4_31

  22. Perona, P., Freeman, W.: A factorization approach to grouping. In: Burkhardt, H., Neumann, B. (eds.) ECCV 1998. LNCS, vol. 1406, pp. 655–670. Springer, Heidelberg (1998). https://doi.org/10.1007/BFb0055696

    Chapter  Google Scholar 

  23. Petitot, J., Tondut, Y.: Vers une neurogéométrie. Fibrations corticales, structures de contact et contours subjectifs modaux. Math. Scien. Humain. 145, 5–101 (1999)

    Google Scholar 

  24. Portegies, J.M., Duits, R.: New exact and numerical solutions of the (convection-)diffusion kernels on \(\rm SE(3)\). Differential Geom. Appl. 53, 182–219 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  25. Sanguinetti, G., Citti, G., Sarti, A.: A model of natural image edge co-occurrence in the rototranslation group. J. Vis. (2010)

    Google Scholar 

  26. Sarti, A., Citti, G.: The constitution of visual perceptual units in the functional architecture of V1. J. Comput. Neurosci. (2015)

    Google Scholar 

  27. Scholl, B., Tepohl, C., Ryan, M.A., Thomas, C.I., Kamasawa, N., Fitzpatrick, D.: A binocular synaptic network supports interocular response alignment in visual cortical neurons. Neuron 110(9), 1573–1584 (2022)

    Article  Google Scholar 

  28. Wagemans, J., et al.: A century of gestalt psychology in visual perception: I perceptual grouping and figure-ground organization. Psych. Bull. 138(6), 1172 (2012)

    Article  Google Scholar 

  29. Zucker, S.W.: Differential geometry from the Frenet point of view: boundary detection, stereo, texture and color. In: Handbook of Mathematical Models in Computer Vision, pp. 357–373. Springer (2006). https://doi.org/10.1007/0-387-28831-7_22

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Acknowledgement

MVB, GC, AS were supported by GHAIA project, H2020 MSCA RISE n. 777622 and by NGEU-MUR-NRRP, project MNESYS (PE0000006) (DN. 1553 11.10.2022). SWZ was supported by NIH Grant EY031059 and NSF CRCNS Grant 1822598.

Author information

Authors and Affiliations

  1. Department of mathematics, University of Bologna, Bologna, Italy

    Maria Virginia Bolelli, Giovanna Citti & Alessandro Sarti

  2. Laboratoire CAMS, CNRS-EHESS, Paris, France

    Maria Virginia Bolelli, Giovanna Citti & Alessandro Sarti

  3. Departments of Computer Science and Biomedical Engineering, Yale University, New Haven, CT, USA

    Steven Zucker

  4. Laboratoire des Signaux et Systèmes, Université Paris-Saclay, CentraleSupèlec, Gif-sur-Yvette, France

    Maria Virginia Bolelli

Authors
  1. Maria Virginia Bolelli
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  2. Giovanna Citti
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  3. Alessandro Sarti
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  4. Steven Zucker
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Corresponding author

Correspondence to Maria Virginia Bolelli .

Editor information

Editors and Affiliations

  1. Sony Computer Science Laboratories Inc., Tokyo, Japan

    Frank Nielsen

  2. THALES Land and Air Systems, Meudon, France

    Frédéric Barbaresco

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Bolelli, M.V., Citti, G., Sarti, A., Zucker, S. (2023). A Neurogeometric Stereo Model for Individuation of 3D Perceptual Units. In: Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information. GSI 2023. Lecture Notes in Computer Science, vol 14071. Springer, Cham. https://doi.org/10.1007/978-3-031-38271-0_6

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  • DOI: https://doi.org/10.1007/978-3-031-38271-0_6

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-38270-3

  • Online ISBN: 978-3-031-38271-0

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