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Computational Vision: Solving 3D Scenes from 2D Images

This article explores the challenges in computational vision, particularly object invariance and visual segmentation, and presents a potential solution based on a model of primary visual cortex. The theory explains pre-attentive segmentation and provides testable predictions, bridging physiological and psychological data in the field. It also calls for exploring the mathematics of dynamical systems in vision research.

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Computational Vision: Solving 3D Scenes from 2D Images

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  1. Computational Vision --- a window to our brain Li Zhaoping, University College London At CUSPEA conference on “Physics in twenty first century” June 2002, Beijing

  2. From eye to primary visual cortex

  3. Vision: solving for 3D scene from 2D image A difficult problems, many possible solutions, one (or a few) perceptions Two of the most difficult problems (1) Object invariance, (2) visual segmentation, still unsolved.

  4. The segmentation problem Dilemma: segmentation requires recognition, recognition requires segmentation.

  5. Human Eye and Retina

  6. Human Cone Lattice

  7. Retina sampling (From B. Olshausen)

  8. Receptive fields of a retinal ganglion cell (on center cell )

  9. Two cells in primary visual cortex

  10. Neurons in Human Cortex

  11. Visual areas in the brain

  12. Visual Area wiring diagram

  13. Some numbers: Retinal size: 5 cm x 5 cm; 0.4 mm thick One degree of visual angle = 0.3 mm on the retina Number of cones in each retina: 5x106 Number of rods in each retina: 108 Peak cone density: 1.6 x 105 cones/mm Total number of cortical neurons: 1010; 4 x 103 synapses/neuron; Number of macaque (monkey) visual areas: 30 Size of each area V1: 3 cm by 8 cm Half of area V1 represents the central 10 deg (2% of the visual field)

  14. Binocular Rivalry

  15. Color Phenomena

  16. Hering Illusion

  17. Hermann Grid Illusion

  18. A variaton

  19. Subjective Contours (Kaniza triangle)

  20. Color Afterimage

  21. Neon Disk

  22. Adelson Illusion

  23. Color Illusion

  24. Reversible ripple

  25. Focus on segmentation problem in vision --- region segmentation A region can be characterized by its average luminance, regularity, smoothness, and many other measures.

  26. Biological experimental background In early visual stages (retina or primary visual cortex), output from a neuron can be well or poorly approximated as images passed through a linear filter (kernel). These filters are called receptive fields.

  27. These filters (kernels K) are all very small, compared to the sizes of visual objects (e.g., apple)

  28. Local interactions between cortical neurons As manifested in experiments showing contextual influences of neural responses. From local to global !!!

  29. Model output Highlighting important image locations that signal the breaking of translation invariance Input to model My Theory: V1 produces a saliency map from images V1model Details of this theory is published in Trends in Cognitive Sciences, Vol. 6. No. 1, Jan, 2002, p. 9-16.

  30. Examples of pre-attentive segmentation explained by the model

  31. The theory: • explains many experimental data; • linking physiological and psychological data (two research communities do not talk to each other as much without such theories); • provides experimental testable predictions; motivating new experiments, and promoting theoretical approach in the traditionally experimental field. • calls for new explorations of interesting mathematics of dynamical systems not yet encounted in traditional physics.

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