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

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.