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A Human Eye Retinal Cone Synthesizer Michael F. Deering

A Human Eye Retinal Cone Synthesizer Michael F. Deering. Implementation Sketch For The SIGGRAPH 2005 Paper:. A Photon Accurate Model of the Human Eye Michael F. Deering. Use Graphics Theory To Simulate Vision. Goal.

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A Human Eye Retinal Cone Synthesizer Michael F. Deering

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  1. A Human Eye Retinal Cone Synthesizer Michael F. Deering

  2. Implementation Sketch For The SIGGRAPH 2005 Paper: A Photon Accurate Model of the Human Eye Michael F. Deering

  3. Use Graphics Theory To Simulate Vision

  4. Goal • Build a computer program to properly simulate the complex sampling pattern of the human eye retinal cone mosaic. • Use this in a photon by photon simulation of display devices onto the human eye.

  5. Why Eye Sampling Pattern Matters

  6. Overview • Background about human retinal cones • Growth algorithm overview • Cone force equation • Re-forming cone cell borders • Touch-up • Results

  7. Eye Model

  8. What Does A Cone Look Like?

  9. What Do Cone Retinal Arrays Look Like? • For years all we had were photo micrographs of sliced and diced dead eyeballs. • Now we can obtain images of living retinas.

  10. Roorda And Williams Image

  11. Retinal Cone Distribution • Most data is from Curcio et. al. ’90 • Large variation in maximum density • More recent data: Williams, Millar, Roorda • Cone density varies primarily biased on eccentricity, but also by retinal meridian

  12. Terminology: Cell Borders Animals don’t have cell walls; they have cell borders (or cell membranes) Plants have cell walls

  13. High Resolution Foveas Are A Relatively Recent Addition -2 months birth +6 years

  14. Synthetic Retina Generation • Use rectangular lattice. • Use triangular lattice. • Use perturbed triangular lattice. • Take real retinal images as representative patches then flip and repeat. I want all 5 million cones: A new computer model to generate parameterized retinas (not synthesizing rods yet).

  15. Possible Retina Generation Algorithms • Add one new cone at a time, placing each into its final position. • Too simplistic to work • Simulate the interactions of all 5 million cones simultaneously. • Too computationally complex to work

  16. Retina Generation Algorithm • Add new cones in concentric rings, varying target cell density by Curcio data • Merge new cones into existing mosaic • Grow on curved spherical surface • Keep only changing cones in memory

  17. Two Phase Cone Growth Algorithm • Phase I: update the center location of all still active cone cells using the cone force equation. • Phase II: re-form all cone cell borders from updated cone centers using pattern matching algorithm. Run paired phases for 21-41 cycles per ring of new cones added.

  18. Definitions • Normalized distance between cones p and n: • Two cones p and n are neighbors if:

  19. The Cone Force Equation

  20. The Cone Force Picture p p p’ To center of fovea

  21. Definition Of Spline[ ] Function 1 Spline[x] 0 1 x

  22. Re-form Cone Cell Borders From Updated Cone Centers

  23. Why Vornoi Cell Construction Is Inappropriate No way to enforce cell size or shape constraints

  24. Why Vornoi Cell Construction Is Inappropriate Always looking at three vertices at a time. Correct answer here is just a single new border vertex for all 4 cones.

  25. My Cell Border Construction Algorithm • Sequentially visit each cell. • Using spatially indexed data structure, find all the neighbors of the cell and sort them into clockwise order. • Apply cell border construction pattern rules to successive sequences of neighbors. • Result is new set of border edges for that cell.

  26. Sort Neighbors Into Clockwise Order n1 n0 n2 p nj nmax

  27. Try Pattern Rules From Most Complex To Least Complex • Only try a simpler pattern rule after all the more complex ones have failed. • (The following slides will present the rules in the opposite order.)

  28. Three Cone Centers Share Edge Vertex N[ni, ni+1] ni+1 ni ej p

  29. Three Cone Centers Don’t Share Edge Vertex ni ni+1 ej+1 ej p

  30. Four Cone Centers Share Edge Vertex N[ni, ni+1] ni+1 N[ni+1, ni+2] N[ni, ni+2] ni ni+2 ej D[p, ni] < D[p, ni+1] or D[p, ni+2] < D[p, ni+1] p

  31. Complex 5 Vertex Case ni+1 q ni ej ni+2 p

  32. New Completed Cell Border e1 e2 p e0 e3 e5 e4

  33. Touch-ups • Check re-formed cell borders for voids as large or larger than the local cone size; if they persist seed them with new cones. • Check re-formed cell borders for cones too much smaller than their birth target size; if they persist delete them.

  34. Extreme Cone Density Change Test Case • Change the density control knob by a factor of 8 in area within a small distance.

  35. Growth Sequence Movie

  36. Growth Movie Zoom

  37. Retinal Zoom Out Movie

  38. 3D Fly By Movie

  39. Larger View Of My Synthetic Retina

  40. Roorda Blood Vessel

  41. Roorda vs. Synthetic

  42. 30x30 Pixel Face Input

  43. Retinal Image Results

  44. 30x30 Pixel Movie

  45. Result Movie

  46. Acknowledgements • Michael Wahrman for the RenderMan™ rendering of the cone data. • Julian Gómez and the anonymous SIGGRAPH reviewers for their comments on the paper.

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