Ret Talk

							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

• 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.
Why Eye Sampling Pattern
Matters
Overview

• Background about human retinal cones
• Growth algorithm overview
• Cone force equation
• Re-forming cone cell borders
• Touch-up
• Results
Eye Model
What Does A Cone Look Like?
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.
Roorda And Williams Image
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
Terminology: Cell Borders




 Plants have cell walls    Animals don’t have
                          cell walls; they have
                               cell borders
                          (or cell membranes)
High Resolution Foveas Are
A Relatively Recent Addition




   -2 months       birth       +6 years
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).
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
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
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.
Definitions

• Normalized distance between cones p and n:
                        p-n
            D[p,n] 
                     (p.r+n.r)

• Two cones p and n are neighbors if:
           N[p,n] = D[p,n]  1.5
The Cone Force Equation

    p =     p

           + K1  pn

           + K2  r
                    N[p,n]
                                              n-p
           - K3     n
                             spline[D[p,n]] 
                                              n-p
The Cone Force Picture



              p           p
                              p’




     To center of fovea
Definition Of Spline[ ]
Function
         1




 Spline[x]




         0                1
                    x
Re-form Cone Cell Borders
From Updated Cone Centers
Why Vornoi Cell Construction Is
Inappropriate
No way to enforce
cell size or shape
constraints
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.
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.
Sort Neighbors Into
Clockwise Order
i N[p, n]
         i           n1


             n0
                               n2
                      p


              nmax        nj
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.)
Three Cone Centers Share
Edge Vertex
 N[ni, ni+1]


               ni            ni+1

                    ej



                         p
Three Cone Centers Don’t
Share Edge Vertex
 N[ni, ni+1]


       ni                       ni+1


                ej       ej+1


                     p
Four Cone Centers Share
Edge Vertex
N[ni, ni+1]
                           ni+1
N[ni+1, ni+2]
N[ni, ni+2]

                     ni   ej       ni+2

D[p, ni] < D[p, ni+1]
          or
D[p, ni+2] < D[p, ni+1]        p
Complex 5 Vertex Case

N[p, q]
                ni+1
                            q

           ni
                     ej


                          ni+2
                 p
New Completed Cell Border


            e1       e2



      e0         p          e3



           e5         e4
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.
Extreme Cone Density
Change Test Case
• Change the density control knob by a factor
 of 8 in area within a small distance.
Growth Sequence Movie
Growth Movie Zoom
Retinal Zoom Out Movie
3D Fly By Movie
Larger View Of My Synthetic
Retina
Roorda Blood Vessel
Roorda   vs.   Synthetic
30x30 Pixel Face Input
Retinal Image Results
30x30 Pixel Movie
Result Movie
Acknowledgements

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