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 cycles per ring of new cones added.

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

The Cone Force Equation

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

Definition Of Spline[ ] Function x Spline[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 p n0n0 n1n1 n2n2 njnj n max

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 p nini n i+1 ejej N[n i, n i+1 ]

Three Cone Centers Don’t Share Edge Vertex p nini n i+1 ejej e j+1

Four Cone Centers Share Edge Vertex p nini n i+2 ejej n i+1 N[n i, n i+1 ] N[n i+1, n i+2 ] N[n i, n i+2 ] D[p, n i ] < D[p, n i+1 ] or D[p, n i+2 ] < D[p, n i+1 ]

Complex 5 Vertex Case p nini n i+2 ejej n i+1 q

New Completed Cell Border p e0e0 e1e1 e2e2 e3e3 e4e4 e5e5

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.