An Experiment with An Experiment with Evolution Evolution – –

Developing an EyeDeveloping an Eye

Michael Guzman

21/2/2007

Outline Outline

• Introduction and Background

• Project details

• Selected results

• Summary

Introduction and BackgroundIntroduction and Background

• Genetic Algorithm

• Eye evolution – What we know by now

• Learn optics in 30 seconds

Genetic AlgorithmGenetic Algorithm

• Genetic algorithm is a probabilistic search algorithm.

• Iteratively transforms a population of individuals, each with an associated fitness value, into a new population of offspring objects.

• Darwinian principle of natural selection

• Applying operations which imitate nature’s genetic operations, such as crossover (sexual recombination) and mutation.

Genetic AlgorithmGenetic Algorithm

Eye evolution – What we knowEye evolution – What we know

Learn optics in 30 secondsLearn optics in 30 seconds

Learn optics in 30 secondsLearn optics in 30 seconds

Project detailsProject details

• Representation – The Genome

• Assumptions and Constants

• Fitness function

Representation – The GenomeRepresentation – The Genome

The purpose is to assume nothing

• The shape of the eye will we an ellipse – A-axis, B-axis

• The width of the opening to let light in

• Lens width

• Lens vertical location

• Lens focal length

Representation – The Representation – The GenomeGenome

A

B

Lens Y

Lens Width

Opening

Assumptions and ConstantsAssumptions and Constants

• Mirror symmetry• We start with very small B-axis almost a flat

patch with the widest opening possible• The starting focal length is very big – same

as starting with no lens.

• Mutation probability 5%• Mutation magnitude 5%• Crossover probability 90%

Fitness functionFitness function• We consider the following factors

1. The smearing of a point on the retina

2. Area πAB

3. Perimeter – Ramanujan approximation

4. Illumination power - (2×L-radius)^2/focal^2

5. Resolution – different points projected on different photoreceptors.

6. Opening size – how much light goes in

Fitness functionFitness function

• All factors normalized by their max-value

• The maximal values for the axes are 4 times bigger than the biggest eye existing today.

Selected resultsSelected results

• Why selected results?

Selected resultsSelected results – – eye #1eye #10

500

2000

5000

Selected resultsSelected results – – eye #2eye #20

1000

5000

Selected resultsSelected results – – eye #3eye #3

• Flat wide eye

• Minimal opening

• Lens adjacent to retina

• Very big focal length

What went wrong?

SummarySummary• Using an unconditioned (almost) model of the eye,

the results are nevertheless reasonable, and similar eyes can be found in nature.

• The project tries to simulate natural process from nature and therefore imposes some initial conditions on the individuals, a fact which prevents the genetic algorithm to show it full power.

• Some of the result are very improbable and they occur because of the method used to select the “parents” in each generation.

• It seems that otherwise than in size, no better eye than those we know from nature, has developed during the running of the algorithm.

Future work

• Finding a better general fitness function, giving more weight to : usage of the retina, ratio between axes etc…

• Trying special fitness function according to environmental conditions.

• Making a interactive web applet incorporating all of these .

ReferencesReferences• IBCV 2007 LectureNotes• Evolutionary Computation and Artificial Life - BGU course Le

cture• Wikipedia• A pessimistic estimate of the time required for an eye to

evolve Nilsson & Pelger.• Feynman lectures on physics Vol I ch.31• Field guide to Visual and Ophthalmic Optics bgu-lib QP.475.S385

• Mathematics handbook by Korn&Korn McGRAW-HILL

• Various physics and analytical geometry books (russian)