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An Experiment with
Evolution –
Developing an Eye
Michael Guzman
21/2/2007
Outline
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Introduction and Background
Project details
Selected results
Summary
Introduction and Background
• Genetic Algorithm
• Eye evolution – What we know by now
• Learn optics in 30 seconds
Genetic 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 Algorithm
Eye evolution – What we know
Learn optics in 30 seconds
Learn optics in 30 seconds
Project details
• Representation – The Genome
• Assumptions and Constants
• Fitness function
Representation – The Genome
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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
Genome
Opening
Lens Width
Lens Y
A
B
Assumptions 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 function
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We consider the following factors
The smearing of a point on the retina
Area πAB
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 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 results
• Why selected results?
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Selected results – eye #1
Selected results – eye #2
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5000
Selected results – eye #3
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Flat wide eye
Minimal opening
Lens adjacent to retina
Very big focal length
What went wrong?
Summary
• 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 .
References
• IBCV 2007 LectureNotes
• Evolutionary Computation and Artificial Life - BGU course
Lecture
• 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)