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An Experiment with Evolution – Developing an Eye

An Experiment with Evolution – Developing an Eye. Michael Guzman 21/2/2007. Outline. 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.

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An Experiment with Evolution – Developing an Eye

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  1. An Experiment with Evolution – Developing an Eye Michael Guzman 21/2/2007

  2. Outline • Introduction and Background • Project details • Selected results • Summary

  3. Introduction and Background • Genetic Algorithm • Eye evolution – What we know by now • Learn optics in 30 seconds

  4. 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.

  5. Genetic Algorithm

  6. Eye evolution – What we know

  7. Learn optics in 30 seconds

  8. Learn optics in 30 seconds

  9. Project details • Representation – The Genome • Assumptions and Constants • Fitness function

  10. Representation – 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

  11. Opening Lens Width Lens Y A B Representation – The Genome

  12. 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%

  13. Fitness function • We consider the following factors • The smearing of a point on the retina • Area πAB • Perimeter – Ramanujan approximation • Illumination power - (2×L-radius)^2/focal^2 • Resolution – different points projected on different photoreceptors. • Opening size – how much light goes in

  14. 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.

  15. Selected results • Why selected results?

  16. Selected results– eye #1 0 500 2000 5000

  17. Selected results– eye #2 0 1000 5000

  18. Selected results– eye #3 • Flat wide eye • Minimal opening • Lens adjacent to retina • Very big focal length What went wrong?

  19. 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.

  20. 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 .

  21. 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)

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