Genetic Programming for Image Processing

1
Genetic Programming for Image Processing

• Brian A. Smith
• 2007.04.18

2
Natural Evolution

• Requirements for evolution
• Representation
• Selection Pressure
• Recombination
• Diversity

3
Natural Evolution

• Representation DNA
• Selection Pressure Survival, Reproduction
  (determined implicitly by environment)
• Recombination Mating, Replicating
• Diversity Population

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Natural EvolutionPanthera leo

• Representation
• Linear DNA
• Diploid cells
• Selection Pressure
• Rate of Reproduction
• Recombination
• Sexual reproduction
• Diversity
• Prides, with some inter-pride exchange

Image courtesy of Wikimedia Commons. (CCA 2.0
License, author yaaaay)
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Natural Evolution Streptococcus pyogenes

• Representation
• Circular DNA
• Monoploid cells
• Selection Pressure
• Rate of Reproduction
• Recombination
• Binary fission (asexual)
• Diversity
• Very little
• Occasional mutations

Image courtesy of Center for Disease Control and
Prevention, via Wikipedia. (Public domain image)
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Artificial Evolution Genetic Algorithms

• Genetic algorithms are arguably the simplest
  class of evolutionary algorithms
• GAs make use of simple representation,
  reproduction, and diversity mechanisms
• These aspects are usually independent of the
  problem domain

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Artificial Evolution Genetic Algorithms

• Representation Linear chromosome
• (array of values)
• Selection Pressure Explicit fitness function,
• Selection algorithms
• Recombination Crossover, Mutation
• Diversity Fixed-size population

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Artificial Evolution Genetic Algorithms

• Representation Linear chromosome
• (array of values)

0 1 1 0 1 1 0 1 0 1 0 1
0.5 1.2 0.0 0.2 1.0 -2.1 -1.0 0.5 -0.3
0.6 3.1 0.2
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Artificial Evolution Genetic Algorithms

• Representation Linear chromosome
• (array of values)
• Chromosome can be Boolean-valued, integer-valued,
  real-valued, complex-valued, etc.

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Artificial Evolution Genetic Algorithms

• Selection Pressure Explicit fitness function
• Fitness function is problem-specific. The only
  limits are those of imagination and practicality.
• The fitness function usually assigns a
  real-valued fitness score that does not change.

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Artificial Evolution Genetic Algorithms

• Selection Pressure Selection algorithms
• Selection algorithms are usually applied to
  choose which individuals reproduce
• and sometimes which individuals are culled.

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Artificial Evolution Genetic Algorithms

• Selection Pressure Selection algorithms
• Common selection algorithms include
• Roulette wheel selection,
• Rank-based selection,
• and Tournament selection (my favorite).

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Artificial Evolution Genetic Algorithms

• Recombination Crossover

Parent 0
One-point Xover
Parent 1
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Artificial Evolution Genetic Algorithms

• Recombination Crossover

Parent 0
One-point Xover
Parent 1
Child 0
Child 1
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Artificial Evolution Genetic Algorithms

• Recombination Crossover

Parent 0
Two-point Xover
Parent 1
Child 0
Child 1
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Artificial Evolution Genetic Algorithms

• Recombination Crossover

Parent 0
Uniform Xover
Parent 1
Child 0
Child 1
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Artificial Evolution Genetic Algorithms

• Recombination Mutation

Parent 0
Point Mutation
Child 0
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Artificial Evolution Genetic Algorithms

• Recombination Duplication

Parent 0
Used for Elitism
Child 0
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Artificial Evolution Genetic Algorithms

• Diversity Fixed-size population
• Generational GAs use individuals from current
  generation to create an entirely new generation
  of the same size.
• Steady-state GAs replace individuals one or two
  at a time.

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GA Example Noise Reduction
Images courtesy of me.
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GA Example Noise Reduction

• Reasonable choices
• Pick a window size of nn
• Use a real-valued chromosome of length n2
• Use a blending crossover
• Use a modest mutation operator
• Apply mask to noisy images
• Set fitness to the Euclidean distance between
  original images and noisy images

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GA Example Noise Reduction

• Would we expect the evolved solution to work well
  for BW noise?
• Would we expect the evolved solution to work well
  for images from other domains?

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GA Example Noise Reduction

• You get what you evolve for!
• So write your fitness function carefully.
• Diversity is very important.

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GA Example Noise Reduction

• Barring some much more creative way of using the
  linear chromosome, we cant evolve a simple
  median filter using this representation.
• Wouldnt it be nice if we could evolve algorithms
  instead of masks or arrays?

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Artificial Evolution Genetic Programs

• Genetic programs are a (slightly) more complex
  class of evolutionary algorithms.
• The main difference is in the representation,
  which allows for arbitrarily complex algorithms
  to evolve.

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Artificial Evolution Genetic Programs

• Representation Program tree

if
z
ifgt0
4
1
y

y
x
exp
x
x
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Artificial Evolution Genetic Programs

• Representation Program tree
• The user must specify a function set and a
  terminal set.

if
y

x
z

1
v
0
A Boolean function set
A Boolean terminal set
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Artificial Evolution Genetic Programs

• Representation Program tree
• Chromosome can be Boolean-valued, integer-valued,
  real-valued, complex-valued, etc.
• Chromosome can also be null-valued where nodes
  perform some action (such as moving a robot
  forward) but have no return value.

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Artificial Evolution Genetic Programs

• Representation Program tree
• Chromosome can also be strongly-typed where
  multiple node types are used subject to some
  constraints.

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Artificial Evolution Genetic Programs

• Selection Pressure Explicit fitness function
• Problem specific, same as GA
• Selection Pressure Selection algorithms
• Same as GA

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Artificial Evolution Genetic Programs

• Recombination Crossover

Parent 0
Parent 1
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Artificial Evolution Genetic Programs

• Recombination Crossover

Parent 0
Parent 1
Child 0
Child 1
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Artificial Evolution Genetic Programs

• Recombination Crossover
• Because crossover does not preserve the
  morphology of the tree, diversity is not as
  important in the GP paradigm.

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Artificial Evolution Genetic Programs

• Recombination Mutation

Grow an entire new subtree
Parent 0
Child 0
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Artificial Evolution Genetic Programs

• Diversity Population
• Generational and steady-state populations are
  common. Same as GA.

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GP Example Landslide Detection

• From Rosin and Hervás 2002 paper
  Image Thresholding for
  Landslide Detection by Genetic Programming.

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GP Example Landslide Detection

• Focused on the task of identifying landslide
  areas in an image using before and after
  satellite images from Veneto, Italy.
• Desired output is a binary image with the pixels
  in the landslide area colored black and all other
  pixels white.
• Previous work using more conventional image
  processing techniques were unsatisfactory.

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GP Example Landslide Detection
Images from Rosin and Hervás (2002).
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GP Example Landslide Detection

• Representation Real-valued program tree
• Function set
  , , -, /, abs, sigmoid, min, max
• Terminal set random constants, difference image
  pixel values, smoothed difference values, pixel
  values from various other transforms
• Maximum depth 7

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GP Example Landslide Detection

• Interpretation Positive landslide
• Negative no landslide
• 0? (not reported in paper)
• Fitness function of correctly
  classified pixels
• Selection algorithms
• Not reported in paper
• Recombination
• Standard Xover and mutation

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GP Example Landslide Detection

• Diversity Generational GP
• Population size 20,000
• of generations 200-300

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GP Example Landslide Detection

• Results best-of-run
• s10 is Gaussian smoothing with st. dev. of 10
• o15 is opened image with a 15x15 mask
• dt is distance transformed pixel value
• difference is the difference image pixel value

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GP Example Landslide Detection
Best-of-run result on entire image
Ground truth
Images from Rosin and Hervás (2002).
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GP Example Landslide Detection

• Problems with the methodology
• Very few details, would be difficult to reproduce
• Only used a portion (3) of a single image for
  training
• Used the same image for evaluation!!!
• Did not report fitness scores for experiments,
  rely instead on the readers subjective measure
  of accuracy

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GP Example Landslide Detection

• Strong points of the research
• Shows benefit of using pre-processed inputs
• Evolved better classifier than the authors were
  able to design themselves
• Shows that intuitive understanding of final
  result is unnecessary

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Concluding points

• Evolutionary algorithms such as GP may be
  suitable for evolving, rather than designing,
  image processing algorithms
• Evolutionary algorithms are not guaranteed to
  produce an optimal solution
• Evolutionary algorithms may take a long time
  (hours, days, or even weeks) to complete

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Questions or comments?
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Resources

• Dawkins, Richard. 1976. The Selfish Gene. Oxford
  University Press, Oxford, UK.
• Introduces Dawkins selfish gene theory, which
  argues that the gene- not the individual or the
  species- is the unit of evolutionary selection.
  Extremely important for understanding natural
  evolution, with some ramifications for artificial
  evolution, as well.
• Eiben, A.E. and J.E. Smith, ed. 1998.
  Introduction to Evolutionary Computing.
  Springer-Verlag, Berlin, Germany.
• Provides very brief introductions to all of the
  major classes of evolutionary algorithms. Good
  for breadth, but not for depth.

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Resources

• Goldberg, D.E. 1989. Genetic Algorithms in
  Search, Optimization, and Machine Learning.
  Addison-Wesley.
• The bible of the simple GA. Focuses on the
  Boolean (bit string) representation and gives
  theoretic justifications for its success.
• Holland, J.H. 1975. Adaptation in Natural and
  Artificial Systems. The University of Michigan
  Press, Ann Arbor, MI.
• From the man who is credited with inventing the
  genetic algorithm and birthing the field of
  evolutionary algorithms. (Though I have read that
  von Neumann suggested the idea of evolutionary
  algorithms in a letter decades earlier.) This
  work is the foundation of all future GA work.

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Resources

• Koza, J.R. 1992. Genetic Programming On the
  Programming of Computers by Means of Natural
  Selection. MIT Press, Cambridge, MA.
• Introduces the genetic program. Some earlier work
  can arguably be said to fall under the title
  genetic program, but Koza was the first to
  treat it as a rigorous methodology. The work is a
  tour de force in the technique, using GPs to
  efficiently solve a broad range of problems. 800
  pages, but it reads very quickly.
• Koza, J.R. 1992. Genetic Programming II
  Automatic Discovery of Reusable Programs. MIT
  Press, Cambridge, MA.
• Introduces the automatically defined function.
  ADFs allow for the evolution of functions with
  arbitrary arguments. Dramatically improves the
  performance of GPs in a number of domains.

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Resources

• Rosin, P.L. and J. Hervás. 2002. Image
  Thresholding for Landslide Detection by Genetic
  Programming, in L. Bruzzone and P. Smiths, ed,
  Analysis of Multi-Temporal Remote Sensing Images,
  pp. 65-72. World Scientific.