Sisteme de programe pentru timp real

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Sisteme de programepentru timp real

• Universitatea Politehnica din Bucuresti
• 2005-2006
• Adina Magda Florea
• http//turing.cs.pub.ro/sptr_06

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Curs Nr. 9

• Genetic Algorithms applications
• GAIA

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1 Generating new images using Genetic Algorithms

• The Gaia program has been developed as a tool to
  generate new kind of images.
• Based on the paper Artificial Evolution for
  Computer Graphics from Karl Sims (Computer
  Graphics, Volume 25, Number 4, July 1991), it
  uses the ideas of genetic algorithms and
  evolution to assist the user in the creation of
  new images.
• Every image is generated evaluating a mathematic
  formula in the real domain.
• The problem is to find formulas which, when
  evaluated, give us interesting images. We use
  genetic algorithms to find this formulas.

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Generating new images using Genetic Algorithms

• Starting from a random and simply formula, the
  program generates multiple variations of the
  current image modifying slightly the formula.
• The new formulas are evaluated and the results
  presented to the user, which will choose and
  select the most interesting one based on his
  artistic criterion.
• The selected formula becomes the new generator
  and the process is repeated again, closing this
  way the cycle.
• The concept of evolution is used to find new
  formulas from the current ones the new formulas
  become not so simply, and the associated images
  quite good looking.

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Generating new images using Genetic Algorithms

• (lerp (0.524 0.389 -0.394) (- (triwave (RAD))
  0.590) (PHY))
• (color_grad "earth" (gradient (log ( ( (lerp
  (PHY) (-0.080 0.408 0.254) (RAD)) (RAD))
  (-0.098 -0.277 -0.840)))))
• (color_noise (mod (warped_color_noise (X) -0.003
  -0.296 (-0.359 0.020 -0.790)) (Y)) (color_noise
  (X) (invert (Y))))

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Generating new images using Genetic Algorithms

• (lerp ( (vector -0.422 (warped_bw_noise (RAD)
  (-0.468 -0.375 -0.624) (Y) (RAD)) (RAD)) (X))
  (RAD) (bw_noise (PHY) (log 0.529)))
• (triwave (- ( ( (RAD) (PHY)) (PHY)) (-0.176
  0.738 -0.928)))
• (mynoise (triwave ( (RAD) (PHY))) (RAD))

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Generating new images using Genetic Algorithms

• (lerp ( (X) (X)) (/ (/ (0.204 0.166 0.711)
  (RAD)) (RAD)) (bw_noise (RAD) (RAD)))
• (triwave (lerp (min (lerp (PHY) (lerp (PHY) 0.033
  (RAD)) (0.050 0.137 -0.586)) (PHY)) (IRAD)
  (RAD)))
• (color_noise (cos ( (bw_noise (mod (X) (Y))
  (-0.419 -0.415 0.673)) (Y))) 0.296)

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Generating image transitions using Genetic
Algorithms

• The program can also generate smooth transitions
  between any images generated in the program.
• The user selects the source and the target
  images, and the program finds the frames which
  will transform the source image in the target
  image.
• If the formulas used to compute the images have
  nothing in common, the transition will be a pure
  melt
• If the formulas have some similarities, we obtain
  an interesting transition of forms.

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Generating image transitions using Genetic
Algorithms
Source (triwave (abs (RAD))) Target (triwave
(abs (X)))
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Generating image transitions using Genetic
Algorithms
Source (triwave (abs (X))) Target (triwave (
(PHY) (PHY)))
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Generating image transitions using Genetic
Algorithms
Source (/ ( (Y) (X)) (RAD)) Target (/ ( (Y)
(RAD)) (RAD))
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2 Genotype

• Gaia codes every image generated with a formula
  and a domain.
• Both elements are the genotype of the solutions.
• The formulas are mathematical expressions built
  from a set of operators and constants.
• The expression is stored in Lisp format, and
  tells Gaia how the image should be evaluated.
• The domain tells Gaia where the formula should be
  evaluated.
• The domain is simply a region of the real plane
  specified as the limits in both directions.
• The default domain used is -1..1 x -1..1.

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2 Genotype

• The formulas can be as long as desired, they have
  no fixed length.
• The formulas are frequently shown in tree
  representation, showing how the expression is
  evaluated. Every node in the expression has one
  branch for each argument it needs, where it hangs
  more nodes. The operators with no arguments are
  the leafs of the tree, while the root node is
  that with no parent the last one begin
  evaluated.
• Lisp Expression Domain
• ( ( (X) (Y)) (Y)) 0..1 x 0..1
• (gradient (invert (- (0.5) (RAD)))) -1..1 x
  -1..1
• (abs (lerp (mynoise (/ (triwave (mod (PHY)
  -0.190)) (RAD)) (min (RAD) -0.873)) (Y)
  (X))) -1..1 x -1..1

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3 Formulas operators

• Formulas are sequences of operators and functions
  arranged in tree form.
• There are five classes of operators
• Domain operators Those like X,Y,RAD,PHY which
  depends on the domain where the formula is being
  evaluated.
• X, Y
• Returns an image which is directly the values
  of the domain in the X-axis or Y-axis directions.
  So the resulting images are horizontal and
  vertical ramps of luminance. These images where
  obtained with the domain 0..1 x 0..1

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3 Formulas operators

• RAD
• The resulting image depends directly on the
  domain where it is evaluated. The luminance of
  each pixel in the image is directly the distance
  from the coordinates of the pixel in the domain
  to the origin, typically at the center.
• IRAD
• Similar to the operador RAD, the luminance of
  each pixel is the distance measured to the
  nearest odd integer in the domain. The black
  corners represents the four integer coords
  (-1,-1) (-1,1) (1,1) (1,-1) of the domain where
  the image was rendered.

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3 Formulas operators

• PHY
• The luminance of the resulting image represents
  the angular coordinate of the pixel, with the
  zero heading down.There where the value is
  greater than 1 a white pixel is used.

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3 Formulas operators

• 2. One argument functions From a single image,
  returns a new image after applying some function
  to the pixels values of the argument.
• Some examples of functions are compute his cos,
  sin, normalize, gradient, abs, round, triwave,
  ...
• TRIWAVE
• This operator is important because it is bounded
  in the interval 0..1 for all the source values.
  This means that we can feed this operator with
  any image with any pixel values, that the
  resulting image will be limited between 0 and 1.

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3 Formulas operators

• 3. Simply operators Combines two images to
  return the result of the operator. The
  combination operator can be as easy as add the
  images, substract, multitply, or combine
  logically at pixel level.
• 4. Complex operators Need more than two images
  as arguments and returns a more complex
  combination of them. They usually use some of
  them as parameters of the combination. Examples
  LERP, noise functions, color grad, ...
• 5. Misc operators Here are included the
  operators which uses external images imported
  from other programs or those which uses the
  templates of the program

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3 Formulas operators

• LERP
• It takes three images as arguments A,B,C. and
  computes the resulting image as
  A(B-A)Triwave(C). So it makes a linear
  interpolation from A to B, using C as weight of
  the interpolation. The operator Triwave is
  included to limit C in the interval 0..1.

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4 Mutation

• Evolution is achived by two methods Mutation and
  Combination.
• Mutations
• A mutation can be though as a modification of the
  genotype.
• From a starting genotype we can generate similar
  images performing changes in the genotype and
  evaluating the new formulas.
• If we are using a long formula to obtain an
  image, and make some little changes in the
  formula, the final image will be in general quite
  similar but different.
• Mutations are normally applied on a single node,
  and affects this node and maybe nodes in lower
  levels. This node is chosen randomly in the tree.

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4 Mutation

• New Node The selected node is substituted by a
  new simply random node. This type of mutation can
  achieve important changes when the original tree
  is big, and the node is near the root of the
  tree.
• Adjust Node The node is modified by another one
  with the same number of parameters. The tree
  maintains the same structure, but instead of
  computing the cos (maybe) we will compute the
  sin, or maybe we will change a constant with
  value 0.7 by a new one with value 0.5. This type
  of mutation makes light changes.
• Node as arg The selected node becomes the
  argument of a new random node which is placed in
  his previous location in the tree, and the old
  node hanging from it. If the new node needs more
  arguments they are generated randomly.

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4 Mutation

• Arg as node The inverse operation. One of the
  arguments of the node substitutes the node
  itself. The new tree is simpler than the
  original. If the original node got more
  arguments, they are discarded.
• Node as uncle The node is substituted by a copy
  of a node in upper levels of the tree.
• Reorder arguments This operator changes the
  order of the arguments of the selected node
  (assuming it has more than two). It can be very
  different to compute X / RAD or RAD / X.
• The more mutations we apply, the more differences
  we get between parent and child images. The
  default number of mutations applied is one, but
  when formulas become bigger, it is preferable to
  use two or three.
• In Gaia, there is only one parent. Children are
  obtained by performing different types of
  mutations in different nodes of the same parent.

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4 Mutation examples

• Parent expression
• (triwave (mod (triwave (PHY)) (RAD)))
• Domain -1..1 x -1..1

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4 Mutation examples

1. (triwave (mod (lerp (PHY) (Y) (Y)) (RAD)))
2. (mod (triwave (PHY)) (RAD))
3. (triwave (mod ( (triwave (PHY)) (X)) (RAD)))
4. (triwave (mod (PHY) (RAD)))
5. (triwave (lerp (mod (triwave (PHY)) (RAD)) (Y)
   (RAD)))
6. (triwave (mod (max (triwave (PHY)) (RAD)) (RAD)))
   
7. (triwave (sin (triwave (PHY))))
8. (triwave (mod ( (triwave (PHY)) (RAD)) (RAD)))
9. (triwave (mod (triwave (PHY)) (warped_color_noise
   (RAD) (0.653 0.865 -0.369) (0.683 0.337 -0.625)
   (X))))
10. (mod (mod (triwave (PHY)) (RAD)) (PHY))
11. (triwave (mod (RAD) (triwave (PHY))))
12. (triwave (rotate (mod (triwave (PHY)) (RAD))
    (RAD)))
13. (triwave (mod (gradient (triwave (PHY))) (RAD)))
14. (invert (triwave (mod (triwave (PHY)) (RAD))))
15. (triwave ( (mod (triwave (PHY)) (RAD)) (X)))
16. (triwave (mod (abs (PHY)) (RAD)))

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4 Mutation examples
(triwave (mod (triwave (PHY)) (RAD)))
(triwave (mod (lerp (PHY) (Y) (Y)) (RAD)))
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5 Combination

• With this type of evolution we want to find a
  method to generate images that share
  characteristics of two previously generated
  images.
• To accomplish this we will rely on the fact that
  the relation between formulas and images is
  basically associated to the sequences of
  operators used in the genotypes, rather than the
  individual operators used.
• So we will try to maintain sequences of nodes of
  the parent and mother in the new genotypes.

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5 Combination

• The steps to generate new offspring by combining
  two genotypes are
• Select one random node in the parent tree, and
  one random node in the mother tree.
• Break the trees by this points. Parent is divided
  in P1 and P2, and mother in M1 and M2.
• Interchange the parts of the genders. Create two
  new expressions C1P1M2 and C2M1P2
• Repeat the process choosing other nodes in the
  parent and mother trees.

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5 Combination
Mother
Parent
Child 1
Child 2
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5 Combination examples

• Parent expression
• (lerp ( (vector -0.422 (warped_bw_noise (RAD)
  (-0.468 -0.375 -0.624) (Y) (RAD)) (RAD)) (X))
  (RAD) (bw_noise (PHY) (log 0.529)))
• Domain -1..1 x -1..1
• Mother expression
• (lerp (triwave (PHY)) ( (lerp (0.524 0.389
  -0.394) (- (triwave (RAD)) 0.590) (PHY)) (triwave
  (mod (triwave (PHY)) (RAD)))) (RAD))
• Domain -1..1 x -1..1

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5 Combination examples
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5 Combination examples

• (lerp (triwave (RAD)) ( (lerp (0.524 0.389
  -0.394) (- (triwave (RAD)) 0.590) (PHY)) (triwave
  (mod (triwave (PHY)) (RAD)))) (RAD))
• (lerp (triwave (PHY)) ( (lerp (0.524 0.389
  -0.394) (bw_noise (PHY) (log 0.529)) (PHY))
  (triwave (mod (triwave (PHY)) (RAD)))) (RAD))
• (lerp (triwave (PHY)) ( (lerp (0.524 0.389
  -0.394) (- (triwave (RAD)) 0.590) (PHY)) (triwave
  (mod (-0.468 -0.375 -0.624) (RAD)))) (RAD))
• ( (lerp (0.524 0.389 -0.394) (- (triwave (RAD))
  0.590) (PHY)) (triwave (mod (triwave (PHY))
  (RAD))))
• (lerp (triwave (PHY)) ( (lerp (0.524 0.389
  -0.394) (- (triwave (RAD)) 0.590) (X)) (triwave
  (mod (triwave (PHY)) (RAD)))) (RAD))
• (lerp ( (vector -0.422 (warped_bw_noise (RAD)
  (-0.468 -0.375 -0.624) (Y) (RAD)) (RAD)) (-
  (triwave (RAD)) 0.590)) (RAD) (bw_noise (PHY)
  (log 0.529)))
• (lerp (triwave (PHY)) ( (lerp (0.524 0.389
  -0.394) (- (triwave (RAD)) 0.590) (PHY)) (triwave
  (mod (triwave (PHY)) (RAD)))) (bw_noise (PHY)
  (log 0.529)))
• (lerp ( (vector -0.422 (warped_bw_noise (RAD)
  (-0.468 -0.375 -0.624) (Y) (lerp (0.524 0.389
  -0.394) (- (triwave (RAD)) 0.590) (PHY))) (RAD))
  (X)) (RAD) (bw_noise (PHY) (log 0.529)))

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5 Combination examples

• (lerp (triwave (PHY)) ( (lerp (0.524 0.389
  -0.394) (- (triwave (RAD)) 0.590) (PHY)) (triwave
  (mod (triwave (PHY)) (RAD)))) (RAD))
• (lerp (triwave (PHY)) ( (lerp (0.524 0.389
  -0.394) (RAD) (PHY)) (triwave (mod (triwave
  (PHY)) (RAD)))) (RAD))
• (lerp ( (vector (PHY) (warped_bw_noise (RAD)
  (-0.468 -0.375 -0.624) (Y) (RAD)) (RAD)) (X))
  (RAD) (bw_noise (PHY) (log 0.529)))
• (lerp ( (vector -0.422 (warped_bw_noise (RAD)
  (-0.468 -0.375 -0.624) (Y) (RAD)) (RAD)) (X))
  (RAD) (bw_noise (PHY) (log (RAD))))
• (lerp (triwave (PHY)) (log 0.529) (RAD))
• (lerp ( (vector -0.422 (warped_bw_noise (RAD)
  (-0.468 -0.375 -0.624) (Y) (RAD)) (RAD)) (X)) (
  (lerp (0.524 0.389 -0.394) (- (triwave (RAD))
  0.590) (PHY)) (triwave (mod (triwave (PHY))
  (RAD)))) (RAD))
• (lerp (triwave (PHY)) ( (lerp (0.524 0.389
  -0.394) (- (triwave (RAD)) 0.590) (PHY)) (triwave
  (bw_noise (PHY) (log 0.529)))) (RAD))
• (lerp (triwave (-0.468 -0.375 -0.624)) ( (lerp
  (0.524 0.389 -0.394) (- (triwave (RAD)) 0.590)
  (PHY)) (triwave (mod (triwave (PHY)) (RAD))))
  (RAD))

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6 Image transitions

• The software is able to make smooth transitions
  between images
• This means that the user selects one image as the
  source, and another as the target, and Gaia will
  make automatically a smooth transition between
  both images.
• Depending on the semblance of both source and
  target, the transition will be a simply melt if
  the genotypes have nothing in common, but it can
  be an interesting transition if there are some
  similarities in the genotypes.
• We say that two genotypes are similar if they
  share the upper nodes of the genotypes (the nodes
  near the root node).
• The more nodes they share, the more similar they
  are. If both expressions have different root
  nodes, the expressions have nothing in common.

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6 Image transitions

• To obtain the animation, Gaia generates a new
  genotype parametrized in time.
• This new genotype has the common nodes of source
  and target images, and interpolates in time the
  nodes which are different.
• This means that when the parameter t  0, the
  genotype is equivalent to the source genotype,
  while when t  1, the genotype match the target.
  Between, the genotype is a proportional mix of
  both genotypes.
• Important here making a simply melt of the
  different nodes, but when apply the operators,
  the melt is visualized as a transformation of
  forms in the image, and not just as an
  interpolation of colors.

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6 Image transitions

• Source genotype Target genotype New genotype
• The blue nodes are common to both source and
  target genotypes, while the red and green nodes
  are different. The gray nodes are inserted to
  interpolate in time the different nodes. The
  program inserts this special join node every time
  the nodes of source and target differs.

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6 Image transitions

• Source genotype Target genotype New genotype
• Source genotype ( (X) ( (RAD) (Y))) X RADY
• Target genotype ( (X) ( (RAD) (Cos ( (2)
  (PHY))))) X RAD(Cos(2PHY))
• New genotype ( (X) ( (RAD) ( ( (1-t) (Y)) (
  (t) (Cos ( (2) (PHY))))))) X RAD ((1-t)(Y)
  (t)(Cos(2PHY)))

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6 Image transitions

• Another type of animation is accomplished when
  the domains are different.
• In this case, the intermediate domains is also a
  proportional mix of the source and target
  domains, finding an easy way to get zooms
  (magnification and reduction) and displacements
  of the images.

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6 Image transitions
Source (triwave (abs (X))) Target (triwave (
(PHY) (PHY)))
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6 Image transitions
Source (lerp (/ (gradient ( (PHY) (RAD)))
(RAD)) (Y) (0.545 0.495 0.981)) Target (lerp
(Y) (0.545 0.495 0.981) (/ (gradient ( (PHY)
(RAD))) (RAD)))
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