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Segmentation
via
Genetic Programming
Segmentation
Segmentation
 Splitting an image into segments
 Hard problem
 Conceptually ill-defined
Segmentation
Which segmentation is the correct one?
Segmentation
Which segmentation is the correct one?
Segmentation
Which segmentation is the correct one?
Segmentation
Defining the problem
 Tagging function:
seg x, y  : R  R  segment1 , segment 2 ,, segment n 
 Deciding function:
seg x, y  : R  R  true, false
Segmentation
The Dataset
 Berkley’s segmentation dataset
and benchmark:
• Images + Human made segmentation
maps
• Benchmark for segmentation
algorithms
Genetic Programming
What is Genetic Programming?
 Bio-Inspired Artificial Intelligence
method
 Inspired by Darwin’s evolutionary
principles
Genetic Programming
Darwin’s principles
 Variety of species individuals
within the population
 Competition for limited resources
 Overproduction of offspring
generation
 Survival of the fittest
Origin of Species, 1859
Genetic Programming
The computational model
Gn
Gn+1
fitness
55
44
12
31
95
32
87
12
0
65
53
2
91
73
crossover
+
=
mutation
Segmentation via GP
Individual Representation
 Individuals are represented as
LISP-like functions
X2  (* x x)
2x-1  (- (* (+ 1 1) x) 1)
Segmentation via GP
Individual Representation
 Equivalent to tree representation
*
x
x
*
+
1
1
x
1
Segmentation via GP
Genetic Operators
 Crossover
*
x
x
*
+
1
1
x
1
*
+
1
x
1
*
x
1
x
Segmentation via GP
Genetic Operators
 Mutation
*
+
1
1
*
x
*
1
1
x
x
1
1
Segmentation via GP
Building the trees
 Function Set:
{+, -, *, %, neg, conv, opp, sqrt}
 Terminal Set:
{image, 0, 1, const, gradx, grady, ckernel}
 Strongly-Typed GP:
conv(matrix,kernel)
+(matrix,matrix), +(kernel,kernel),
+(kernel,number), …
Segmentation via GP
Building the trees
 An example: Gradient Magnitude
(sqrt
(+
(* (conv image gradx)
(conv image gradx))
(* (conv image grady)
(conv image grady))))
Segmentation via GP
Fitness measure
 Accuracy:
acc 
result  segmap
result  segmap
 Modified Accuracy:
acc 
1  result  segmap
1  result  segmap
Segmentation via GP
Threshold
 Individuals produce ‘soft boundary
maps’, need threshold value
 Value too low – more points are
reported (false positives)
 Value too high – less points are
reported (true negatives)
Segmentation via GP
Threshold
 Berkley’s benchmark: split the threshold
range into N equal parts, threshold and
keep best.
 My method: split the threshold range into
N unequal parts, by equal increase in
reported points, proportional to number
of points in the human made
segmentation map.
Segmentation via GP
Miscellaneous Evolutionary Parameters
 Population size: 60-150
 Generation count: unspecified
 Crossover rate: 90%
 Mutation rate: 10%
 Selection: tournament of 3
 Tree depth: limited to 6-9
Sean Luke’s ECJ13 was used for running GP sessions
Results
A typical GP session
Results
A typical GP session
 Generation 0:
0.176 best, 0.08 average
 Generation 93:
0.262 best, 0.242 average
 Fitness does not always increase!
 Fitness leaps in best individual
Results
Best Individual
Segmentation function
(- (- (conv (* (conv image gradx) (conv image
gradx)) (- (- (kernel 5.381114 -8.362269 8.888325
1.1866289 -6.4069843 -8.251046 -9.389916 6.183886 7.817788) grady) (- (kernel -2.334486 -4.6182337 9.115009 8.010966 -3.0507333 3.22619 2.068446 2.932576 -6.243905) 0.0))) (conv (* (conv image
gradx) (conv image gradx)) (- (- (kernel 2.4412537
-8.362269 8.888325 1.1866289 -6.4069843 -8.251046 9.389916 6.183886 -7.817788) grady) (- (kernel
9.936699 -4.6182337 -9.115009 8.010966 -3.0507333
3.22619 2.068446 -2.932576 -6.243905) 0.0)))) (- ((- (conv image grady) (* 1.0 9.336973)) (% (* 1.0
9.336973) 9.336973)) (% (% (* -3.9138038 0.0) (*
0.0 0.0)) (% (* 1.0 9.336973) (* 1.0 9.336973)))))
Results
Best Individual
Segmentation function
(- (- (conv (* (conv image gradx) (conv image
gradx)) (- (- (kernel 5.381114 -8.362269 8.888325
1.1866289 -6.4069843 -8.251046 -9.389916 6.183886 7.817788) grady) (- (kernel -2.334486 -4.6182337 9.115009 8.010966 -3.0507333 3.22619 2.068446 2.932576 -6.243905) 0.0))) (conv (* (conv image
gradx) (conv image gradx)) (- (- (kernel 2.4412537
-8.362269 8.888325 1.1866289 -6.4069843 -8.251046 9.389916 6.183886 -7.817788) grady) (- (kernel
9.936699 -4.6182337 -9.115009 8.010966 -3.0507333
3.22619 2.068446 -2.932576 -6.243905) 0.0)))) (- ((- (conv image grady) (* 1.0 9.336973)) (% (* 1.0
9.336973) 9.336973)) (% (% (* -3.9138038 0.0) (*
0.0 0.0)) (% (* 1.0 9.336973) (* 1.0 9.336973)))))
Results
Best Individual
Segmentation function
(- (- (conv (* (conv image gradx) (conv image
gradx)) (- (- (kernel 5.381114 -8.362269 8.888325
1.1866289 -6.4069843 -8.251046 -9.389916 6.183886 7.817788) grady) (- (kernel -2.334486 -4.6182337 9.115009 8.010966 -3.0507333 3.22619 2.068446 2.932576 -6.243905) 0.0))) (conv (* (conv image
gradx) (conv image gradx)) (- (- (kernel 2.4412537
-8.362269 8.888325 1.1866289 -6.4069843 -8.251046 9.389916 6.183886 -7.817788) grady) (- (kernel
9.936699 -4.6182337 -9.115009 8.010966 -3.0507333
3.22619 2.068446 -2.932576 -6.243905) 0.0)))) (- ((- (conv image grady) (* 1.0 9.336973)) (% (* 1.0
9.336973) 9.336973)) (% (% (* -3.9138038 0.0) (*
0.0 0.0)) (% (* 1.0 9.336973) (* 1.0 9.336973)))))
Results
Best Individual
Segmentation function
(- (- (conv (* (conv image gradx) (conv image
gradx)) (- (- (kernel 5.381114 -8.362269 8.888325
1.1866289 -6.4069843 -8.251046 -9.389916 6.183886 7.817788) grady) (- (kernel -2.334486 -4.6182337 9.115009 8.010966 -3.0507333 3.22619 2.068446 2.932576 -6.243905) 0.0))) (conv (* (conv image
gradx) (conv image gradx)) (- (- (kernel 2.4412537
-8.362269 8.888325 1.1866289 -6.4069843 -8.251046 9.389916 6.183886 -7.817788) grady) (- (kernel
9.936699 -4.6182337 -9.115009 8.010966 -3.0507333
3.22619 2.068446 -2.932576 -6.243905) 0.0)))) (- ((- (conv image grady) (* 1.0 9.336973)) (% (* 1.0
9.336973) 9.336973)) (% (% (* -3.9138038 0.0) (*
0.0 0.0)) (% (* 1.0 9.336973) (* 1.0 9.336973)))))
Results
Best Individual
Accuracy = 0.307 (GM accuracy = 0.280)
Results
Best Individual
Accuracy = 0.172 (GM accuracy = 0.193)
Results
Best Individual
Accuracy = 0.262
(GM accuracy = 0.245)
Results
Best Individual
Accuracy = 0.126
(GM accuracy = 0.119)
Summary
Discussion
 It is possible to evolve segmentation
functions using GP
 Results are good, can be better
 Evolved function ‘beats’ the gradient
magnitude function
 Improve results by more power
Summary
Future Work
 More CPU and RAM
 More functions and terminals
 Use ADFs
 Evolve kernels separately
 Evolve threshold function separately
 Include more inputs: color images,
textures, output of other edge detectors
References
1.
The Berkley Segmentation Dataset and Benchmark
http://www.cs.berkeley.edu/projects/vision/grouping/segbench/
2.
Koza, J. R.: Genetic Programming: On the programming of
computers by natural selection. MIT press, Cambridge, Mass.
(1992)
3.
Tomassini M.: Evolutionary Algorithms. Swiss Scientific
Computing Center, Manno.
4.
Darwin, Charles: On the origin of species by means of natural
selection. London, John Murray, 1859
5.
Montana, D.J.: Strongly typed genetic programming.
Evolutionary Computation 3 (1995) 199–230
6.
Langdon, W.B.: Size fair and homologous tree genetic
programming crossovers.
Genetic Programming and Evolvable Machines 1 (2000) 95–119.
7.
Luke S.: ECJ 13 - a Java based Evolutionary Computation and
Genetic Programming research system
http://cs.gmu.edu/~eclab/projects/ecj
8.
Koza, J. R.: Genetic Programming II: Automatic Discovery of
Reusable Programs. MIT press, Cambridge, Mass. (1994)