1 Segmentation with Global Optimal Contour Xizhou Feng 4/25/2003.
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Transcript of 1 Segmentation with Global Optimal Contour Xizhou Feng 4/25/2003.
1
Segmentation with Global Optimal Contour
Xizhou Feng4252003
2
Outline
Image Segmentation ProblemGlobal optimal contour methodFind global optimal contour with genetic algorithmResults
3
Image Segmentation Problem
Divide an image into a set of disjoint meaningful regionsCan be treated as an optimization problem which consists of three components =gtRepresentation the partitions =gta set of Optimal Criteria to score partitions =gtan Optimization Algorithm to search best
partitions
These three components are interdependent
4
A major problem of most segmentation methods
Highly dependent on the definition of optimal criteria The optimization algorithm is effective
for one optimal criteria but may fail to a slightly modified optimal criteria
The optimal criteria may be not correct It is difficult to incorporate prior
knowledge
5
The global optimal contour methodIdea
Represent partitions using a set of contours Evaluate each partition to score the
contour Search the optimal contour using genetic
algorithm
Advantage Can choose any optimal
criteria Always find regions and
boundaries
6
Representation of Contour
Point representation S = (x1y1) (x2y2)hellip
(xnyn)
Path completion using local navigation
The path between point A and B SAB minimize k1ʃsds+ k2ʃswds
At point P two forces Fs (the shortest path) and Fw (the minimum weight) determine the position of next point
Example of local Navigation
7
Search optimal contourThe contour can be evaluated using any reasonable optimal criterion combining boundary statistics information region statistics information prior information An simple example can be
Search a control point set which optimize the maximize score functions or minimize penalty functions which can be done by Genetic Algorithms
2
2
2
2
1
I
s
s ewds
wdsscore
8
Genetic Algorithm (Holland 1970s)
Framework of Simple GAP_current = init_population()cal_fitness(P_current)for(g=1 glt=maxGen g++)
P_next = reproduction(P_current)P_current = selection(P_candidate)cal_fitness(P_current)statistics(P_current)
Major idea of GA
Population-based stochastic search The optimal solution consists of sub optimal
solution Effective reproduction and selection
mechanism
survived population
candidate population
initial population
ldquobestrdquo population
9
Reproduction by mutation
Produce a new contour with local change could be Add a new control point Delete an original
control point Change a control point
locally
Effective to optimize a solution locally
10
Examples of mutation
11
Reproduction by CrossoverSelect two contour with probability proportional to their fitnessCut each contour into two componentsSwap one component with each otherRecombine the own component and the borrowed component into a new contour
12
Segmentation Results
13
More example
14
ConclusionsProposed global optimal contour for image segmentation Criteria independent optimization method
Can be used to study the best optimal criteria Can incorporate prior knowledge
Expected to always give an approximate optimal segmentation but for current implementation the result still need improvement
2
Outline
Image Segmentation ProblemGlobal optimal contour methodFind global optimal contour with genetic algorithmResults
3
Image Segmentation Problem
Divide an image into a set of disjoint meaningful regionsCan be treated as an optimization problem which consists of three components =gtRepresentation the partitions =gta set of Optimal Criteria to score partitions =gtan Optimization Algorithm to search best
partitions
These three components are interdependent
4
A major problem of most segmentation methods
Highly dependent on the definition of optimal criteria The optimization algorithm is effective
for one optimal criteria but may fail to a slightly modified optimal criteria
The optimal criteria may be not correct It is difficult to incorporate prior
knowledge
5
The global optimal contour methodIdea
Represent partitions using a set of contours Evaluate each partition to score the
contour Search the optimal contour using genetic
algorithm
Advantage Can choose any optimal
criteria Always find regions and
boundaries
6
Representation of Contour
Point representation S = (x1y1) (x2y2)hellip
(xnyn)
Path completion using local navigation
The path between point A and B SAB minimize k1ʃsds+ k2ʃswds
At point P two forces Fs (the shortest path) and Fw (the minimum weight) determine the position of next point
Example of local Navigation
7
Search optimal contourThe contour can be evaluated using any reasonable optimal criterion combining boundary statistics information region statistics information prior information An simple example can be
Search a control point set which optimize the maximize score functions or minimize penalty functions which can be done by Genetic Algorithms
2
2
2
2
1
I
s
s ewds
wdsscore
8
Genetic Algorithm (Holland 1970s)
Framework of Simple GAP_current = init_population()cal_fitness(P_current)for(g=1 glt=maxGen g++)
P_next = reproduction(P_current)P_current = selection(P_candidate)cal_fitness(P_current)statistics(P_current)
Major idea of GA
Population-based stochastic search The optimal solution consists of sub optimal
solution Effective reproduction and selection
mechanism
survived population
candidate population
initial population
ldquobestrdquo population
9
Reproduction by mutation
Produce a new contour with local change could be Add a new control point Delete an original
control point Change a control point
locally
Effective to optimize a solution locally
10
Examples of mutation
11
Reproduction by CrossoverSelect two contour with probability proportional to their fitnessCut each contour into two componentsSwap one component with each otherRecombine the own component and the borrowed component into a new contour
12
Segmentation Results
13
More example
14
ConclusionsProposed global optimal contour for image segmentation Criteria independent optimization method
Can be used to study the best optimal criteria Can incorporate prior knowledge
Expected to always give an approximate optimal segmentation but for current implementation the result still need improvement
3
Image Segmentation Problem
Divide an image into a set of disjoint meaningful regionsCan be treated as an optimization problem which consists of three components =gtRepresentation the partitions =gta set of Optimal Criteria to score partitions =gtan Optimization Algorithm to search best
partitions
These three components are interdependent
4
A major problem of most segmentation methods
Highly dependent on the definition of optimal criteria The optimization algorithm is effective
for one optimal criteria but may fail to a slightly modified optimal criteria
The optimal criteria may be not correct It is difficult to incorporate prior
knowledge
5
The global optimal contour methodIdea
Represent partitions using a set of contours Evaluate each partition to score the
contour Search the optimal contour using genetic
algorithm
Advantage Can choose any optimal
criteria Always find regions and
boundaries
6
Representation of Contour
Point representation S = (x1y1) (x2y2)hellip
(xnyn)
Path completion using local navigation
The path between point A and B SAB minimize k1ʃsds+ k2ʃswds
At point P two forces Fs (the shortest path) and Fw (the minimum weight) determine the position of next point
Example of local Navigation
7
Search optimal contourThe contour can be evaluated using any reasonable optimal criterion combining boundary statistics information region statistics information prior information An simple example can be
Search a control point set which optimize the maximize score functions or minimize penalty functions which can be done by Genetic Algorithms
2
2
2
2
1
I
s
s ewds
wdsscore
8
Genetic Algorithm (Holland 1970s)
Framework of Simple GAP_current = init_population()cal_fitness(P_current)for(g=1 glt=maxGen g++)
P_next = reproduction(P_current)P_current = selection(P_candidate)cal_fitness(P_current)statistics(P_current)
Major idea of GA
Population-based stochastic search The optimal solution consists of sub optimal
solution Effective reproduction and selection
mechanism
survived population
candidate population
initial population
ldquobestrdquo population
9
Reproduction by mutation
Produce a new contour with local change could be Add a new control point Delete an original
control point Change a control point
locally
Effective to optimize a solution locally
10
Examples of mutation
11
Reproduction by CrossoverSelect two contour with probability proportional to their fitnessCut each contour into two componentsSwap one component with each otherRecombine the own component and the borrowed component into a new contour
12
Segmentation Results
13
More example
14
ConclusionsProposed global optimal contour for image segmentation Criteria independent optimization method
Can be used to study the best optimal criteria Can incorporate prior knowledge
Expected to always give an approximate optimal segmentation but for current implementation the result still need improvement
4
A major problem of most segmentation methods
Highly dependent on the definition of optimal criteria The optimization algorithm is effective
for one optimal criteria but may fail to a slightly modified optimal criteria
The optimal criteria may be not correct It is difficult to incorporate prior
knowledge
5
The global optimal contour methodIdea
Represent partitions using a set of contours Evaluate each partition to score the
contour Search the optimal contour using genetic
algorithm
Advantage Can choose any optimal
criteria Always find regions and
boundaries
6
Representation of Contour
Point representation S = (x1y1) (x2y2)hellip
(xnyn)
Path completion using local navigation
The path between point A and B SAB minimize k1ʃsds+ k2ʃswds
At point P two forces Fs (the shortest path) and Fw (the minimum weight) determine the position of next point
Example of local Navigation
7
Search optimal contourThe contour can be evaluated using any reasonable optimal criterion combining boundary statistics information region statistics information prior information An simple example can be
Search a control point set which optimize the maximize score functions or minimize penalty functions which can be done by Genetic Algorithms
2
2
2
2
1
I
s
s ewds
wdsscore
8
Genetic Algorithm (Holland 1970s)
Framework of Simple GAP_current = init_population()cal_fitness(P_current)for(g=1 glt=maxGen g++)
P_next = reproduction(P_current)P_current = selection(P_candidate)cal_fitness(P_current)statistics(P_current)
Major idea of GA
Population-based stochastic search The optimal solution consists of sub optimal
solution Effective reproduction and selection
mechanism
survived population
candidate population
initial population
ldquobestrdquo population
9
Reproduction by mutation
Produce a new contour with local change could be Add a new control point Delete an original
control point Change a control point
locally
Effective to optimize a solution locally
10
Examples of mutation
11
Reproduction by CrossoverSelect two contour with probability proportional to their fitnessCut each contour into two componentsSwap one component with each otherRecombine the own component and the borrowed component into a new contour
12
Segmentation Results
13
More example
14
ConclusionsProposed global optimal contour for image segmentation Criteria independent optimization method
Can be used to study the best optimal criteria Can incorporate prior knowledge
Expected to always give an approximate optimal segmentation but for current implementation the result still need improvement
5
The global optimal contour methodIdea
Represent partitions using a set of contours Evaluate each partition to score the
contour Search the optimal contour using genetic
algorithm
Advantage Can choose any optimal
criteria Always find regions and
boundaries
6
Representation of Contour
Point representation S = (x1y1) (x2y2)hellip
(xnyn)
Path completion using local navigation
The path between point A and B SAB minimize k1ʃsds+ k2ʃswds
At point P two forces Fs (the shortest path) and Fw (the minimum weight) determine the position of next point
Example of local Navigation
7
Search optimal contourThe contour can be evaluated using any reasonable optimal criterion combining boundary statistics information region statistics information prior information An simple example can be
Search a control point set which optimize the maximize score functions or minimize penalty functions which can be done by Genetic Algorithms
2
2
2
2
1
I
s
s ewds
wdsscore
8
Genetic Algorithm (Holland 1970s)
Framework of Simple GAP_current = init_population()cal_fitness(P_current)for(g=1 glt=maxGen g++)
P_next = reproduction(P_current)P_current = selection(P_candidate)cal_fitness(P_current)statistics(P_current)
Major idea of GA
Population-based stochastic search The optimal solution consists of sub optimal
solution Effective reproduction and selection
mechanism
survived population
candidate population
initial population
ldquobestrdquo population
9
Reproduction by mutation
Produce a new contour with local change could be Add a new control point Delete an original
control point Change a control point
locally
Effective to optimize a solution locally
10
Examples of mutation
11
Reproduction by CrossoverSelect two contour with probability proportional to their fitnessCut each contour into two componentsSwap one component with each otherRecombine the own component and the borrowed component into a new contour
12
Segmentation Results
13
More example
14
ConclusionsProposed global optimal contour for image segmentation Criteria independent optimization method
Can be used to study the best optimal criteria Can incorporate prior knowledge
Expected to always give an approximate optimal segmentation but for current implementation the result still need improvement
6
Representation of Contour
Point representation S = (x1y1) (x2y2)hellip
(xnyn)
Path completion using local navigation
The path between point A and B SAB minimize k1ʃsds+ k2ʃswds
At point P two forces Fs (the shortest path) and Fw (the minimum weight) determine the position of next point
Example of local Navigation
7
Search optimal contourThe contour can be evaluated using any reasonable optimal criterion combining boundary statistics information region statistics information prior information An simple example can be
Search a control point set which optimize the maximize score functions or minimize penalty functions which can be done by Genetic Algorithms
2
2
2
2
1
I
s
s ewds
wdsscore
8
Genetic Algorithm (Holland 1970s)
Framework of Simple GAP_current = init_population()cal_fitness(P_current)for(g=1 glt=maxGen g++)
P_next = reproduction(P_current)P_current = selection(P_candidate)cal_fitness(P_current)statistics(P_current)
Major idea of GA
Population-based stochastic search The optimal solution consists of sub optimal
solution Effective reproduction and selection
mechanism
survived population
candidate population
initial population
ldquobestrdquo population
9
Reproduction by mutation
Produce a new contour with local change could be Add a new control point Delete an original
control point Change a control point
locally
Effective to optimize a solution locally
10
Examples of mutation
11
Reproduction by CrossoverSelect two contour with probability proportional to their fitnessCut each contour into two componentsSwap one component with each otherRecombine the own component and the borrowed component into a new contour
12
Segmentation Results
13
More example
14
ConclusionsProposed global optimal contour for image segmentation Criteria independent optimization method
Can be used to study the best optimal criteria Can incorporate prior knowledge
Expected to always give an approximate optimal segmentation but for current implementation the result still need improvement
7
Search optimal contourThe contour can be evaluated using any reasonable optimal criterion combining boundary statistics information region statistics information prior information An simple example can be
Search a control point set which optimize the maximize score functions or minimize penalty functions which can be done by Genetic Algorithms
2
2
2
2
1
I
s
s ewds
wdsscore
8
Genetic Algorithm (Holland 1970s)
Framework of Simple GAP_current = init_population()cal_fitness(P_current)for(g=1 glt=maxGen g++)
P_next = reproduction(P_current)P_current = selection(P_candidate)cal_fitness(P_current)statistics(P_current)
Major idea of GA
Population-based stochastic search The optimal solution consists of sub optimal
solution Effective reproduction and selection
mechanism
survived population
candidate population
initial population
ldquobestrdquo population
9
Reproduction by mutation
Produce a new contour with local change could be Add a new control point Delete an original
control point Change a control point
locally
Effective to optimize a solution locally
10
Examples of mutation
11
Reproduction by CrossoverSelect two contour with probability proportional to their fitnessCut each contour into two componentsSwap one component with each otherRecombine the own component and the borrowed component into a new contour
12
Segmentation Results
13
More example
14
ConclusionsProposed global optimal contour for image segmentation Criteria independent optimization method
Can be used to study the best optimal criteria Can incorporate prior knowledge
Expected to always give an approximate optimal segmentation but for current implementation the result still need improvement
8
Genetic Algorithm (Holland 1970s)
Framework of Simple GAP_current = init_population()cal_fitness(P_current)for(g=1 glt=maxGen g++)
P_next = reproduction(P_current)P_current = selection(P_candidate)cal_fitness(P_current)statistics(P_current)
Major idea of GA
Population-based stochastic search The optimal solution consists of sub optimal
solution Effective reproduction and selection
mechanism
survived population
candidate population
initial population
ldquobestrdquo population
9
Reproduction by mutation
Produce a new contour with local change could be Add a new control point Delete an original
control point Change a control point
locally
Effective to optimize a solution locally
10
Examples of mutation
11
Reproduction by CrossoverSelect two contour with probability proportional to their fitnessCut each contour into two componentsSwap one component with each otherRecombine the own component and the borrowed component into a new contour
12
Segmentation Results
13
More example
14
ConclusionsProposed global optimal contour for image segmentation Criteria independent optimization method
Can be used to study the best optimal criteria Can incorporate prior knowledge
Expected to always give an approximate optimal segmentation but for current implementation the result still need improvement
9
Reproduction by mutation
Produce a new contour with local change could be Add a new control point Delete an original
control point Change a control point
locally
Effective to optimize a solution locally
10
Examples of mutation
11
Reproduction by CrossoverSelect two contour with probability proportional to their fitnessCut each contour into two componentsSwap one component with each otherRecombine the own component and the borrowed component into a new contour
12
Segmentation Results
13
More example
14
ConclusionsProposed global optimal contour for image segmentation Criteria independent optimization method
Can be used to study the best optimal criteria Can incorporate prior knowledge
Expected to always give an approximate optimal segmentation but for current implementation the result still need improvement
10
Examples of mutation
11
Reproduction by CrossoverSelect two contour with probability proportional to their fitnessCut each contour into two componentsSwap one component with each otherRecombine the own component and the borrowed component into a new contour
12
Segmentation Results
13
More example
14
ConclusionsProposed global optimal contour for image segmentation Criteria independent optimization method
Can be used to study the best optimal criteria Can incorporate prior knowledge
Expected to always give an approximate optimal segmentation but for current implementation the result still need improvement
11
Reproduction by CrossoverSelect two contour with probability proportional to their fitnessCut each contour into two componentsSwap one component with each otherRecombine the own component and the borrowed component into a new contour
12
Segmentation Results
13
More example
14
ConclusionsProposed global optimal contour for image segmentation Criteria independent optimization method
Can be used to study the best optimal criteria Can incorporate prior knowledge
Expected to always give an approximate optimal segmentation but for current implementation the result still need improvement
12
Segmentation Results
13
More example
14
ConclusionsProposed global optimal contour for image segmentation Criteria independent optimization method
Can be used to study the best optimal criteria Can incorporate prior knowledge
Expected to always give an approximate optimal segmentation but for current implementation the result still need improvement
13
More example
14
ConclusionsProposed global optimal contour for image segmentation Criteria independent optimization method
Can be used to study the best optimal criteria Can incorporate prior knowledge
Expected to always give an approximate optimal segmentation but for current implementation the result still need improvement
14
ConclusionsProposed global optimal contour for image segmentation Criteria independent optimization method
Can be used to study the best optimal criteria Can incorporate prior knowledge
Expected to always give an approximate optimal segmentation but for current implementation the result still need improvement