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