Segmentation with Global Optimal Contour

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Segmentation with Global Optimal Contour

• Xizhou Feng
• 4/25/2003

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Outline

• Image Segmentation Problem
• Global optimal contour method
• Find global optimal contour with genetic
  algorithm
• Results

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Image Segmentation Problem

• Divide an image into a set of disjoint meaningful
  regions
• Can 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

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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

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The global optimal contour method

• Idea
• 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

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Representation of Contour

• Point representation
• S (x1,y1), (x2,y2),, (xn,yn)
• Path completion using local navigation
• The path between point A and B, SAB minimize
  k1??sds k2??swds
• At point P, two forces Fs (the shortest path)
  and Fw (the minimum weight) determine the
  position of next point

Example of local Navigation
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Search optimal contour

• The 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

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Genetic Algorithm (Holland 1970s)

• Framework of Simple GA
• P_current init_population()
• cal_fitness(P_current)
• for(g1 gltmaxGen 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

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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

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Examples of mutation
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Reproduction by Crossover

• Select two contour with probability proportional
  to their fitness
• Cut each contour into two components
• Swap one component with each other
• Recombine the own component and the borrowed
  component into a new contour

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Segmentation Results
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More example
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Conclusions

• Proposed 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