1 Segmentation with Global Optimal Contour Xizhou Feng 4/25/2003

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

3 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: =>Representation the partitions =>a set of Optimal Criteria to score partitions =>an 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 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

6 Representation of Contour Point representation S = {(x 1,y 1 ), (x 2,y 2 ),…, (x n,y n )} Path completion using local navigation The path between point A and B, S AB minimize k 1 · ʃ s ds+ k 2 · ʃ s wds 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 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

8 Genetic Algorithm (Holland 1970s) Framework of Simple GA P_current = init_population(); cal_fitness(P_current); for(g=1; g<=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 “best” 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 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

12 Segmentation Results

13 More example

14 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