Hierarchical Distributed Genetic Algorithm for Image Segmentation

1. Hierarchical Distributed Genetic Algorithm for Image Segmentation Hanchuan Peng, Fuhui Long*, Zheru Chi, and Wanshi Siu Email: {fhlong, phc, enzheru}@eie.polyu.edu.hk Center for Multimedia Signal Processing, Department of Electronic & Information Engineering, The Hong Kong Polytechnic University, Hong Kong

2. Abstract A new Hierarchical Distributed Genetic Algorithm (HDGA) is proposed for image segmentation. • Histogram dichotomy: to explore the statistical property of input image and produce a hierarchically quantized image. • HDGA is imposed on the quantized image to explore the spatial connectivity and produce final segmentation result. HDGA is a major improvement of the original Distributed Genetic Algorithm (DGA) and Multiscale Distributed Genetic Algorithm (MDGA): • A priori assumption • Chromosome structure • Fitness function • Genetic operations Our experiments prove the advantages of HDGA.

3. Outline • Introduction • Details of HDGA • Experimental Results • Discussion & Conclusion

4. Introduction: Paradigms for Image Segmentation • A lot of existing algorithms for image segmentation. • Gray-level thresholding of local/global/deterministic/fuzzy/stochastic schemes • Iterative pixel classification (including deterministic and stochastic relaxation) • Parameter space clustering (including probabilistic and fuzzy clustering) • Surface fitting, surface classification and surface/region growing • Edge detection • Statistical models (including Markov Random Field (MRF), Gibbs random field, etc) • Neural networks • Genetic Algorithm (GA)

5. Introduction: Genetic Algorithms for Image Segmentation • Haseyama’s GA: Minimizing an MSE function for segmentation • Bhanu’s GA: Hybrid model and parameter optimization • Bhandarkar’s GA: Region adjacency graph generation & cost function minimization • Kim’s hybrid model of GA & MRF • Horita’s GA: Region segmentation of K-mean clustering • Scheunders’s genetic Lloyd-Max Quantizer (LMQ) • Andrey’s "distributed" GA based on classifier system • Long’s multilevel distributed genetic algorithm • ……

6. Introduction: Genetic Approaches for Image Segmentation • Use GA as an alternative optimization method of traditional image segmentation techniques. • Use GA to remove the sensitivity of the present image segmentation techniques to the initial conditions. Based on existing segmentation techniques • Use GA in a more novel and promising way, which codes the segmentation process model itself, instead of the model parameters. New approach!

7. Introduction: DGA (Distributed Genetic Algorithm) • DGA is novel because it is not based on existing segmentation techniques • distributed GA • classifier system • “Distributed”: the genetic operations, i.e. selection, crossover, mutation, are performed on locally distributed subgroups of chromosomes, but not globally on all chromosomes in the whole population. • Classifier system: a set of symbolic production rules. A classifier is a condition/action rule. It exchanges message with environment through detectors and effectors.

8. Introduction: DGA – Paradigm • Image segmentation: a function that takes an image as input and a labeled image as output. • The function is represented by classifier system, which consists of a set of spatially organized binary-coded production rules imposed on each pixel. • By iteratively modifying the production rules using a distributed genetic algorithm, the rule set encoding the possibly best segmentation can be obtained.

9. Introduction: DGA – Main Problems • predefine region numbers on the feature histogram • unreasonable initialization scheme of chromosome population • redundant and inefficient condition-action chromosome structure

10. Details of HDGA: HDGA – A Major Improvement of DGA • a new unsupervised image segmentation method based on: • hierarchical adaptive thresholding (HAT) • distributed GA

11. Details of HDGA: Paradigm of HDGA

12. Details of HDGA: Role of HAT • HAT explores the statistical property of the input image • provide a reasonable initialization for GA operations • progressive segmentation

13. Details of HDGA: Role of Distributed GA • Distributed genetic algorithm explores the spatial connectivity • New chromosome structure • New fitness function • New genetic operations

14. Details of HDGA: Main Advantages of Our Model • It outperforms Andrey's DGA model: • adaptively and effectively controls the segmentation quality without a priori assumption of the image region number; • produce regions with high homogeneity, high contrast, low noise, and accurate boundaries; • more efficient in both computation and storage.

15. Details of HDGA: Paradigm of HAT The image feature histogram is repeatedly dichotomized into hierarchical continuous intervals until each of the intervals has a pixel-by-pixel MSE less than a given positive threshold TMSE We can prove: the sum of the pixel variances on all intervals in a higher level is always smaller than that in the lower level --- progressive segmentation

16. GA initialization in our model GA initialization in Andrey’s model Details of HDGA: HAT based Initialization

17. Details of HDGA: Distributed GA-based Segmentation 1. HAT based initialization- DLI 2. Evaluation by Fitness Function 3. Genetic Operations 3.1 Selection--- select the cp,q with the largest fitness fp,q in m,n 3.2 Crossover-- produce new offspring 3.3 Mutation – replace cm,n with any chromosome in the whole population randomly according to probability rm 4. Repeat 2, 3 until stop criterion is satisfied

18. Standard Images in Experiments

19. Non-standard Image Samples

20. Progressive Segmentation on Different Levels for "bird" Level 1 Level 2 Level 3 Level 4

21. Segmentation: HDGA vs DGA for “bird” HDGA DGA

22. Segmentation: HDGA vs DGA for “lena” HDGA DGA

23. Segmentation: HDGA vs DGA for “peppers” HDGA DGA

24. Quantitative Evaluation • Region Homogeneity – H • Region Contrast – C • Region boundary accuracy – rA • Number of regions – NR • Speed • convergence speed • computational complexity • Storage complexity Note: For 1,2,3, the larger the better; For 4,5,6, the smaller the better.

25. Region Homogeneity where Region Contrast where Region Boundary Accuracy

26. Region homogeneity (106) in HDGA vs DGA

27. Region Contrast of HDGA vs DGA

28. Region Boundary Accuracies of HDGA vs DGA

29. Segmentation Region Numbers of HDGA vs DGA

30. Average Convergence Speeds of HDGA vs DGA

31. Computational Speeds of HDGA vs DGA

32. Conclusions • HAT explores the statistical property of the input image • provide a reasonable initialization for GA operations • progressive segmentation • Distributed genetic algorithm explores the spatial connectivity • new chromosome structure, fitness function, genetic operations • Our new model outperforms Andrey et al's DGA model • adaptively and effectively controls the segmentation quality • without a priori assumption of the image region number; • produce regions with high homogeneity, high contrast, low noise, and accurate boundaries; • more efficient in both computation and storage.