Hierarchical Distributed Genetic Algorithm for Image Segmentation Hanchuan Peng, Fuhui Long*, Zheru Chi, and Wanshi Siu {fhlong, phc, Center for Multimedia Signal Processing, Department of Electronic & Information Engineering, The Hong Kong Polytechnic University, Hong Kong

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.

Outline Introduction Details of HDGA Experimental Results Discussion & Conclusion

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)

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 ……

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. Use GA in a more novel and promising way, which codes the segmentation process model itself, instead of the model parameters. Based on existing segmentation techniques New approach!

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.

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.

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

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

Details of HDGA: Paradigm of HDGA

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

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

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.

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 T MSE 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 Details of HDGA: Paradigm of HAT

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

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 c p,q with the largest fitness f p,q in  m,n 3.2 Crossover-- produce new offspring 3.3 Mutation – replace c m,n with any chromosome in the whole population randomly according to probability r m 4. Repeat 2, 3 until stop criterion is satisfied

Standard Images in Experiments

Non-standard Image Samples

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

Segmentation: HDGA vs DGA for “ bird ” HDGA DGA

Segmentation: HDGA vs DGA for “ lena ” HDGA DGA

HDGA DGA Segmentation: HDGA vs DGA for “ peppers ”

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

Region Contrast where Region Homogeneity where Region Boundary Accuracy

Region homogeneity (  10 6 ) in HDGA vs DGA

Region Contrast of HDGA vs DGA

Region Boundary Accuracies of HDGA vs DGA

Segmentation Region Numbers of HDGA vs DGA

Average Convergence Speeds of HDGA vs DGA

Computational Speeds of HDGA vs DGA

1.HAT explores the statistical property of the input image provide a reasonable initialization for GA operations progressive segmentation 2.Distributed genetic algorithm explores the spatial connectivity new chromosome structure, fitness function, genetic operations 3.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. Conclusions