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

AbstractA 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 fiel

d, etc) Neural networks Genetic Algorithm (GA)

Introduction: Genetic Algorithms for Image Segmentation

Haseyama’s GA: Minimizing an MSE function for segmentationBhanu’s GA: Hybrid model and parameter optimization Bhandarkar’s GA: Region adjacency graph generation & cost function minimizationKim’s hybrid model of GA & MRFHorita’s GA: Region segmentation of K-mean clustering Scheunders’s genetic Lloyd-Max Quantizer (LMQ)Andrey’s "distributed" GA based on classifier systemLong’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 imageprovide a reasonable initialization for GA

operationsprogressive segmentation

Details of HDGA: Role of Distributed GA

Distributed genetic algorithm explores the spatial connectivity New chromosome structure New fitness functionNew genetic operations

Details of HDGA: Main Advantages of Our Model

It outperforms Andrey's DGA model:adaptively and effectively controls the seg

mentation 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 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

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- DLI2. Evaluation by Fitness Function

)1 ,1(

1

1,,,, ,,

,

,

NnMm

bbN

f nqmpnmqp qpnm

nm

nm

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

qpnmnew ccc ,, )1(

nmsr sr

qp

nm f

fqpP

,,',

',

,),(

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

Standard Images in Experiments

Non-standard Image Samples

Level 1 Level 2

Level 3 Level 4

Progressive Segmentation on Different Levels for "bird"

Segmentation: HDGA vs DGAfor “bird”

HDGA DGA

 

Segmentation: HDGA vs DGAfor “lena”

HDGA DGA

HDGA DGA

Segmentation: HDGA vs DGAfor “peppers”

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.

Region Contrast

ji

jiijC

||

ji ijR

CN

C,2

1where

Region Homogeneity

mRp mpm

m gA

22 )(1

mRp pm

m gA

1

21 mmH

RN

m mR

HN

H1

1where

Region Boundary Accuracy

)(number pixel

)(number pixel

B

EBrA

Region homogeneity (106) 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