Resolution Mosaic EM Algorithm for Medical Image Segmentation

Mohammed A-Megeed Salem, Beate MeffertHigh Performance Computing & Simulation(HPCS)2009 IEEE

Outline

• Introduction• Method–Multiresolution analysis–Resolution Mosaic EM Algorithm– Application for Medical Image Segmentation

• Result• Conclusion

Introduction

• Segmentation is an unconscious activeness by human but in computer it is a logically non-trivial.

• Multiresolution analysis builds different representations of an image with a spatial resolution.

• Multiresolution analysis simplified and improve the segmentation.

Multiresolution Analysis

• 2D Wavelet transform

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高頻分析濾波器

低頻分析濾波器

高頻合成濾波器

低頻合成濾波器低頻數列

高頻數列

原始數列 還原成原始數列

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第二級解析度HL 第一級解析度

HL第二級解析度LH

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Resolution Mosaic EM Algorithm

• Motivation– The interesting regions could be displayed in a

higher resolution than the non-interesting regions.

Resolution Mosaic EM Algorithm

• Generating the Mosaic Map– A label image– The non-relevant parts :high numbers with a

lower resolution. The relevant parts :low numbers indicating a

higher resolution.

Resolution Mosaic EM Algorithm

• Generating the Mosaic Map– Step 1 :Performing two levels of wavelet analysis.

The three detail images of each level are combine together to create a new image, the mask image.

– Step 2: label Mosaic map

Resolution Mosaic EM Algorithm

• Generating the Resolution Mosaic Image– The mosaic map divided into blocks– Do the loop according to (a) (b)

If min(MAP(t,l,b,r))>=CurrentLevelIf min(MAP(t,l,b,r)<CurrentLevel)

Resolution Mosaic EM Algorithm

• Image Segmentation– The Gaussian Mixture Model (GMM)

Resolution Mosaic EM Algorithm

• Image Segmentation– Use EM(Expectation-Maximization) algorithm to

estimate Gaussian distribution parameter.

(1)E:

(2)M: ，

Resolution Mosaic EM Algorithm• Image Segmentation– EM Algorithm for image segmentation

Step1: Input image I and the number of class K.

Step2:Set the initial parameters Θ(0)

Step3:Update the parameters by using Eqs. (1)(2) iteratively until convergence. Step4:Use ΘML in a classifier to generate

classification matrix. Ki = arg max( f i(xi, Θk))

Resolution Mosaic EM Algorithm

Application for Medical Image Segmentation

• Test Data Sets

Application for Medical Image Segmentation

• Test Data Sets :Mean=50,150,200 Std=10,15,20

Application for Medical Image Segmentation

• Mosaic map example

Application for Medical Image Segmentation

• Mosaic map

Resolution level

White :0Light grey:1Dark:2

Segmentation Result

Segmentation Result

STD=10 STD=15 STD=20

EM 99.03% 92.06% 84.96%

RE-ME 99.17% 96.34% 94.55%

Table1 .Overall Accuracies for Simulated MRI

STD=10 STD=15 STD=20

EM 96.15% 73.42% 59.64%

RE-ME 98.01% 87.61% 86.31%

Table2 .Precisions of the Grey Matter class for Simulated MRI

Conclusion

• A new image segmentation algorithm has been proposed based on the resolution mosaic and the EM algorithm.

• The number of iteration needed by the algorithm is reduced from 737 to 25.

• The resolution mosaic introduced here can be used in a wide range of applications.