image thresholding using type ii fuzzy sets source ： 2005, pattern recognition 38, 2363-2372...

Image Thresholding Using Image Thresholding Using Type II Fuzzy SetsType II Fuzzy Sets

Source ： 2005, Pattern Recognition 38, 2363-2372

Author ： Hamid R. TizhooshAdvisor: Chen R. -C. Ph. D(陳榮昌教授 )Speaker: Ma Tsung-han(馬宗瀚 _9514623 )Date: 2007/01/19

利用類型二的模糊集合之影像門檻值技術

Type II fuzzy sets 2

Outline

• Introduction

• Type II fuzzy sets

• Proposed method

• Experimental results

• Conclusions

• Comments

Type II fuzzy sets 3

Introduction(1/6)• The of purpose of thresholding:

Gray-level images( 灰階影像 )

0~255

Binary images( 二值影像 )

[1, 0]

Threshold( 門檻值 )

Feature extraction

Object recognition

Type II fuzzy sets 4

Introduction(2/6)

Thresholding

Gray-level > Threshold= White( 白色 )Gray-level < Threshold= Black( 黑色 )

Uses the fuzzy theory to decide the proper threshold.

Type II fuzzy sets 5

Introduction(3/6)

• Why uses the fuzzy theory in thresholding• Non-uniform illumination• Inherent image vagueness• The result of image thresholding isn’t always

satisfactory.• To Remove the grayness ambiguity/vagueness

during the task of threshold selection.

Type II fuzzy sets 6

Introduction(4/6)

• What fuzzy theory be used in this paper• Type II fuzzy sets• Also called 「 ultrafuzzy sets 」

• Regard thresholds as type II fuzzy sets

類型二模糊集合

超模糊集合

Type II fuzzy sets 7

Introduction(5/6)

• The concept of ultrafuzziness(Type II)

focuses on capture/elimination the

uncertainties( 不確定性 ) whin fuzzy systems using regular fuzzy sets(Type I).

Type II fuzzy sets 8

Introduction(6/6)

• Four approaches exploit fuzzy algorithms in

image thresholding:• Fuzzy clustering( 模糊群聚 )• Rule-based approach( 以規則為主方法 )• Fuzzy-geometrical approach( 幾何模糊方法 )• Information-theoretical approach( 資訊推理方法 )

It’s simple and high speed.Therefore, this approach is the most used.

Type II fuzzy sets 9

Type II fuzzy sets(1/7)• The general algorithm for image thresholding

based on measures of fuzziness:• (1) Select the shape of the membership function.• (2) Select a suitable measure of fuzziness (e.g. Eq. (1)).• (3) Calculate the image histogram.• (4) Initialize the position of the membership function.• (5) Shift the membership function along the gray-level

range and calculate in each position the amount of

fuzziness, for instance using Eq. (1).• (6) Locate the position gopt with maximum fuzziness.• (7) Thresholdthe image with T = gopt.

Type II fuzzy sets 10

Type II fuzzy sets(2/7)

• The most common measure of fuzziness( 模糊性 / 數 / 度 ) is the linear index of fuzziness.

• (1)

1

0

)(1),(min)(2

)(L

gAAl gggh

MNA

Where A is a M x N image subset,and with L gray levels, h(g) stands for the histogram, stands for the membership function( 隸屬函數 )

XA ]1,0[ Lg

)(gX

Type II fuzzy sets 11

Type II fuzzy sets(3/7)

gray-level range anddistribution.

Type II fuzzy sets 12

Type II fuzzy sets(4/7)• Type I fuzzy sets: the assignment of a member-

ship degree to an element/pixel is not certain.

• In order to find a more robust solution,

type II fuzzy sets should be proposed.

• The major motivation of this work to

remove the uncertainty( 不確定性 ) of

membership values by using type II fuzzy

sets.

Type II fuzzy sets 13

Type II fuzzy sets(5/7)• Type II sets are able to model such uncertainty

because their membership functions are fuzzy.

Footprint of uncertainty

Type II fuzzy sets 14

Type II fuzzy sets(6/7)

• The more practical definition of a type II

fuzzy set can be given as follows:

]1,0[),()()(,|))(),(,(~

xxxXxxxA ULxLU

The lower and upper membership degrees The initial(skeleton) membership function μ can be defined by means of linguistic hedges like dilation and concentration:

)()( xx UL 、

75.0

25.1

5.0

2

)]([)(

)]([)(

)]([)(

)]([)(

xx

xx

xx

xx

U

L

U

L

1

)]([)(

)]([)(

xx

xx

U

L

Type II fuzzy sets 15

Type II fuzzy sets(7/7)

• A measure of ultrafuzziness can be defined

as follows:

)]()([)(1

)(1

0

~~

ggghMN LU

L

gA

XA For an M x N image subset with L gray levels .h(g) reprensents the Histogram.Where

]1,0[ Lg

.2,1,)]([)(

)]([)(1

gg

gg

AL

AU

Type II fuzzy sets 16

Proposed method

• The general algorithm for image thresholding based on type II fuzzy sets and measures of

ultrafuzziness can be formulated as follows:

(1)Select the shape of skeleton membership function μ(g) and initialize α.(2) Calculate the image histogram.(3) Initialize the position of the membership function.

Type II fuzzy sets 17

Proposed method(cont.)

(4) Shift the membership function along the

gray-level range.

(5) Calculate in each position the upper and lower

membership values μU(g) and μL(g).(6) Calculate in each position the amount of ultrafuzziness.

(7) Find out the position gopt with maximum ultrafuzziness.

(8) Threshold the image with T = gopt.

Type II fuzzy sets 18

Experimental results

Type II fuzzy sets 19

Conclusions

• Fuzzy set theory provides us with knowledge-based and robust tools for developing new

thresholding techniques.

• Can receive the precise image.

• The usefulness of type II fuzzy sets using in

image thresholding is superior to the other

methods.

Type II fuzzy sets 20

Comments

• The experimental results should be compared with non-fuzzy techniques.

• The proposed method is beneficial for image processing applications, such as

detection of edges, pattern recognition, extra-ction of ROI, etc.

Type II fuzzy sets 21

Q & A

Thanks for your listening