IM Talk1 Final

8/13/2019 IM Talk1 Final

1/67

Applications of Fuzzy Set Theory and

Fuzzy Logic in Image Processing

Jamileh Yousefi CIS 6320, W11


2/67

Outline

2

Fuzzy Image Processing

Why Fuzzy Image Processing

Steps of Fuzzy Image Processing

Applications of Fuzzy Logic in Image Processing


3/67

Fuzzy Image Processing

3

Collection of all approaches that understand, represent

and process the images, their segments and features

as fuzzy sets.

The representation and processing depend on:

The selected fuzzy technique

The problem to be solved


4/67

Example

Gray-levels: gray, dark gray, and light

4


5/67

5

Colour = { yellow, orange, red, violet, blue }

Example


6/67

Example

6

Can we give a crisp definition to light blue?


7/677

Fuzziness Vs. Vagueness

I will be back

sometime

Fuzzy Vague

I will be back

in a fewminutes

Fuzzy

Vagueness=Insufficient SpecificityFuzziness=Unsharp Boundaries


8/67

Why Fuzzy Image Processing?

8

Low-Level

Preprocessing

Grayness

Ambiguity

Intermediate-

Level

Segmentation

Representation

Description

Geometrical

Fuzziness

High-Level

Analysis

Interpretation

Recognition

Vague

Knowledge

Uncertainty


9/67


9

Low-Level

Preprocessing

Grayness

Ambiguity

Intermediate-

Level

Segmentation

Representation

Description

Geometrical

Fuzziness

High-Level

Analysis

Interpretation

Recognition

Vague

Knowledge

Whether a pixel should become darkeror brighter than it already is


10/67


10

Low-Level

Preprocessing

Grayness

Ambiguity

Intermediate-

Level

Segmentation

Representation

Description

Geometrical

Fuzziness

High-Level

Analysis

Interpretation

Recognition

Vague

Knowledge

Where is the boundary betweentwo image segments


11/67


11

Low-Level

Preprocessing

Grayness

Ambiguity

Intermediate-

Level

Segmentation

Representation

Description

Geometrical

Fuzziness

High-Level

Analysis

Interpretation

Recognition

Vague

Knowledge

What is a tree in a scene analysisproblem


12/67


12

Membership

Modification

Image

Defuzzification

Image

Fuzzification

Input

Image

Output

Image

Fuzzy Logic

Fuzzy Set Theory

Expert Knowledge


13/67


13

Membership

Modification

Image

Defuzzification

Image

Fuzzification

Input

Image

Output

Image

Gray-leve

lp

lane

50 55 63

58 205 210

215 223 230

Fuzzy Logic

Fuzzy Set Theory

Expert Knowledge


14/67


14

Membership

Modification

Image

Defuzzification

Image

Fuzzification

Input

Image

Output

Image

Me

mbers

hipp

lane

Fuzzy Logic

Fuzzy Set Theory

Expert Knowledge

.19 .21 .25

.23 .80 .82

.84 .87 90


15/67


15

Membership

Modification

Image

Defuzzification

Image

Fuzzification

Input

Image

Output

Image

Me

mbers

hipp

lane

Fuzzy Logic

Fuzzy Set Theory

Expert Knowledge

.07 .09 .12

.10 .92 .93

.95 .97 .97


16/67


16

Membership

Modification

Image

Defuzzification

Image

Fuzzification

Input

Image

Output

Image

Fuzzy Logic

Fuzzy Set Theory

Expert Knowledge

Gray-leve

lp

lane

18 23 31

25 234 237

242 247 250


17/67

17

Contrast Enhancement

Edge Detection

Noise Detection and Removal

Segmentation

Geometric measurement

Scene analysis (Region Labeling)

Applications of Fuzzy Logic in Image

Processing


18/67

Contrast Enhancement


19/67

Fuzzy Contrast Enhancement

Approaches for Fuzzy Contrast Enhancement

Minimization of fuzziness

Equalization using fuzzy expected value

Fuzzy Hyperbolization

Rule-based approach

19


20/67

Fuzzy Contrast Image Enhancement

approaches

20

Original Image


21/67


approaches

21

Minimization of

fuzziness


22/67

Fuzzy Contrast Image enhancement

approaches

22

Equalization using

Fuzzy Expected

Value


23/67

Fuzzy Contrast Image enhancement

approaches

23

Fuzzy

Hyperbolization


24/67


approaches

24

Fuzzy Rule-

based approach


25/67

25

Contrast Enhancement with Fuzzy

Histogram Hyperbolization (Tizhoosh 1995/1997)

1. Set the membership function

1. Set the value of fuzzifier (a linguistic hedge)

2. Calculate of membership values for each gray level

3. Modify the membership values by linguistic hedge

4. Generate new gray-levels using equation


26/67

26

Contrast Enhancement with Fuzzy Histogram

Hyperbolization (Tizhoosh 1995/1997)


27/67

Contrast Improvement based on Fuzzy If-

Then Ruels (Tizhoosh 1997)

1. Setting the parameter of inference system

input features, membership functions,..

2. Fuzzification of the actual pixel

memberships to the dark, gray and bright sets of pixels

27


28/67

3. Modify the membership values

28



Fuzzy rules:

If Y is Dark => Yeis Darker

If Y is Gr ay => Yeis Midgray

If Y is Brig ht => Yeis Br ighter

4. Defuzzification of the fuzzy result


29/67

29




30/67

Edge Detection


31/67

Techniques of fuzzy edge detection:

Membership function edge detection

Rule-based fuzzy edge detection

Fuzzy Edge Detection


32/67

Membership Function Edge Detection(Tizhoosh, 1997)

A membership function indicates the degree of

edginess in each neighborhood.

The membership function is determined heuristically.

It is fast but the performance is limited.

32


33/67


33


34/67

Membership function edge detection(Tizhoosh, 1997)

34

Membership functions of the fuzzy sets associated

to the input and to the output


35/67

35

E

E

E

E

EE

If If Then Then

Checked pixel

is Edge

Checked pixel

is Edge

Checked pixel

is Edge

Checked pixel

is Edge

Checked pixel

is Edge

Checked pixel

is Edge

Checked pixel

is Edge

Checked pixel

is Edge

E

E

Membership function edge detection(Tizhoosh, 1997)


36/67


36


37/67

Rule-based Fuzzy Edge Detection (Tizhoosh,1997)

37Else

If If Then Then


38/67

Rule-based Fuzzy Edge Detection (Tizhoosh,1997)

38


39/67

Noise Reduction


40/67

Edges and Noise

40

Both represent a variation in intensity

Usually edge has a large variation between adjacent

pixels, compared to additive noise

Directional gradients is used to capture variations


41/67

Noise Reduction Using Fuzzy Filtering ( N.Baker et al., 2008)

Let:

D dir = {NW, W, SW, S, SE, E, NE, N}

D(x,y) : Derivative value

Small derivative: most likely caused by noiseLarge derivative: most likely caused by an edge

41

.

.

NW N NE

W (x,y) E

SW S SE


42/67


42

Edge

DetectionFiltering

Post-Processing

Averaging

& Rescaling(x,y)s


43/67


43

Edge

DetectionFiltering

Post-Processing

Averaging

& Rescaling(x,y)s

Drives a fuzzy derivative values for each direction

No edge is present in this direction

Rule 1:


44/67


44

Edge

DetectionFiltering

Post-Processing

Averaging

& Rescaling(x,y)s

Separating Noise from Edges


45/67


45

Edge

DetectionFiltering

Post-Processing

Averaging

& Rescaling(x,y)s

For each direction: if is not edge

Then compute the correction term (s)


46/67


46

Edge

DetectionFiltering

Post-Processing

Averaging

& Rescaling(x,y)

Calculate corrected terms

Adds to pixel luminance value of location (x, y)

s


47/67

47

Colour Image Noise Reduction Using Fuzzy

Filtering ( N. Baker et al., 2008)


48/67

Image Segmentation


49/67

Fuzzy Segmentation Approaches

Fuzzy clustering algorithm to build segments

Fuzzy c-means clustering algorithm

Fuzzy Rule-based Segmentation

Extraction of Fuzzy IF-THEN rules

Fuzzy Thresholding

Minimization of image fuzziness

Fuzzy Geometry

49


50/67

Linear VS. Fuzzy Segmentation

50

Region is assigned to a fuzzy

set of labels:{rock/0.89,sand/0.46}

Sea segments

are mergedcorrectly

Oversegmentation

Undersegmentation


51/67

Fuzzy Rule-Based Segmentation

Interpret the image features as linguistic variables

Use fuzzy if-then rules to build segmenats

Example:

IF

The pixel is dark

AND its neighborhood is also dark

AND homogeneous

THEN

it belongs to the background 51


52/67

52

Fuzzy Rule-Based Segmentation


53/67

Fuzzy Thresholding

1. A membership function is moved pixel by pixel over the

existing range of gray levels.

2. In each position, a measure of fuzziness is calculated.

3. The position with a minimum amount of fuzziness is a suitable

threshold.

53


54/67

A comparison between fuzzy and Otsu thresholding

algorithm

54

Test Image

Thresholded by fuzzy method Thresholded by Otsu algorithm

Fuzzy Thresholding


55/67

Use to measure the geometrical fuzziness of different

regions of an image:

Fuzzy Area

Fuzzy Perimeter

Fuzzy compactness

Fuzzy Geometry


56/67

Fuzzy Area and Fuzzy Perimeter

Let :

(x) is the membership value of a pixel

O is the set of pixels corresponding to the object

PO is the set of pixels corresponding to theperimeter of the object

The image is fuzzified by the fuzzy binarization

algorithm

56


57/67

Fuzzy Region Labeling is used to:

Solve over-segmentation problems

Assign labels with confidence values to regions

Link labels with concepts existing in ontologies

Fuzzy Region labeling


58/67

58

Fuzzy Region Labeling

For each region:

Visual Descriptor matching with the instances of the

concepts in the domain ontology

Calculation of a combined distance from multipledescriptors

Assignment of labels (concepts) along with a

confidence of value (fuzzy set of labels)

Hierarchical merging of regions based on the fuzzy set

of labels


59/67

59

Sky

Sky

Fog

Mountain

Mountain

Mountain

Field

Field

FieldField

Field

RoofWall

Sky

Mountain

Field

House

Fuzzy Region Labeling


60/67

60

Conclusion

linear approaches not able to handle the disturbances

occurring in processing an image.

Fuzzy Image Processing techniques are the mostefficient solution for this problem.

These techniques with fuzzy sets give much-improved

image compared to the others.


61/67

61

Thank You


62/67

References

62

1. Tizhoosh, H.R.

Fast and Robust Fuzzy Edge Detection, Fuzzy Filters for Image

Processing, M. Nachtegael, D. Van der Weken, D. Van De Ville &

E.E. Kerre (Eds.), Springer, Studies in Fuzziness and SoftComputing, 2002

2. Tizhoosh, H.R.

Fuzzy Image Enhancement: An Overview, Fuzzy Techniques in

Image Processing, Springer, Studies in Fuzziness and Soft

Computing, pp. 137-171, 2000


63/67

References

63

3. Munther N. Baker , Ali A. Al-Zuky

ColourImage Noise Reduction Using Fuzzy Filtering, Journal of

Engineering and Development, June 2008,Vol. 12, No. 2, 157-166

4. Abdallah A. Alshennawy, and Ayman A. Aly

Edge Detection in Digital Images Using Fuzzy Logic Technique,

Engineering and Technology 51, 2009;46:178186.

5. Mario.I. Chacon. M

Fuzzy logic for image processing, Advanced Fuzzy logic

Techniques in industrial applications, 2006.


64/67

References

64

6. F.Russo

Edge Detection In Noisy Images Using fuzzy reasoning IEEE

Trans. on instrumentation and measurement,Vol 47,1998, pp 1102-

1105

7. M.I. Chacon, and L. Aguilar

A fuzzy Approach to Edge level detection. The 10th IEEE

international Conference on Fuzzy system Melbourne, Australia,

December 2001, pp 809-812.


65/67

References

65

8. Todd Law, Hidenori Itoh, and Hirohisa Seki

Image Filtering, Edge Detection,and Edge Tracing Using Fuzzy

Reasoning, IEEE Ttransaction on Pattern Analysis and Machine

Inteligence, VOL. 18, NO. 5, MAY 1996 48 1

9. Fabrizio Russo

Edge Detection in Noisy Images Using Fuzzy Reasoning, IEEE

Instrumentation and Measurement Technology Conference, USA,

May 1998, pp 369- 372


66/67

References

66

10. Fabrizio Russo and Giovanni Ramponi

A Fuzzy Operator for the Enhancement of Blurred and Noisy Images,

IEEE Transaction on Image Processing, VOL. 4. NO. 8. AUGUST

1995, pp 1169-1174

11. Yau-Hwang Kuo, Chang-Shing Lee and Chao-Chin Liu

A New Fuzzy Edge Detection Method for Image Enhancement , FU

ZZ-IEEE 97, pp 1069-1074

12. Fabrizio Russo

Recent Advances in Fuzzy Techniques for Image Enhancement,

IEEE TRANSACTIONS ON INSTRUMENTATION AND

MEASUREMENT, VOL. 47, 1998, pp 1428-1439.


67/67

References

13. Han-Pang Huang, Yi-Hung Liu, Li-Wei Liu, Chun-Shin Wong

Applications of Advanced Fuzzy Logic Techniques in Fuzzy Image

Processing Scheme, Advances in Fuzzy Mathematics, Volume 5,

Number 1 (2010), pp. 7176

14. Farzam F., Menhaj M. B., Motamedi Seyed A. , and M.T. Hagan

A New Fuzzy Logic Filter for Image Enhancement, IEEE

TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICSPART

B: CYBERNETICS, VOL. 30, NO. 1, FEBRUARY 2000, pp 110-119.

Documents

IM Talk1 Final