im talk1 final
TRANSCRIPT
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Applications of Fuzzy Set Theory and
Fuzzy Logic in Image Processing
Jamileh Yousefi CIS 6320, W11
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Outline
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Fuzzy Image Processing
Why Fuzzy Image Processing
Steps of Fuzzy Image Processing
Applications of Fuzzy Logic in Image Processing
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Fuzzy Image Processing
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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
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Example
Gray-levels: gray, dark gray, and light
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Colour = { yellow, orange, red, violet, blue }
Example
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Example
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Can we give a crisp definition to light blue?
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Fuzziness Vs. Vagueness
I will be back
sometime
Fuzzy Vague
I will be back
in a fewminutes
Fuzzy
Vagueness=Insufficient SpecificityFuzziness=Unsharp Boundaries
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Why Fuzzy Image Processing?
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Low-Level
Preprocessing
Grayness
Ambiguity
Intermediate-
Level
Segmentation
Representation
Description
Geometrical
Fuzziness
High-Level
Analysis
Interpretation
Recognition
Vague
Knowledge
Uncertainty
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Why Fuzzy Image Processing?
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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
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Why Fuzzy Image Processing?
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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
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Why Fuzzy Image Processing?
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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
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Steps of Fuzzy Image Processing
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Membership
Modification
Image
Defuzzification
Image
Fuzzification
Input
Image
Output
Image
Fuzzy Logic
Fuzzy Set Theory
Expert Knowledge
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Steps of Fuzzy Image Processing
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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
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Steps of Fuzzy Image Processing
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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
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Steps of Fuzzy Image Processing
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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
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Steps of Fuzzy Image Processing
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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
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Contrast Enhancement
Edge Detection
Noise Detection and Removal
Segmentation
Geometric measurement
Scene analysis (Region Labeling)
Applications of Fuzzy Logic in Image
Processing
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Contrast Enhancement
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Fuzzy Contrast Enhancement
Approaches for Fuzzy Contrast Enhancement
Minimization of fuzziness
Equalization using fuzzy expected value
Fuzzy Hyperbolization
Rule-based approach
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Fuzzy Contrast Image Enhancement
approaches
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Original Image
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Fuzzy Contrast Image Enhancement
approaches
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Minimization of
fuzziness
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Fuzzy Contrast Image enhancement
approaches
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Equalization using
Fuzzy Expected
Value
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Fuzzy Contrast Image enhancement
approaches
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Fuzzy
Hyperbolization
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Fuzzy Contrast Image Enhancement
approaches
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Fuzzy Rule-
based approach
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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
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Contrast Enhancement with Fuzzy Histogram
Hyperbolization (Tizhoosh 1995/1997)
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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
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3. Modify the membership values
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Contrast Improvement based on Fuzzy If-
Then Ruels (Tizhoosh 1997)
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
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Contrast Improvement based on Fuzzy If-
Then Ruels (Tizhoosh 1997)
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Edge Detection
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Techniques of fuzzy edge detection:
Membership function edge detection
Rule-based fuzzy edge detection
Fuzzy Edge Detection
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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.
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Membership Function Edge Detection(Tizhoosh, 1997)
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Membership function edge detection(Tizhoosh, 1997)
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Membership functions of the fuzzy sets associated
to the input and to the output
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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)
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Membership Function Edge Detection(Tizhoosh, 1997)
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Rule-based Fuzzy Edge Detection (Tizhoosh,1997)
37Else
If If Then Then
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Rule-based Fuzzy Edge Detection (Tizhoosh,1997)
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Noise Reduction
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Edges and Noise
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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
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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
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.
.
NW N NE
W (x,y) E
SW S SE
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Noise Reduction Using Fuzzy Filtering ( N.Baker et al., 2008)
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Edge
DetectionFiltering
Post-Processing
Averaging
& Rescaling(x,y)s
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Noise Reduction Using Fuzzy Filtering ( N.Baker et al., 2008)
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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:
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Noise Reduction Using Fuzzy Filtering ( N.Baker et al., 2008)
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Edge
DetectionFiltering
Post-Processing
Averaging
& Rescaling(x,y)s
Separating Noise from Edges
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Noise Reduction Using Fuzzy Filtering ( N.Baker et al., 2008)
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Edge
DetectionFiltering
Post-Processing
Averaging
& Rescaling(x,y)s
For each direction: if is not edge
Then compute the correction term (s)
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Noise Reduction Using Fuzzy Filtering ( N.Baker et al., 2008)
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Edge
DetectionFiltering
Post-Processing
Averaging
& Rescaling(x,y)
Calculate corrected terms
Adds to pixel luminance value of location (x, y)
s
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Colour Image Noise Reduction Using Fuzzy
Filtering ( N. Baker et al., 2008)
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Image Segmentation
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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
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Linear VS. Fuzzy Segmentation
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Region is assigned to a fuzzy
set of labels:{rock/0.89,sand/0.46}
Sea segments
are mergedcorrectly
Oversegmentation
Undersegmentation
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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
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Fuzzy Rule-Based Segmentation
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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.
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A comparison between fuzzy and Otsu thresholding
algorithm
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Test Image
Thresholded by fuzzy method Thresholded by Otsu algorithm
Fuzzy Thresholding
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Use to measure the geometrical fuzziness of different
regions of an image:
Fuzzy Area
Fuzzy Perimeter
Fuzzy compactness
Fuzzy Geometry
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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
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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
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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
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Sky
Sky
Fog
Mountain
Mountain
Mountain
Field
Field
FieldField
Field
RoofWall
Sky
Mountain
Field
House
Fuzzy Region Labeling
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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.
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Thank You
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References
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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
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References
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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.
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References
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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.
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References
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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
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References
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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
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A New Fuzzy Edge Detection Method for Image Enhancement , FU
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References
13. Han-Pang Huang, Yi-Hung Liu, Li-Wei Liu, Chun-Shin Wong
Applications of Advanced Fuzzy Logic Techniques in Fuzzy Image
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A New Fuzzy Logic Filter for Image Enhancement, IEEE
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