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Fuzzy Medical Image Segmentation. Presentation-I for Pattern Recognition Class Mohammed Jirari. Fuzzy Logic. Fuzzy Logic Definition: A branch of logic that uses degrees of membership in sets rather than a strict true/false membership. Fuzzy Logic.

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fuzzy medical image segmentation

Fuzzy Medical Image Segmentation

Presentation-I for

Pattern Recognition Class

Mohammed Jirari

fuzzy logic
Fuzzy Logic
  • Fuzzy Logic Definition:

A branch of logic that uses degrees of membership in sets rather than a strict true/false membership.

fuzzy logic3
Fuzzy Logic
  • A tool to represent imprecise, ambiguous, and vague information
  • Its power is the ability to perform meaningful and reasonable operations
  • Fuzzy logic is not logic that is fuzzy -- it is a logic of fuzziness.
  • It extends conventional Boolean logic to recognize partial truths and uncertainties.
linguistic variables
Linguistic Variables
  • Fuzzy logic quantifies and reasons about vague

or fuzzy terms that appear in our natural language

  • Fuzzy Terms are referred to as linguistic variables

Definition: Linguistic Variable

Term used in our natural language to describe some

concept that usually has vague or fuzzy values


Linguistic Variable Typical Values

Temperature hot, cold

Height short, medium, tall

Speed slow, creeping, fast

example of a fuzzy set
Example of a Fuzzy Set
  • The graph shows how one might assign fuzzy values to various temperatures based on 68 degrees = room temp.
  • Climate for a given temperature is defined as:
    • 60d = {1 c, 0 w, 0 h}
    • 68d = {0.5 c, 1 w, 0.5 h}
    • 70d = { 0.15 c, 0.15 w, 0.85 h}
  • Sum of fuzzy values not always 1 -- often it is more than 1



60 d

68 d

76 d




example of a fuzzy set asymmetric version
Example of a Fuzzy Set:Asymmetric Version
  • Fuzzy sets are rarely symmetric.
  • This might be considered by some to be a more accurate description of a room climate:
    • 60d = {1 c, 0 n, 0 w, 0 h}
    • 68d = {0.5 c, 1 n, 0.8 w, 0.5 h}
    • 70d = { 0.15 c, 0.7n, 0.95 w, 0.85 h}

Could also be represented as:

WARM = (0/60, .8/68, .95/70)



60 d

68 d

76 d






Short Medium Tall






4 5 6 7

Height in Feet

An individual at 5’5 feet would be said to be a member of “medium” persons with a

membership value of 1, and at the same time, a member of “short” and “tall” persons

with a value of 0.25.

Fuzzy Rule: IF The person’s height is tall

THEN The person’s weight is heavy

A fuzzy rule maps fuzzy sets to fuzzy sets

fuzzy sets
Fuzzy Sets
  • Fuzzy sets are used to provide a more reasonable

interpretation of linguistic variables

  • A fuzzy set assigns membership values between

0 and 1 that reflects more naturally a member’s

association with the set

  • A fuzzy set is an extension of the traditional set theory

That generalizes the membership concept by using the

Membership function that returns a value between

0 and 1 that represents the degree of membership an

object x has to set A.

employing fuzzy rules
Employing Fuzzy Rules
  • Conventional expert system - when a condition becomes true, the rule fires.
  • Fuzzy expert system - if the condition is true to any degree, the rule fires.
    • Example rules:
      • If the room is hot, circulate the air a lot
      • If the room is cool, leave the air alone
      • If the room is cool and moist, circulate the air slightly
fuzzy expert system process
Fuzzy Expert System Process
  • Fuzzification -- convert data to fuzzy sets
  • Inference -- fire the fuzzy rules
  • Composition -- combine all the fuzzy conclusions to a single conclusion
    • Different fuzzy rules might conclude that the air needs different circulation levels
  • Defuzzification -- convert the final fuzzy conclusion back to raw data
fuzzy logic vs probability theory
Fuzzy Logic vs. Probability Theory
  • Probability = likelihood that a future event will occur
    • probability event is in a set
  • Fuzzy Logic = measures ambiguity of event that has already occurred
    • degree of membership in a set
  • Limitations of Fuzzy Logic:
    • Increases complexity of the expert system
      • For large systems, fuzzy logic might be horribly inefficient -- combining with conventional logic is often difficult
    • Validation and verification can be complex
image interpretation
Image Interpretation

The process of labeling image data, typically in the form of image regions or features, with respect to domain knowledge

Centers on the problem of how extracted image features are bound to domain knowledge

All image interpretation methods rely to some extent on image segmentation and feature extraction

image segmentation
Image Segmentation

Boundary-driven methods extract features such as edges, lines,

corners or curves that are typically derived via filtering models

which model or regularize differential operators in various ways

Region-based methods typically involve clustering, region

growing, or statistical models

Methods can be combined into a hierarchical feature

extraction/segmentation model which partitions images into

regions as a function of how these partitions can minimize the

statistical variations within feature regions

seed segmentation
Seed Segmentation

1-Compute the histogram

2-Smooth the histogram by averaging to remove small peaks

3-Identify candidate peaks and valleys

4-Detect good peaks by peakiness test

5-Segment the image using thresholds

6-Apply connected component algorithm

what next
What next?
  • Use fuzzy logic to do segmentation
  • Use fuzzy region growing to do segmentation
  • Compare the results of the two methods
  • Compare results with other non-fuzzy methods