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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
• 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
• 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
Examples:
Linguistic Variable          Typical Values
Temperature                  hot, cold
Height                       short, medium, tall
Speed                        slow, creeping, fast
             Example of a Fuzzy Set

• The graph shows how one
  might assign fuzzy values to
  various temperatures based on     1
  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}                      0
• Sum of fuzzy values not always
                                        60 d           68 d   76 d
  1 -- often it is more than 1
                                               Cold   Warm    Hot
             Example of a Fuzzy Set:
              Asymmetric Version
• Fuzzy sets are rarely
  symmetric.
• This might be considered by      1
  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}
                                   0
Could also be represented as:
                                       60 d                 68 d          76 d
WARM = (0/60, .8/68, .95/70)                  Cold   Nice          Warm   Hot
                          Short       Medium           Tall
                 1
Membership
  Value         0.5


                 0
                      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 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
• 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
• 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
• 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
                 Weaknesses
• 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
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
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
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?
• 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

				
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