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Fuzzy Medical Image Segmentation

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

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  1. Fuzzy Medical Image Segmentation Presentation-I for Pattern Recognition Class Mohammed Jirari

  2. Fuzzy Logic • Fuzzy Logic Definition: A branch of logic that uses degrees of membership in sets rather than a strict true/false membership.

  3. 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.

  4. 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

  5. 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 1 0 60 d 68 d 76 d Cold Warm Hot

  6. 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) 1 0 60 d 68 d 76 d Cold Nice Warm Hot

  7. 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

  8. 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.

  9. 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

  10. 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

  11. 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

  12. 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

  13. 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

  14. 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

  15. 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

  16. 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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