1. Image Thresholding Using Type II Fuzzy Sets Source ： 2005, Pattern Recognition 38, 2363-2372 Author ： Hamid R. Tizhoosh Advisor: Chen R. -C. Ph. D( 陳榮昌教授 ) Speaker: Ma Tsung-han( 馬宗瀚 _9514623 ) Date: 2007/01/19 利用類型二的模糊集合之影像門檻值技術

2. Type II fuzzy sets2 Outline Introduction Type II fuzzy sets Proposed method Experimental results Conclusions Comments

3. Type II fuzzy sets3 Introduction(1/6) The of purpose of thresholding: Gray-level images ( 灰階影像 ) 0~255 Binary images ( 二值影像 ) [1, 0] Threshold ( 門檻值 ) Feature extraction Object recognition

4. Type II fuzzy sets4 Introduction(2/6) Thresholding Gray-level > Threshold= White( 白色 ) Gray-level < Threshold= Black( 黑色 ) Uses the fuzzy theory to decide the proper threshold.

5. Type II fuzzy sets5 Introduction(3/6) Why uses the fuzzy theory in thresholding Non-uniform illumination Inherent image vagueness The result of image thresholding isn’t always satisfactory. To Remove the grayness ambiguity/vagueness during the task of threshold selection.

6. Type II fuzzy sets6 Introduction(4/6) What fuzzy theory be used in this paper Type II fuzzy sets Also called 「 ultrafuzzy sets 」 Regard thresholds as type II fuzzy sets 類型二模糊集合 超模糊集合

7. Type II fuzzy sets7 Introduction(5/6) The concept of ultrafuzziness(Type II) focuses on capture/elimination the uncertainties( 不確定性 ) whin fuzzy systems using regular fuzzy sets(Type I).

8. Type II fuzzy sets8 Introduction(6/6) Four approaches exploit fuzzy algorithms in image thresholding: Fuzzy clustering( 模糊群聚 ) Rule-based approach( 以規則為主方法 ) Fuzzy-geometrical approach( 幾何模糊方法 ) Information-theoretical approach( 資訊推理方法 ) It’s simple and high speed. Therefore, this approach is the most used.

9. Type II fuzzy sets9 Type II fuzzy sets(1/7) The general algorithm for image thresholding bas ed on measures of fuzziness: (1) Select the shape of the membership function. (2) Select a suitable measure of fuzziness (e.g. Eq. (1)). (3) Calculate the image histogram. (4) Initialize the position of the membership function. (5) Shift the membership function along the gray-level range and calculate in each position the amount of fuzziness, for instance using Eq. (1). (6) Locate the position gopt with maximum fuzziness. (7) Thresholdthe image with T = gopt.

10. Type II fuzzy sets10 Type II fuzzy sets(2/7) The most common measure of fuzziness( 模 糊性 / 數 / 度 ) is the linear index of fuzziness. (1) Where A is a M x N image subset, and with L gray levels, h(g) stands for the histogram, stands for the membership function( 隸屬函數 )

11. Type II fuzzy sets11 Type II fuzzy sets(3/7) gray-level range and distribution.

12. Type II fuzzy sets12 Type II fuzzy sets(4/7) Type I fuzzy sets: the assignment of a member- ship degree to an element/pixel is not certain. In order to find a more robust solution, type II fuzzy sets should be proposed. The major motivation of this work to remove the uncertainty( 不確定性 ) of membership values by using type II fuzzy sets.

13. Type II fuzzy sets13 Type II fuzzy sets(5/7) Type II sets are able to model such uncertainty because their membership functions are fuzzy. Footprint of uncertainty

14. Type II fuzzy sets14 Type II fuzzy sets(6/7) The more practical definition of a type II fuzzy set can be given as follows: The lower and upper membership degrees The initial(skeleton) membership function μ can be defined by means of linguistic hedges like dilation and concentration:

15. Type II fuzzy sets15 Type II fuzzy sets(7/7) A measure of ultrafuzziness can be defined as follows: For an M x N image subset with L gray levels. h(g) reprensents the Histogram. Where

16. Type II fuzzy sets16 Proposed method The general algorithm for image thresholding based on type II fuzzy sets and measures of ultrafuzziness can be formulated as follows: (1)Select the shape of skeleton membership function μ(g) and initialize α. (2) Calculate the image histogram. (3) Initialize the position of the membership function.

17. Type II fuzzy sets17 Proposed method(cont.) (4) Shift the membership function along the gray-level range. (5) Calculate in each position the upper and lower membership values μ U(g) and μL(g). (6) Calculate in each position the amount of ultrafuzziness. (7) Find out the position g opt with maximum ultrafuzziness. (8) Threshold the image with T = g opt.

18. Type II fuzzy sets18 Experimental results

19. Type II fuzzy sets19 Conclusions Fuzzy set theory provides us with knowledge- based and robust tools for developing new thresholding techniques. Can receive the precise image. The usefulness of type II fuzzy sets using in image thresholding is superior to the other methods.

20. Type II fuzzy sets20 Comments The experimental results should be compared with non-fuzzy techniques. The proposed method is beneficial for image processing applications, such as detection of edges, pattern recognition, extra- ction of ROI, etc.

21. Type II fuzzy sets21 Q & A Thanks for your listening