2. Hybrid neural- fuzzy analysis Harvey Cohen Achan (Software) harveycohen@aanet.com.au

3. A case study based on edge detection in image processing. continued What is fuzzy-neural PR ? Approach of Bezdek How to go beyond Thoughts for future

4. Fuzzy V Neural Membership fns = a priori probability Rules for combining Predictions after defuzzification NN with hidden layers Trained on prototypes Sigmoids Outputs perhaps fuzzy

5. NN: Role of Sigmoid Fns

6. Binary 3x3 Prototypes 8 non-central locations 2 8 / 2 = 128

7. Sobel Edge Detector Assigns numeric value 0 -1 to each pixel in image Usually thresholded at about 0.65 Natural “edgedness” membership fn

8. Bezdek et al Neural-fuzzy edge detector Train NN to give same values as Sobel for ALL (=128) binary prototypes Good results

10. Harvey A Cohen

11. Achan (Software) Pty Ltd.

12. Bezdek Fuzzy- Neural Sobel

13. Cohen-McKinnon FuzzyNN Sobel

14. 512 (!) 3x3 binary exemplars NN trained 2 min f0r Sobel 2 25 5x5 binary exemplars NN training will take 45 days  no possible application to large scale features as in biology

15. But worse – have assumed N linearity – On 3x3 Sobel scores have only 4 values, but larger scale operators have many values in range 0..1

16. One idea – in previous paper (DICTA NZ 1997) – score to crisp values: speeds up computation greatly, yet has similar output for fuzzy neural 3x3.

18. Train on small number of super quality artificial (=binary) exemplars plus 1000 scored ‘natural’ examples

20. 5x5 exemplars for Plessy

23. Around Harvey

24. Eclipse over Africa Frames from MeteoSat6, June 21, 2001