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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
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
NN: Role of Sigmoid Fns
Binary 3x3 Prototypes
8 non-central locations 28 /2 = 128
Sobel Edge Detector
Assigns numeric value 0 -1 to each pixel in image
Usually thresholded at about 0.65
Natural “edgedness” membership fn
Bezdek et al
Neural-fuzzy edge detector
Train NN to give same values as Sobel for ALL (=128) binary prototypes
Good results
Harvey A Cohen
Achan (Software) Pty Ltd.
Bezdek Fuzzy- Neural Sobel
Cohen-McKinnon FuzzyNN Sobel
512 (!) 3x3 binary exemplars NN trained 2 min f0r Sobel
225 5x5 binary exemplars
NN training will take
45 days
no possible application to large scale features as in biology
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
One idea – in previous paper (DICTA NZ 1997) – score to
crisp values: speeds up computation greatly, yet has
similar output for fuzzy neural 3x3.
Train on small number of super quality artificial (=binary)
exemplars plus 1000
scored ‘natural’ examples
5x5 exemplars for Plessy
Around Harvey
Eclipse over Africa
Frames from MeteoSat6, June 21, 2001
