Fuzzy Techniques for Image Segmentation Outline ... - SSIP-2013
Fuzzy Techniques for Image Segmentation Outline ... - SSIP-2013
Fuzzy Techniques for Image Segmentation Outline ... - SSIP-2013
Create successful ePaper yourself
Turn your PDF publications into a flip-book with our unique Google optimized e-Paper software.
<strong>Fuzzy</strong><br />
<strong>Techniques</strong> <strong>for</strong><br />
<strong>Image</strong><br />
<strong>Segmentation</strong><br />
László G. Nyúl<br />
Let X be the universal set.<br />
<strong>Fuzzy</strong> set<br />
<strong>Fuzzy</strong><br />
<strong>Techniques</strong> <strong>for</strong><br />
<strong>Image</strong><br />
<strong>Segmentation</strong><br />
László G. Nyúl<br />
Probability vs.<br />
grade of membership<br />
<strong>Outline</strong><br />
<strong>Fuzzy</strong> systems<br />
<strong>Fuzzy</strong> sets<br />
<strong>Fuzzy</strong> image<br />
processing<br />
<strong>Fuzzy</strong><br />
connectedness<br />
For (sub)set A of X<br />
µ A (x) =<br />
{<br />
1 if x ∈ A<br />
0 if x ∉ A<br />
For crisp sets µ A is called the characteristic function of A.<br />
<strong>Outline</strong><br />
<strong>Fuzzy</strong> systems<br />
<strong>Fuzzy</strong> sets<br />
<strong>Fuzzy</strong> image<br />
processing<br />
<strong>Fuzzy</strong><br />
connectedness<br />
Probablility<br />
• is concerned with occurence of events<br />
• represent uncertainty<br />
• probability density functions<br />
Compute the probability that an ill-known variable x of the<br />
universal set U falls in the well-known set A.<br />
A fuzzy subset A of X is<br />
<strong>Fuzzy</strong> sets<br />
A = {(x,µ A (x)) |x ∈ X }<br />
where µ A is the membership function of A in X<br />
• deal with graduality of concepts<br />
• represent vagueness<br />
• fuzzy membership functions<br />
µ A : X → [0,1]<br />
Compute <strong>for</strong> a well-known variable x of the universal set U to<br />
what degree it is member of the ill-known set A.<br />
<strong>Fuzzy</strong><br />
<strong>Techniques</strong> <strong>for</strong><br />
<strong>Image</strong><br />
<strong>Segmentation</strong><br />
László G. Nyúl<br />
<strong>Outline</strong><br />
Probability vs.<br />
grade of membership<br />
Examples<br />
<strong>Fuzzy</strong><br />
<strong>Techniques</strong> <strong>for</strong><br />
<strong>Image</strong><br />
<strong>Segmentation</strong><br />
László G. Nyúl<br />
<strong>Outline</strong><br />
<strong>Fuzzy</strong> membership functions<br />
<strong>Fuzzy</strong> systems<br />
<strong>Fuzzy</strong> systems<br />
<strong>Fuzzy</strong> sets<br />
<strong>Fuzzy</strong> sets<br />
<strong>Fuzzy</strong> image<br />
processing<br />
<strong>Fuzzy</strong> image<br />
processing<br />
<strong>Fuzzy</strong><br />
connectedness<br />
• This car is between 10 and 15 years old (pure imprecision)<br />
• This car is very big (imprecision & vagueness)<br />
<strong>Fuzzy</strong><br />
connectedness<br />
triangle<br />
trapezoid<br />
• This car was probably made in Germany (uncertainty)<br />
• The image will probably become very dark (uncertainty &<br />
vagueness)<br />
gaussian<br />
singleton
Change language