Fuzzy Techniques for Image Segmentation Outline ... - SSIP-2013
Fuzzy Techniques for Image Segmentation Outline ... - SSIP-2013
Fuzzy Techniques for Image Segmentation Outline ... - SSIP-2013
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<strong>Fuzzy</strong><br />
<strong>Techniques</strong> <strong>for</strong><br />
<strong>Image</strong><br />
<strong>Segmentation</strong><br />
László G. Nyúl<br />
<strong>Fuzzy</strong> connected object<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>Fuzzy</strong> connectedness as<br />
a graph search problem<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 />
Theory<br />
Algorithm<br />
Variants<br />
Applications<br />
The fuzzy κ θ object O θ (o) of C containing o is<br />
{<br />
η(c) if c ∈ O θ (o)<br />
µ Oθ (o)(c) =<br />
0 otherwise<br />
that is<br />
µ Oθ (o)(c) =<br />
{<br />
η(c)<br />
if c ∈ Ω θ (o)<br />
0 otherwise<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 />
Theory<br />
Algorithm<br />
Variants<br />
Applications<br />
• Spels → graph nodes<br />
• Spel faces → graph edges<br />
• <strong>Fuzzy</strong> spel-affinity relation → edge costs<br />
• <strong>Fuzzy</strong> connectedness → all-pairs shortest-path problem<br />
where η assigns an objectness value to each spel perhaps based<br />
on f (c) and µ K (o,c).<br />
• <strong>Fuzzy</strong> connected objects → connected components<br />
<strong>Fuzzy</strong> connected objects are robust to the selection of seeds.<br />
<strong>Fuzzy</strong><br />
<strong>Techniques</strong> <strong>for</strong><br />
<strong>Image</strong><br />
<strong>Segmentation</strong><br />
László G. Nyúl<br />
Computing fuzzy connectedness<br />
Dynamic programming<br />
<strong>Fuzzy</strong><br />
<strong>Techniques</strong> <strong>for</strong><br />
<strong>Image</strong><br />
<strong>Segmentation</strong><br />
László G. Nyúl<br />
Computing fuzzy connectedness<br />
Dynamic programming<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 />
Theory<br />
Algorithm<br />
Variants<br />
Applications<br />
Algorithm<br />
Input: C, o ∈ C, κ<br />
Output: A K-connectivity scene C o = (C o , f o ) of C<br />
Auxiliary data: a queue Q of spels<br />
begin<br />
set all elements of C o to 0 except o which is set to 1<br />
push all spels c ∈ C o such that µ κ (o, c) > 0 to Q<br />
while Q ≠ ∅ do<br />
remove a spel c from Q<br />
f val ← max d∈Co [min(f o (d), µ κ (c, d))]<br />
if f val > f o (c) then<br />
f o (c) ← f val<br />
push all spels e such that µ κ (c, e) > 0<br />
endif<br />
endwhile<br />
end<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 />
Theory<br />
Algorithm<br />
Variants<br />
Applications<br />
Algorithm<br />
Input: C, o ∈ C, κ<br />
Output: A K-connectivity scene C o = (C o , f o ) of C<br />
Auxiliary data: a queue Q of spels<br />
begin<br />
set all elements of C o to 0 except o which is set to 1<br />
push all spels c ∈ C o such that µ κ (o, c) > 0 to Q<br />
while Q ≠ ∅ do<br />
remove a spel c from Q<br />
f val ← max d∈Co [min(f o (d), µ κ (c, d))]<br />
if f val > f o (c) then<br />
f o (c) ← f val<br />
push all spels e such that f val > f o (e)<br />
endif<br />
endwhile<br />
end
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