1. IMAGE SEGMENTATION – CONNECTED COMPONENT LABELING
Segmentation can be viewed as a process of pixel classification; the image is segmented into objects or regions by assigning individual pixels to classes.
Connected Component Labeling assigns pixels to specific classes by verifying if an adjoining pixel (i.e., neighboring pixel) already belongs to that class.
There are two “standard” definitions of pixel connectivity: 4 neighbor connectivity and 8 neighbor connectivity.

2. IMAGE SEGMENTATION – CONNECTED COMPONENT LABELING
4 Neighbor Connectivity
8 Neighbor Connectivity
Pi,j
Pi,j

3. CONNECTED COMPONENT LABELING: FIRST PASS
EQUIVALENCE:
B=C A A A B B C C B B B C C B B B B B B

4. CONNECTED COMPONENT LABELING: SECOND PASS
TWO OBJECTS! A A A B B C B B C B B B B C B C B B B B B B

5. CONNECTED COMPONENT LABELING: EXAMPLE (DEMO)

6. CONNECTED COMPONENT LABELING: TABLE OF EQUIVALENCES2 = 5 16 27 50 81
112
127 9 28 39 86
134 34 51
137 10 37 87
138 46
111 66
113 12 40 41 72
119
120 18 76 23
122

7. CONNECTED COMPONENT LABELING: TABLE OF EQUIVALENCES2 = 5 37 86
111
138 9 39 87 10 40 41
112 12 46
113 16 50
119 18 51
120 23 66
122 27 72
127 28 76
134 34 81
137

8. Basic Connected Component Labeling
Binary Image with Background=0, Objects=1
x =

9. Basic Connected Component Labeling
Binary Image with Background=0, Objects=1
x(1,:)=0;
x(:,1)=0;
imshow(x,[0 1]);
K=1;
cnt=2;
for J=2:H
for I=2:W
if x(J,I)== %% Object found
if (x(J-1,I)==0 && x(J,I-1)==0)
x(J,I)=cnt; %% New Object
cnt=cnt+1;
else
if x(J-1,I)~=0
x(J,I)=x(J-1,I);
if (x(J,I-1)~=0) && (x(J,I-1)~=x(J-1,I))
eq(K,1)=x(J-1,I);
eq(K,2)=x(J,I-1);
K=K+1;
end;
x(J,I)=x(J,I-1);
end

10. Basic Connected Component Labeling
eq =
Basic Connected Component Labeling
First Pass
x =

11. Connected Component Labeling with Line Correction
Binary Image with Background=0, Objects=1
x =

12. Connected Component Labeling with Line Correction
Binary Image with Background=0, Objects=1
if (x(J-1,I)==0 && x(J,I-1)==0)
x(J,I)=cnt; %% New Object
cnt=cnt+1;
S=I;
else
if x(J-1,I)~=0
x(J,I)=x(J-1,I);
if (x(J,I-1)~=0) && (x(J,I-1)~=x(J-1,I))
if S>0
for R=I:-1:S
x(J,R)=x(J-1,I);
end;
S=0;
cnt=cnt-1;
eq(K,1)=x(J-1,I);
eq(K,2)=x(J,I-1);
K=K+1;
end
x(J,I)=x(J,I-1);
x(1,:)=0;
x(:,1)=0;
imshow(x,[0 1]);
K=1;
cnt=2;
for J=2:H
S=0;
for I=2:W
if x(J,I)== %% Object found

13. Connected Component Labeling with Line Correction
First Pass
x =

14. Basic Connected Component Labeling
Binary Image with Background=0, Objects=1
x =

15. Basic Connected Component Labeling
First Pass
x =
eq =

16. Connected Component Labeling with Line Correction
Binary Image with Background=0, Objects=1
x =

17. Connected Component Labeling with Line Correction
First Pass
x =
eq =