05 pixel connectivity b

Khawar Khurshid, 20121

Advanced Digital Image Processing

Pixel Connectivity



(X,Y) (X+1,Y)

(X,Y‐1)

(X‐1,Y)

(X,Y+1)

(X+1,Y‐1)(X‐1,Y‐1)

(X+1,Y+1)(X‐1,Y+1)

Neighbors of pixel are the pixels that are adjacent to the identified pixel.

Pixel Neighborhood

(4 Connectivity)

(Diagonal Pixels)

(8 Connectivity)

City Block Distance – D4

Chess Board Distance – D8

Euclidean Distance - DE

Distance Measures


We can divide distance between pixels in following categories


Distance Measures

City block distance (D4 distance)

0 11

1

12

22

2

4 ( , )D p q x s y t


Distance Measures

Euclidean Distance

2 2( , ) ( ) ( )eD p q x s y t

p(x,y)

q(s,t)

D = {(1‐4)^2 + (1‐4)^2}^0.5

D = 4.24


Distance Measures

Chessboard distance (D8 distance)

0

111

1

111

1

22222

2

2

2

2 2 2 2 2

2

2

2

8 ( , ) max( , )D p q x s y t

D8 = D4 U Dd


Distance Measures

Find minimum number of pixels between highlighted pixels using

4 Connectivity ?8 Connectivity ?Euclidean Distance ?

4 connectivity = 12

8 connectivity = 6

Euclidean Distance = 8.05


Distance Measures

Which color is representing 4 connectivity , 8 connectivityor both

Black = 4 & 8 Connectivity

Red = 8 Connectivity

Yellow = 4 & 8 Connectivity

Green = 8 Connectivity

Blue = 4 & 8 Connectivity


Distance Measures

What is result of two Connected D4 objects as whole ?

• Establishing boundaries of objects and components ofregions in an image.

• Group the same region by assumption that the pixelsare of same color or equal intensity

• Two pixels p & q are connected if

– They are adjacent in some sense– If their gray levels satisfy a specified criterion of

similarity

Connectivity


V: Set of gray levels used to define the criterion of similarity

p,q: Pixels being observed

4( , ) , ( )p q V and q N p

Set of gray levels V = {1}Set of gray levels V = {1}

4-Connectivity


V: Set of gray levels used to define the criterion of similarity

P,q: Pixels being observed

Set of gray levels V = {1}Set of gray levels V = {1}

8-Connectivity


8( , ) , ( )p q V and q N p

13

Process the image from left toright, top to bottom:1.) If the next pixel to process is 1

i.) If only one of its neighbors(top or left) is 1, copy its label.

ii.) If both are 1 and have the same label, copy it.

iii.) If they have different labels Copy the label from the left. Update the equivalence table.

iv.) Otherwise, assign a new label.

Re‐label with the smallest of equivalentlabels

Pass 1

Pass 2

4-Connectivity Labeling




1

Table : 1

2 2 2 2 2

2

13 3 3

3

2 2 13 3 2 2 2 2

, 2

3 2 2 222 2 2

4 4 4

4

2

What will be values of table in second scan ?

Background pixel

Unlabeled Pixel

Background pixel

Unlabeled Pixel

Label 1



Background pixel

Unlabeled Pixel

Label 1

Label 2

Background pixel

Unlabeled Pixel

Label 1

Label 2

Label 3



Background pixel

Unlabeled Pixel

Label 1

Label 2

Label 3

Background pixel

Unlabeled Pixel

Label 1

Label 2

Label 3



Background pixel

Label 1

Label 2

Label 3

Unlabeled pixel

Background pixel

Label 1

Label 2

Label 3

Unlabeled pixel



Background pixel

Label 1

Label 2

Label 3

Unlabeled pixel

Label 4

Background pixel

Label 1

Label 2

Label 3

Unlabeled pixel

Label 4



Labeling - Example


Original Image Labeled Objects

21

Labeling - Example


Original Image Labeled Objects

22


EndPixel Connectivity

05 pixel connectivity b

Technology

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