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Digital Image Processing: Labeling Connected Components

This document discusses connected components and labeling in digital image processing. It defines 4-connected and 8-connected adjacency and how they determine connected components. Pixels are considered connected if there exists a path between them consisting of foreground pixels. The number of connected components depends on whether 4-adjacency or 8-adjacency is used. Connected components are also referred to as objects. Regionprops can be used to extract properties of connected components/objects in an image.

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Hung Le Quang
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50 views9 pages

Digital Image Processing: Labeling Connected Components

This document discusses connected components and labeling in digital image processing. It defines 4-connected and 8-connected adjacency and how they determine connected components. Pixels are considered connected if there exists a path between them consisting of foreground pixels. The number of connected components depends on whether 4-adjacency or 8-adjacency is used. Connected components are also referred to as objects. Regionprops can be used to extract properties of connected components/objects in an image.

Uploaded by

Hung Le Quang
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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Digital Image Processing

Labeling Connected Components

PGS.TS. NGUYEN TAN LUY


Course Website: http://www.comp.dit.ie/bmacnamee
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Contents
• The concepts discussed thus far are applicable mostly to
all foreground (or all background) individual pixels and
their immediate neighbors.
• In this section we consider the important "middle ground"
between individual foreground pixels and the set of all
foreground pixels.
• This leads to the notion of connected components, also
referred to as objects in the following discussion.
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Labeling Connected Components
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Labeling Connected Components

N8(p).

N4(p). ND(p).
A pixel p at coordinates (x, y) has
two horizontal and two vertical
neighbors (x + 1, y), (x - 1, y), (x,
y + 1 ), and (x, y - 1), N4(p).
 N8(p) (x+1, y+1), (x + 1, y - 1),
(x - 1, y+1 ), (x - 1, y - 1).

N4(p) N8(p)
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Two pixels p and q are said to be 4-adjacent if 𝑞 ∈ 𝑁4 (𝑝). Similarly, p and q


are said to be 8-adjacent if 𝑞 ∈ 𝑁8 (𝑝). Figures above illustrate these
concepts.

A path between pixels 𝑝1 and 𝑝𝑛 is a sequence of pixels 𝑝1 , 𝑝2 , • • • , 𝑝𝑛−1 ,


𝑝𝑛 , such that 𝑝𝑘 is adjacent to 𝑝𝑘+1 for 1 ≤ 𝑘 < 𝑛. A path can be 4-
connected or 8-connected, depending on the type of adjacency used.

Two foreground pixels p and q are said to be 4-connected if there exists


a 4-connected path between them, consisting entirely of foreground pixels.
They are 8-connected if there exists an 8-connected path between them.
For any foreground pixel, p, the set of all foreground pixels connected to it is
called the connected component containing p.
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Quick Example
A connected component was just
defined in terms of a path, and the
Images taken from Gonzalez & Woods, Digital Image Processing (2002)

definition of a path in turn depends on


the type of adjacency used. This
implies that the nature of a connected
component depends on which form of
adjacency we choose, with 4- and 8-
adjacency being the most common.
Figure on the left illustrates the effect
that adjacency can have on
determining the number of connected
components in an image. Figure (a)
shows a small binary image with four
4-connected components. Figure (b)
shows that choosing 8-adjacency
reduces the number of connected
components to two

a) N4(p) b) N8(p)
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clc
f=im2double(rgb2gray(imread('h6.jpg')));
f=im2bw(f,graythresh(f));
imshow(f)
hold on
[L, n] = bwlabel(f);
for k =1:n
[r, c] = find (L==k) ;
rbar = mean(r) ;
cbar = mean(c) ;
plot ( cbar , rbar , 'Marker' , 'o' , 'MarkerEdgeColor', 'k'
,'MarkerFaceColor' , 'k' , 'MarkerSize', 10 ) ;
plot (cbar, rbar , 'Marker' , '*' , 'MarkerEdgeColor', 'w' ) ;
end h6.jpg
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Function regionprops
D = regionprops ( L , properties)

D i s a structure of length max(L (:))


- properties

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