Graphics Reference
In-Depth Information
problem as a clustering problem. Given an image, we therefore try to form
several clusters by assigning each pixel into a cluster. The assignment of a
pixel into a cluster may depend on the image properties. One should keep in
mind, while forming a cluster, that the distance between any two points of a
cluster is smaller compared to the distance between any two points of different
clusters. A cluster can be thought of as an image region.
2.2.1 Contour-based Segmentation
Contours or edges are the line segments (curved or straight) that separate one
region from the other. Therefore, an edge detection technique can be used for
segmentation. One of the major drawbacks of this segmentation technique
is that it does not provide any guarantee for connected edges. However, we
can use an edge linking algorithm to connect fragmented edges. Since edge
is a feature of an image, edge-based or contour-based segmentation can also
be thought of as a feature-based segmentation. Different techniques for edge
detection are already in use.
Gradient Operator
The simplest edge detect
ion proc
edure is the gradient operator. The mag-
nitude of the gradient
∂
∂x
+
∂
∂y
can be used to locate the edge pixels. On
the edges, values of the gradient magnitude are high, while in object and
background regions, it is low.
The Laplacian Operator
∂
2
f
∂
2
x
+
∂
2
f
The Laplacian operator over an image
f
(
x, y
) is given by
∂
2
y
. Edges
are located at pixels where the Laplacian changes its sign.
Laplacian of Gaussian Operator
Marr and Hildreth [119] suggested the Laplacian of the Gaussian operator for
edge detection. The Gaussian, G(x,y) is given by
1
x
2
+
y
2
2
σ
2
2
πσ
2
e
−
G
(
x, y
)=
.
Laplacian of Gaussian is, therefore
x
2
+
y
2
2
πσ
2
1
2
πσ
4
(2
x
2
+
y
2
2
σ
2
2
G
=
)
e
−
∇
−
−
.
(2.1)
They developed a refined approach considering difference of Gaussian opera-
tor, given by
x
2
2
σ
2
y
2
2
σ
2
1
2
πσ
1
1
2
πσ
2
e
−
e
−
DOG
(
σ
1
,σ
2
)=
1
+
2
.
(2.2)
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