Image Processing Reference

In-Depth Information

Fig. 5.15
Prewitt and Sobel kernels

Fig. 5.16
Sobel kernels applied to an image. Each individual kernel finds edges that the other

does not find. When they are combined a very nice resulting edge is created. Depending on the

application, the threshold value can be manipulated to include or exclude the vaguely defined

edges

are switched, i.e.,
g
x
(x, y)

≈

f(x

−

1
,y)

−

f(x

+

1
,y)
and
g
y
(x, y)

≈

f(x,y

−

1
)

1
)
. Normally the order does not matter as we will see below.

Equation
5.10
is applied to each pixel in the input image. Concretely this is done

using correlation. We correlate the image with a 1

−

f(x,y

+

×

3 kernel containing the fol-

lowing coefficients:

1, 0, 1. Calculating the gradient using this kernel is often too

sensitive to noise in the image and the neighbors are therefore often also included

into the kernel. The most well know kernels for edge detection are illustrated in

Fig.
5.15
:the
Prewitt kernels
and the
Sobel kernels
. The difference is that the Sobel

kernels weight the row and column pixels of the center pixel more than the rest.

Correlating the two Sobel kernels with the image in Fig.
5.11
yields the edge

images in Fig.
5.16
. The image to the left enhances horizontal edges, while the

image to the right enhances vertical edges. To produce the final edge image we use

−