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
−
