Image Processing Reference
In-Depth Information
Fig. 4.21
Global automatic thresholding.
To p l e f t
: Input image.
Top right
: Input image thresh-
olded by the value found by Otsu's method.
Bottom left
: Histogram of input image.
Bottom right
:
C(T )
as a function of
T
.Seetext.The
vertical dashed line
illustrates the minimum value, i.e., the
selected threshold value
number of pixels used to calculate it. A very efficient implementation is described
in [14]. The method works very well in situations where two distinct modes are
present in the histogram, see Fig.
4.21
, but it can also produce good results when
the two modes are not so obvious.
σ
1
(T )
σ
2
(T )
C(T )
=
M
1
(T )
·
+
M
2
(T )
·
(4.15)
where
M
1
(T )
is the number of pixels to the left of
T
and
M
2
(T )
is the rest of the
pixels in the image.
σ
1
(T )
and
σ
2
(T )
are the variances of the pixels to the left and
right of
T
, respectively.
Automatic Thresholding: Local Method
In Fig.
4.23
an image with non-even illuminating is shown. The consequence of this
type of illumination is that an object pixel in one part of the image is identical to
a background pixel in another part of the image. The image can therefore not be
thresholded using a single (global) threshold value, see Fig.
4.23
. But if we crop
out a small area of the image and look at the histogram, we can see that two modes
are present and that this image can easily be thresholded, see Fig.
4.22
.Fromthis
follows that thresholding is possible locally, but not globally.
We can view thresholding as a matter of finding object pixels and these are
per definition different from background pixels. So if we had an image of the
background, we could then subtract it from the input image and the object pix-
