Overview of Image Processing
59
o
50
100
150
200
250
Fig. 2.3. Histogram of image shown in Fig. 2.2
nipulation is contrast enhancement. A histogram may be viewed as an approximation to the probability density function (PDF) of a random variable. Each
gray value in the image would then be an instance of a realization of a random
variable. The image, therefore, is a collection of realized values of the random
variable. A histogram thus does not reveal spatial information. Whereas there
is only one histogram corresponding to an image, there may be multiple images corresponding to a given histogram. Suppose we have an image of size
M x N pixels where MN = 256 and there are nk pixels of intensity value k for
k = 0,1, ... ,255. Obviously L nk = MN. Then there are
( MN) (MN - no) .. . (MN - ~ nk)
no
nl
k-O
n254
(2.4)
distinct images with the same histogram. In spite of this limitation, image
histograms turn out to be very useful (Gonzalez and Woods 1992; Richards
and Jia 1999).
Histogram equalization is a common procedure for contrast enhancement.
The process creates a new image whose histogram is nearly flat across all gray
levels. An example is shown in Fig. 2.4 where the top panel shows the original
image along with its histogram and the bottom panel shows resulting image
and histogram after equalization.
There are several objects, for example, the river that is visible in the
histogram-equalized image is not in the original image. The equalization
process is based on transforming the PDF of a continuous random variable to
the uniform distribution. Suppose a random variable x has a PDF fx(x) and
59
o
50
100
150
200
250
Fig. 2.3. Histogram of image shown in Fig. 2.2
nipulation is contrast enhancement. A histogram may be viewed as an approximation to the probability density function (PDF) of a random variable. Each
gray value in the image would then be an instance of a realization of a random
variable. The image, therefore, is a collection of realized values of the random
variable. A histogram thus does not reveal spatial information. Whereas there
is only one histogram corresponding to an image, there may be multiple images corresponding to a given histogram. Suppose we have an image of size
M x N pixels where MN = 256 and there are nk pixels of intensity value k for
k = 0,1, ... ,255. Obviously L nk = MN. Then there are
( MN) (MN - no) .. . (MN - ~ nk)
no
nl
k-O
n254
(2.4)
distinct images with the same histogram. In spite of this limitation, image
histograms turn out to be very useful (Gonzalez and Woods 1992; Richards
and Jia 1999).
Histogram equalization is a common procedure for contrast enhancement.
The process creates a new image whose histogram is nearly flat across all gray
levels. An example is shown in Fig. 2.4 where the top panel shows the original
image along with its histogram and the bottom panel shows resulting image
and histogram after equalization.
There are several objects, for example, the river that is visible in the
histogram-equalized image is not in the original image. The equalization
process is based on transforming the PDF of a continuous random variable to
the uniform distribution. Suppose a random variable x has a PDF fx(x) and