Image Negative
Image Negative
• There are a number of applications in which negative of the digital images are quite useful. Such as displaying
of medical images and photographing a screen with monochrome positive film with an idea of using the
resulting negatives as normal slides.
• The negative of the digital image is obtained by using the transformation function s = T(r), and it is shown in
Figure.
• In the above figure L is the number of gray levels. The idea behind is to reverse the order from black to white
so that the intensity of the output image decreases as the intensity of the input increases.
Contrast Stretching
During image acquisition low contrast images may be captured due
to any one of the following reasons
1. Poor Illumination
2. Lack of dynamic range in the image sensor
3. Wrong setting of the lens aperture.
The idea behind contrast stretching is to increase the dynamic range of gray
levels in the image being processed. Figure shows a typical transformation
function used for contrast stretching.
Linear function
• From the Figure r1 =s1, r2 = s2; r3 =s3
linearly proportional so both are same.
• s-processed image r-original image this
kind of transform is called linear
function.
Transfer function
• From the Figure the location of the
points (r1, s1) and (r2, s2) control the
shape of the transformation function.
• If r1 = r2, s1 = 0 and s2 = L – 1 the
transformation
becomes
the
thresholding function and creates a
binary
image.
This
kind
of
transformation is called thresholding
function.
Transformation function
• Intermediate values of r1, s1 and r2, s2
produces various degree of spread in the gray
levels at the output image, thus affecting its
contrast shown in Figure
Contrast stretching is obtained by setting
(r1, s1) = (rmin, 0)
(r2, s2) = (rmax, L–1)
rmax = maximum gray level
rmin = minimum gray level
Thresholding
Gray level Slicing
• An enhancement technique in which
all the gray levels in the range of
interest are displayed using high
values and all other gray levels are
displayed using low gray levels.
• In the first approach, all the gray
levels in the range of interest are
displayed using low values. The
corresponding
transformation
function used is shown in Figure and
this results in a binary image.
• The second approach is based
on transformation function
shown in Figure. This transfer
function brightens the desired
range of gray levels but
preserves the background and
the gray level tonalities in the
image.
Bit plane slicing
Histogram based Enhancement
Histogram of an image represents the relative frequency of occurrence of various
gray levels in the image
3000
2500
2000
1500
1000
500
0
0
50
100
150
200
19
Histogram Equalization
• Histogram of a digital image is the probability of occurrence associated with the
gray levels in the range 0 to 255.
• Histogram can be expressed using discrete function as
• Where rk is the kth gray level, nk is the number of pixels in the image with that
gray level, n is the total number of pixels in the image and k = 0, 1, 2, ……. 255.
• In general P(rk) gives an estimate of the probability of occurrence of gray level rk.
The plot of P(rk) for all values of k is called histogram of the image and it gives a
global description of the appearance of an image.
Histogram Equalization
• Let r be the variable representing the gray levels in the image to be enhanced.
Assume that the gray levels in this image after normalization are in the range from
0 to 1. For any value of r in the original image in the internal (0, 1) the
transformation is the form s = T(r)
• Which produce a level s for every pixel value r in the original image. It is assumed
that the transformation function given in equation satisfies the conclusion.
Histogram Equalization
• Image Addition
• Image addition refers to addition of two or more images. It is used in image enhancement and segmentation
Image Subtraction
• Image subtraction plays a vital role in medical applications. The difference between two images
f(x, y) and h(x, y) is expressed as g(x, y) = f(x, y) – h(x, y)
Image Averaging
• Consider a noisy image z(x, y) obtained by adding the noise term ɳ(x, y) to the original image f(x, y).
z(x, y) = f(x, y) + ɳ(x, y)
• where f(x, y) = original image ɳ(x, y) = noise
• g(x, y) is a noise image. g(x, y) is obtained by adding the noise term ɳ(x, y) to the original image f(x, y). The
noise term ɳ(x, y) is considered as a random phenomenon and it is correlated; so the average value of the
noise results in a zero value.
Illustration of Spatial filtering
7
9
11
10
50
8
9
5
6
Original Image
1/9
1
1
1
1
1
1
1
1
1
3 x 3 Averaging
Mask
0
0
0
0
0
7
9
11
0
0
10
50
8
0
0
9
5
0
0
0
0
6
0
Input Image after zero padding
0
0
Movement of Spatial Mask
1/9
1/9
1/9
1/9
1/9
1/9
1/9
1/9
1/9
1/9
0
1/9
0
1/9
0
0
0
1/9
0
1/9
7
1/9
9
11
0
1/9
0
1/9
10
1/9
50
8
0
0
9
5
6
0
0
0
0
0
0
0 x 1/9 + 0 x 1/9 + 0 x 1/9 + 0 x 1/9 + 7 x 1/9 + 9 x 1/9 + 0 x 1/9 + 10 x 1/9 + 50 x 1/9
= 8.4
Movement of Spatial Mask (Cont..)
1/9
0
1/9
1/9
0
1/9
1/9
0
1/9
0
0
1/9
0
1/9
1/9
8.4
1/9
1/9
9
1/9
11
0
1/9
0
1/9
1/9
10
1/9
1/9
50
1/9
8
0
0
9
5
6
0
0
0
0
0
0
0 x 1/9 + 0 x 1/9 + 0 x 1/9+ 8.4 x 1/9 + 9 x 1/9 + 11 x 1/9 +10 x 1/9 +50 x 1/9 + 8 x 1/9
= 10.7
Movement of Spatial Mask (Cont..)
0
1/9
0
1/9
1/9
0
1/9
1/9
0
1/9
0
0
1/9
8.4
1/9
1/9
10.7
1/9
1/9
11
1/9
0
0
1/9
10
1/9
1/9
50
1/9
1/9
8
1/9
0
0
9
5
6
0
0
0
0
0
0
0 x 1/9 + 0 x 1/9 + 0 x 1/9+10.7 x 1/9 +11 x 1/9 + 0 x 1/9 + 50 x 1/9 + 8 x 1/9 + 0 x 1/9
= 8.8
Movement of Spatial Mask (Cont..)
1/9
0
1/9
0
1/9
0
0
0
1/9
0
1/9
8.4
1/9
1/9
10.7
1/9
8.8
1/9
0
1/9
0
1/9
10
1/9
1/9
50
1/9
8
1/9
0
1/9
0
1/9
9
1/9
5
6
0
0
0
0
0
0
0 x 1/9 + 8.4 x 1/9 +10.7 x 1/9 + 0 x 1/9 +10 x 1/9 + 50 x 1/9 + 0 x 1/9 + 9 x 1/9 + 5 x 1/9
= 10.3
Movement of Spatial Mask (Cont..)
0
0
1/9
0
1/9
1/9
8.4
1/9
0
1/9
0
0
0
0
0
1/9
1/9
10.7
1/9
8.8
0
1/9
1/9
10.3
1/9
1/9
50
1/9
8
0
1/9
1/9
9
1/9
1/9
5
1/9
6
0
0
0
0
0
8.4 x 1/9+ 10.7 x 1/9+ 8.8 x 1/9 +10.3 x 1/9 + 50 x 1/9+8 x 1/9 + 9 x 1/9 +5 x 1/9 + 6 x 1/9
= 12.9
Movement of Spatial Mask (Cont..)
0
0
0
0
0
0
1/9
8.4
1/9
1/9
10.7
1/9
1/9
8.8
1/9
0
0
1/9
10.3
1/9
1/9
12.9
1/9
1/9
8
1/9
0
0
1/9
9
1/9
1/9
5
1/9
1/9
6
1/9
0
0
0
0
0
0
10.7 x 1/9 + 8.8 x 1/9 + 0 x 1/9 + 12.9 x 1/9 + 8 x 1/9 + 0 x 1/9 + 5 x 1/9+ 6 x 1/9 + 0 x 1/9
= 5.7
Movement of Spatial Mask (Cont..)
0
0
0
0
0
8.4
1/9
10.7
1/9
8.8
1/9
0
1/9
0
1/9
10.3
1/9
1/9
12.9
1/9
5.7
1/9
0
1/9
0
1/9
9
1/9
1/9
5
1/9
6
1/9
0
1/9
0
1/9
0
1/9
0
0
0
0
0 x 1/9 + 10.3 x 1/9 +12.9 x 1/9 + 0 x 1/9 + 9 x 1/9 + 5 x 1/9 + 0 x 1/9 + 0x 1/9 + 0 x 1/9
= 4.1
Movement of Spatial Mask (Cont..)
0
0
0
0
0
0
8.4
10.7
8.8
0
1/9
0
1/9
10.3
1/9
1/9
12.9
1/9
5.7
0
1/9
0
1/9
4.1
1/9
5
1/9
6
0
1/9
0
1/9
0
1/9
0
1/9
0
0
10.3 x 1/9 +12.9 x 1/9 + 5.7x 1/9 + 4.1 x 1/9 + 5 x 1/9 + 6 x 1/9 + 0 x 1/9 + 0 x 1/9 + 0 x 1/9
= 4.6
Movement of Spatial Mask (Cont..)
0
0
0
0
0
0
8.4
10.7
8.8
0
0
1/9
10.3
1/9
12.9
1/9
1/9
5.7
1/9
0
0
1/9
4.1
1/9
4.6
1/9
6
1/9
0
0
1/9
0
1/9
0
1/9
0
1/9
0
12.9 x 1/9 + 5.7 x 1/9 + 0 x 1/9 + 4.6 x 1/9 + 6 x 1/9+ 0 x 1/9 + 0 x 1/9 + 0 x 1/9 + 0 x 1/9
= 3.2
Movement of Spatial Mask (Cont..)
0
0
0
0
0
0
8.4
10.7
8.8
0
0
10.3
12.9
5.7
0
0
4.1
4.6
3.2
0
0
0
0
0
0
Result of Averaging filter
7
9
11
8.4
10.7
10
50
8
10.3
12.9
5.7
9
5
6
4.1
4.6
3.2
Original Image
8.8
Image after Spatial Averaging
Smoothing Filters
• Smoothing filters are used for blurring and noise reduction. Noise reduction can be accomplished by blurring
with a linear filter by a nonlinear filter. Two types of smoothing filters are spatial LPF and Median Filter.
• Low Pass Spatial Filters
• The Low Pass Spatial Filters are used to reduce the noise such as bridging of small gaps in the lines or curves
in a given image. The spectrum of the spatial Low Pass Filter is shown in Figure
3 X3 Low pass spatial mask
Median Filter
Sharpening Filters
• The principal objective of sharpening Filter is to highlight fi ne details
and enhance edge (sharp) details. Sharpening Filters are divided into
three types.
• They are
• Spatial HPF,
• High Boost Filter and
• Derivative Filter.
High Pass Spatial Filter
• The High Pass Spatial Filter attenuates low frequency components heavily and pass the
high frequency components. This results in an image with sharp details such as edges and
high contrast. Additionally, HPF can provide more visible details that are obscured, hazy
and of poor focus in the original image. Spatial HPF response is shown in Figure.
The center of the mask has a positive value and all its neighbour
coefficients have negative values.
The center pixel has the gray level of 200 and the remaining pixels have gray level
of 10, then the corresponding response of the mask is given as