2. 56
Spatial domain: Image Enhancement
Three basic type of functions are used for image enhancement. image
enhancement point processing techniques:
Linear ( Negative image and Identity transformations) Logarithmic transformation
(log and inverse log transformations) Power law transforms (nth power and nth
root transformations) Grey level slicing
Bit plane slicing
We are dealing now with image processing methods that are based only on the
intensity of single pixels.
Intensity transformations (Gray level transformations)
Linear function Negative and identity Transformations
Logarithm function
Log and inverse-log transformation Power-law
function
nth power and nth root transformations
3. Image Negatives
Here, we consider that the digital image that we are considering
that will have capital L number of intensity levels represented
from 0 to capital L minus 1 in steps of 1.
The negative of a digital image is obtained by the transformation
function
sT(r)L1r
57
4. Logarithmic Transformations
The general form of the log transformation is s
= c * log (1 + r)
C is a constant and r is assumed to be ≥ 0
The log transformation maps a narrow range of low input grey level
values I nto a wider range of output values. The inverse log
transformation
performs the opposite transformation s = log(1 + r)
We usually set c to 1. Grey levels must be in the range [0.0, 1.0]
Identity Function
Output intensities are identical to input intensities.
Is included in the graph only for completeness
Power Law Transformations Why power laws are popular?
58
Viewing images properly on monitors requires γ‐
correction
Power law transformations have the following form s =
c
* r γ c and γ are positive constants
s = r γ
We usually set c to 1. Grey levels must be in the range [0.0,
1.0]
improvements
s = c (r+ ϵ) γ , and this offset is to provide a
measurable
Gamma correction is used for
display Some times it is also
written as output even when
input values are zero
6. Effect of decreasing gamma
When the γ is reduced too much, the image begins to reduce contrast to the point where the image
started to have very slight “wash-out” look, especially in the background
a) image has a
washed-
out
appearance, it needs
a
61
of
gray
compressio
n levels
needs γ > 1
(b)result
after
transformati
on 3.0
(suitable)
power-
law with
γ =
(c)transformation with γ
= 4.0
(suitable)
(d)transformation with
γ
= 5.0
(high contrast, the
image has areas
that are too
dark,
some detail is lost)
8. 63
Piecewise Linear Transformation Functions
Piecewise functions can be arbitrarily complex
•A disadvantage is that their specification requires significant user input
•Example functions :
–Contrast stretching
–Intensity-level slicing
–Bit-plane slicing
Contrast Stretching
Low contrast images occur often due to poor or non uniform lighting conditions, or due to
nonlinearity,
or small dynamic range of the imaging sensor.
Purpose of contrast stretching is to process such images so that the dynamic range of the
image will be very high, so that different details in the objects present in the image will be
clearly visible. Contrast stretching process expands dynamic range of intensity levels in an
image so that it spans the full intensity range of the recording medium or display devices.
9. Control points (r1,s1) and (r2,s2) control the shape of the transform T(r)
•if r1=s1 and r2=s2, the transformation is linear and produce no
changes in
intensity levels
•r1=r2, s1=0 and s2=L-1 yields a thresholding function that creates a
binary image
•Intermediate values of (r1,s1) and (r2,s2) produce various degrees of
spread in the intensity levels
In general, r1 r2
≤ and s1≤ s2 is assumed so that the junction is
single
valued and monotonically increasing.
If (r1,s1)=(rmin,0) and (r2,s2)=(rmax,L-1), where rmin and r max
are minimum and maximum levels in the image. The
transformation stretches the levels linearly from their original range to
the full range (0,L-1)
64
10. Two common approaches
– Set all pixel values within a range of
interest to one value (white) and all
others to another value (black)
•Produces a binary image
That means, Display high value for
range of interest, else low value
(„discard background )
‟
– Brighten (or darken) pixel values in a
range of interest and leave all others
Unchanged. That means , Display high
value for range of interest, else original
value („preserve background )
‟
65
11. Bit Plane Slicing
Only by isolating particular bits of the pixel values in a image we can highlight interesting aspects
of that image.
High order bits contain most of the significant visual information Lower bits contain subtle details
Reconstruction is obtained
by:
N
66
I (i, j) 2
In(i,
j)
n1
n0t1o127 can be
mapped
a0s, 128 to 256 can
be
mapped as 1
For an 8 bit image,
the above forms a binary
image. This occupies
less storage space.
12. Image Dynamic Range, Brightness and Control
The dynamic range of an image is the exact subset of gray values ( 0,1,2, L-1) that are present
in the image. The image histogram gives a clear indication on its dynamic range.
When the dynamic range of the image is concentrated on the lower side of the gray scale, the
image will be dark image.
When the dynamic range of an image is biased towards the high side of the gray scale,
the
image will be bright or light image
An image with a low contrast has a dynamic range that will be narrow and
concentrated
to the
middle of the gray scale. The images will have dull or washed out look.
When the dynamic range of the
image is
contrast and the distribution of pixels will
be ne
significantly broad, the image will have a
high
ar un
ifor
m.
67
15. HISTOGRAM EQUALISATION IS NOT ALWAYS DESIRED.
Some applications need a specified histogram to their
requirements This is called histogram specification or histogram
matching
. two-step process
- perform histogram equalization on the image
- perform a gray-level mapping using the inverse of the desired cumulative
histogram
70
17. Addition:
Image averaging will reduce the noise. Images are to be registered before adding.
An important application of image averaging is in the field of astronomy, where
imaging with very low light levels is routine, causing sensor noise frequently to
render single images virtually useless for analysis
g(x, y) = f(x, y)
+
η (x, y)
As K increases, indicate that the variability (noise) of the pixel values at
each location (x, y) decreases
In practice, the images gi(x, y) must be registered (aligned) in order to avoid
the
introduction of blurring and other artifacts in the output image.
72
18. Subtraction
A frequent application of image subtraction is in the enhancement of differences
between images. Black (0 values) in difference image indicate the location
where
there is no difference between the images.
One of the most commercially successful and beneficial uses of image subtraction
is in the area of medical imaging called mask mode radiography
g(x, y) = f(x, y) - h (x, y)
mage of a digital angiography. Live image and mask image with fluid
injected.
Difference will be useful to identify the blocked fine blood vessels.
The difference of two 8 bit images can range from -255 to 255, and the sum of two
mages can range from 0 to 510.
Given and f(x,y) image, f m = f - min (f) which creates an image whose min value is
ero.
s = k [fm / max ( fm) ],
s is a scaled image whose values
of k are 0 to 255. For 8 bit
image
=255,
mask
imag
e
73
an image (taken
after injection of a
contrast medium
(iodine) into the
bloodstream) with
mask
19. AND operation is the set of
coordinates common to
A and B
74
The output pixels belong
to either A or B or Both
Exclusive or: The output pixels
belong to either A or B but not
to Both
The output pixels are set of
elements not in A.All elements in A
become zero and the others to 1All
20. 75
g(x,
y)
f(x, y)
An image multiplication and Division
An image multiplication and Division method is used in shading
correction.
g(x, y) = f(x, y) x h (x, y)
is sensed
image
is perfect
image
h (x, y) is shading function.
If h(x,y) is known, the sensed image can be multiplied with inverse of h(x,y) to
get
f(x,y) that is dividing g(x,y) by h(x,y)
Another use of multiplication is Region Of Interest
(ROI).
Multiplication of a given
There can be
more
image by mask image that has 1s in the ROI and 0s
elsewhere.
than one ROI in the mask image.
![Logarithmic Transformations
The general form of the log transformation is s
= c * log (1 + r)
C is a constant and r is assumed to be ≥ 0
The log transformation maps a narrow range of low input grey level
values I nto a wider range of output values. The inverse log
transformation
performs the opposite transformation s = log(1 + r)
We usually set c to 1. Grey levels must be in the range [0.0, 1.0]
Identity Function
Output intensities are identical to input intensities.
Is included in the graph only for completeness
Power Law Transformations Why power laws are popular?
58
Viewing images properly on monitors requires γ‐
correction
Power law transformations have the following form s =
c
* r γ c and γ are positive constants
s = r γ
We usually set c to 1. Grey levels must be in the range [0.0,
1.0]
improvements
s = c (r+ ϵ) γ , and this offset is to provide a
measurable
Gamma correction is used for
display Some times it is also
written as output even when
input values are zero](https://image.slidesharecdn.com/slide1-250311170013-c1ec1130/85/Image-Processing-Unit-II-Image-Enhancement-discussed-4-320.jpg)
![Subtraction
A frequent application of image subtraction is in the enhancement of differences
between images. Black (0 values) in difference image indicate the location
where
there is no difference between the images.
One of the most commercially successful and beneficial uses of image subtraction
is in the area of medical imaging called mask mode radiography
g(x, y) = f(x, y) - h (x, y)
mage of a digital angiography. Live image and mask image with fluid
injected.
Difference will be useful to identify the blocked fine blood vessels.
The difference of two 8 bit images can range from -255 to 255, and the sum of two
mages can range from 0 to 510.
Given and f(x,y) image, f m = f - min (f) which creates an image whose min value is
ero.
s = k [fm / max ( fm) ],
s is a scaled image whose values
of k are 0 to 255. For 8 bit
image
=255,
mask
imag
e
73
an image (taken
after injection of a
contrast medium
(iodine) into the
bloodstream) with
mask](https://image.slidesharecdn.com/slide1-250311170013-c1ec1130/85/Image-Processing-Unit-II-Image-Enhancement-discussed-18-320.jpg)
