The document discusses digital image processing and is presented by M K Kar of Balasore College of Engineering and Technology. It covers fundamentals of digital image processing including representation of digital images, intensity transformations, spatial filtering, frequency domain representation, and applications in medicine, agriculture, industry and more. Transformation techniques like contrast stretching and histogram equalization are described. Spatial filters like averaging, median and Laplacian filters are covered along with sharpening and smoothing effects.

1. Digital Image Processing
M K Kar
Balasore college of Engineering and Technology
July 12, 2020
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2. Overview
1 Fundamentals of Digital Image Processing
2 Representation of digital image
3 Intensity Transformation
4 Relation between pixels
5 Image Histogram
6 Fundamentals of Spatial Filtering
7 Frequency domain representation
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3. Fundamentals of Digital Image Processing
Image processing involves changing the nature of an image in order to
either
improve its pictorial information for human interpretation.
render it more suitable for autonomous machine perception.
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4. Definitions
An Image may be defined as a two dimensional function f (x, y) where
x and y are spatial coordinates and the amplitude of ’f ’ at any pair of
coordinates (x,y) is called the intensity value or gray level of the
image at that point.
An image is called a digital image when the spatial coordinates x, y
and the intensity value of ’f’ all are finite and discrete quantities.
A digital image is an array of real or complex numbers represented by
a finite number of bits.
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5. Representation of digital image
A digital image is formed by sampling and quantization containing M
rows and N columns.
f (x, y) =





f (0, 0) f (0, 1) . . . f (0, N − 1)
f (1, 0)
...
f (1, 1) · · ·
...
f (1, N − 1)
...
f (M − 1, 0) f (M − 1, 0) · · · f (M − 1, N − 1)





Each element of this matrix is called an image element or picture
element or pixels.
The origin of a digital image is at the top left with the + x axis
extending downward and the + y axis extending to the right.
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6. Representation of digital image
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7. Types of digital image
An Image may be classified in to three types
Color Image
Grey Image
Binary Image
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8. Application
Medicine
Agriculture
Industry
Law enforcement
Entertainment
Weatherforecast
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9. Application
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10. Intensity Transformations
The spatial domain processes can be denoted by the expression
g(x, y) = T[f (x, y)]
where f (x, y) is the input image and g(x, y) is the output image
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11. Image Negatives
The negative of an image with intensity levels in the range [0, L − 1]
is obtained by using the negative transformation, given by the
expression s = (L − 1) − r.
Figure: image negetive
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12. Log Transformations
The general form of log transformation is given by
s = c log(1 + r)
The general form of power law (gamma)transformation is given by
s = crγ
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13. Contrast stretching
Contrast stretching is a process that expands the range of intensity
levels in an image so that it spans the full intensity range of the
recording medium or display device.
The result of contrast stretching is obtained by setting
(r1, s1) = (rmin, 0)
and
(r2, s2) = (rmax, L − 1)
where rmin and rmaxdenote the minimum and maximum intensity
levels in the image respectively.
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14. Contrast stretching
Figure: Original image, Contrast image
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15. Image Histogram
The histogram of a digital image with intensity levels in the range
[0,L-1] is a discrete function h(rk) = nk, where rk is the kth intensity
value and nkis the number of pixels in the image with intensity rk.
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16. Histogram Equalization
The histogram equalization of a digital image with intensity levels in
the range [0, L − 1] is a discrete function sk = T(rk), where rk is the
kth intensity value and nkis the number of pixels in the image with
intensity rk is.
sk = T(rk) = (L − 1)
k
j=0
pr (rj ) =
(L − 1)
MN
k
j=0
(nj )
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17. Histogram Equalization
0
1000
2000
3000
0 100 200
0
2000
4000
0 100 200
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18. Fundamentals of Spatial Filtering
The spatial filter consist of a neighborhood and a predefined
operation that is performed on the image pixels encompassed by the
neighborhood.Filtering creates a new pixel with coordinates equal to
the coordinates of the center of the neighborhood and whose value is
the result of the filtering operation.
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19. Image smoothing using Averaging/Box filter
Replacing the value of every pixel in an image by the average of the
intensity levels in the neighborhood defined by the filter mask, which
results in an image with reduced sharp transitions.
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20. Image smoothing using Median filter
Median filter replaces the value of a pixel by the median of the
intensity values in the neighborhood of that pixel including the
original value of that pixel.
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21. Image sharpening using Laplacian
Laplacian is the simplest isotropic derivative operator(rotation
invarient) which is defined for an image function f (x, y) is given by
2
f =
∂2f
∂x2
+
∂2f
∂y2
.
For any image pixel f (x, y) , the laplacian is given by
2
f (x, y) = f (x+1, y)+f (x−1, y)+f (x, y +1)+f (x, y −1)−4f (x, y)
This equation can be implemented using the filter mask given below


0 1 0
1 −4 1
0 1 0


or 

0 −1 0
−1 4 −1
0 −1 0


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22. Image sharpening using Laplacian
Figure: Sharpened Image and Laplacian Image.
Figure: Laplacian Image and Sharpened Image.
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23. Image Representation in frequency Domain
A fourier transform is used to transform an intensity image in to the
domain of spatial frequency using the 2D-DFT.
F(u, v) =
M−1
x=0
N−1
y=0
f (x, y)e
−j2πux
M e
−j2πvy
N
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24. Image Representation in frequency Domain
Figure: Fourier transformed Image and spectral Image.
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25. References
Rafael C. Gonzalez, Richard E. Woods (2008)
Digital Image Processing
Pearson Education 2009,Third Edition.
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26. The End
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