# Digital Image Processing: Image Enhancement - Duong Anh Duc

Digital Image Processing
Image Enhancement

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Duong Anh Duc - Digital Image Processing

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Image Enhancement
 To process an image so that output is “visually better”
than the input, for a specific application.
 Enhancement is therefore, very much dependent on
the particular problem/image at hand.
 Enhancement can be done in either:
– Spatial domain: operate on the original image

g(m,n) = T[f(m,n)]
– Frequency domain: operate on the DFT of the original image

G(u,v) = T[F(u,v)],

where

F(u,v) = F[f(m,n)], and G(u,v) = F [g(m,n)],

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Duong Anh Duc - Digital Image Processing

2

Image Enhancement Techniques

Point Operations

Image Negative
Contrast
Stretching
Compression of
dynamic range
Graylevel slicing
Image
Subtraction
Image Averaging
Histogram
operations

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Smoothing
operations
Median Filtering
Sharpening
operations
Derivative
operations
Histogram
operations

Transform Operations

Coloring Operations

Low pass
Filtering
Hi pass Filtering
Band pass
Filtering
Homomorphic
Filtering
Histogram
operations

Duong Anh Duc - Digital Image Processing

False Coloring
Full color
Processing

3

Point Operations
 Output pixel value g(m, n) at pixel (m, n) depends only on the input
pixel value at f(m, n) at (m, n) (and not on the neighboring pixel
values).
 We normally write s = T(r), where s is the output pixel value and r is the
input pixel value.

 T is any increasing function that maps [0,1] into [0,1].
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Duong Anh Duc - Digital Image Processing

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Image Negative

T(r) = s = L-1-r, L: max grayvalue
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Duong Anh Duc - Digital Image Processing

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Negative Image

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Duong Anh Duc - Digital Image Processing

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Contrast Stretching

Increase the dynamic range of grayvalues in the input image.
Suppose you are interested in stretching the input intensity values in the
interval [r1, r2]:

Note that (r1- r2) < (s1- s2). The grayvalues in the range [r1, r2] is stretched into
the range [s1, s2].

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Duong Anh Duc - Digital Image Processing

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Contrast Stretching
 Special cases:
– Thresholding or
binarization
r1 = r2 , s1 = 0 and s2 = 1
– Useful when we are
only interested in the
shape of the objects
and on on their actual
grayvalues.
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Duong Anh Duc - Digital Image Processing

8

Contrast Stretching

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Duong Anh Duc - Digital Image Processing

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Contrast Stretching
 Special cases (cont.):
– Gamma correction:
S1 = 0, S2 = 1 and
0, r
g

T r

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r1

r r1
, r1 r
r2 r1
1, r r2

r2

Duong Anh Duc - Digital Image Processing

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Contrast Stretching
Gamma correction

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Duong Anh Duc - Digital Image Processing

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Compression of Dynamic
Range
 When the dynamic range of the input
grayvalues is large compared to that of
the display, we need to “compress” the
grayvalue range --- example: Fourier
transform magnitude.
 Typically we use a log scale.
s = T(r) = c log(1+ r )

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Duong Anh Duc - Digital Image Processing

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Compression of Dynamic
Range

Saturn Image

Mag. Spectrum

Mag. Spectrum
in log scale

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Duong Anh Duc - Digital Image Processing

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Compression of Dynamic
Range
 Graylevel Slicing: Highlight a specific
range of grayvalues.

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Duong Anh Duc - Digital Image Processing

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Compression of Dynamic
Range
 Example:

Highlighted Image (no background)

Original Image

Highlighted Image (with background)
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Duong Anh Duc - Digital Image Processing

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Compression of Dynamic
Range
 Bitplane Slicing: Display the different
bits as individual binary images.

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Duong Anh Duc - Digital Image Processing

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Compression of Dynamic
Range

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Duong Anh Duc - Digital Image Processing

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Image Subtraction
 In this case, the difference between two
“similar” images is computed to highlight
or enhance the differences between
them:
g(m,n) = f1(m,n)-f2(m,n)
 It has applications in image segmentation
and enhancement

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Duong Anh Duc - Digital Image Processing

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f1(m, n): Image before dye injection
f2(m, n): Image after dye injection
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g(m, n): Image after dye injection,
followed by subtraction

Duong Anh Duc - Digital Image Processing

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Image Averaging for noise
reduction
 Noise is any random (unpredictable)
phenomenon that contaminates an image.
 Noise is inherent in most practical systems:
– Image acquisition
– Image transmission
– Image recording

 Noise is typically modeled as an additive process:
g(m,n) = f(m,n) + (m,n)
Noisy
Image

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Noise-free
Image

Duong Anh Duc - Digital Image Processing

Noise

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Image Averaging for noise
reduction
 The noise h (m, n) at each pixel (m, n) is modeled
as a random variable.
 Usually, h (m, n) has zero-mean and the noise values
at different pixels are uncorrelated.
 Suppose we have M observations {gi(m, n)}, i=1, 2, …,
M, we can (partially) mitigate the effect of noise by
“averaging”

g m, n

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1
M

M

g i m, n

i 1

Duong Anh Duc - Digital Image Processing

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Image Averaging for noise
reduction
 In this case, we can show that:
E g m, n
Var g m, n

f m, n
1
Var
M

m, n

 Therefore, as the number of observations
increases (M
), the effect of noise
tends to zero.
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Duong Anh Duc - Digital Image Processing

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Image Averaging Example

Noise-free Image

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Noisy Image
Noise Variance = 0.05

Duong Anh Duc - Digital Image Processing

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Image Averaging Example

M =2

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M =5

Duong Anh Duc - Digital Image Processing

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Image Averaging Example

M =10

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Duong Anh Duc - Digital Image Processing

M =25

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