Digital image processing
Chapter 6. Image enhancement
IMAGE ENHANCEMENT
Introduction
Image enhancement algorithms & techniques
Point-wise operations
Contrast enhancement; contrast stretching
Grey scale clipping; image binarization (thresholding)
Image inversion (negative)
Grey scale slicing
Bit extraction
Contrast compression
Image subtraction
Histogram modeling: histogram equalization/ modification
Spatial operations
Spatial low-pass filtering
Unsharp masking and crispening
Spatial high-pass and band-pass filtering
Inverse contrast ratio mapping and statistical scaling
Magnification and interpolation (image zooming)
Digital image processing
Chapter 6. Image enhancement
Transform domain image processing
Generalized linear filtering
Non-linear filtering
Generalized cepstrum and homomorphic filtering
Image pseudo-coloring
Color image enhancement
Applications: biomedical image enhancement
Types and characteristics of biomedical images
Contour detection in biomedical images
Anatomic segmentation of biomedical images
Histogram equalization and pseudo-coloring in biomedical images
Digital image processing
Chapter 6. Image enhancement
Introduction
• Def.: Image enhancement = class of image processing operations whose goal is to
produce an output digital image that is visually more suitable as appearance for its visual
examination by a human observer
The relevant features for the examination task are enhanced
The irrelevant features for the examination task are removed/reduced
• Specific to image enhancement:
- input = digital image (grey scale or color)
- output = digital image (grey scale or color)
• Examples of image enhancement operations:
- noise removal;
- geometric distortion correction;
- edge enhancement;
- contrast enhancement;
- image zooming;
- image subtraction;
- pseudo-coloring.
• Classification of image enhancement operations:
- Based on the type of the algorithms: grey scale transformations; spatial operations;
transform domain processing; pseudo-coloring
- Based on the class of applications – as in the examples above.
Digital image processing
Chapter 6. Image enhancement
A. Point-wise operations
Def.: The new grey level (color) value in a spatial location (m,n) in the resulting image depends
only on the grey level (color) in the same spatial location (m,n) in the original image
=> “point-wise” operation, or grey scale transformation (for grey scale images).
v(m, n)  f u(m, n), m  0,1,...,M  1; n  0,1,...,N  1;
f : 0,1,...,LMax   0,1,...,LMax 
U[M×N]
V[M×N]
m
m
n
u(m,n)
n
Point-wise operation
(grey scale transformation)
f(∙) => v=f(u)
v(m,n) = f(u(m,n))
Digital image processing
Chapter 6. Image enhancement
Contrast enhancement/contrast stretching
V
VL

Vb

mu
, 0  u  a , m  tg

v  n(u  a)  v a , a  u  b , n  tg
 p(u  b)  v ,b  u  L , p  tg
b


Va

U
a
b
Contrast enhancement, if:
 m<1, for the dark regions (under aL/3).
 n>1, for the medium grey scale (between a and b, b(2/3)L)
 p<1, for the bright regions (above b).
Digital image processing
Chapter 6. Image enhancement
Grey scale clipping; image thresholding
•Grey scale clipping is a particular case of contrast enhancement, for m=p=0:
 0 ,0  u  a

f(u)  nu , a  u  b
 L ,b  u  L

(6.2)
V
U
a
b
Fig. 6.3. Grey scale clipping
V
U
Fig. 6.4 Image thresholding
Processed
histogram
Original histogram
Digital image processing
Chapter 6. Image enhancement
Fig. 6.5 Image thresholding - example
The inverse image (negative image):
v = L-u
v
(6.3)
v
v
L
L
L
Fig. 6.6 Image inverting
U
L
a
b
U
a
b
Fig. 6.7 Grey scale slicing (windowing)
U
Digital image processing
Chapter 6. Image enhancement
GREY SCALE SLICING (WINDOWING):
L , a  u  b
v  
0 ,otherwise
L , a  u  b
v  
 u ,otherwise
or
(6.4)
(6.5)
BIT EXTRACTION:
u=k12B-1+k22B-2+...+kB-12+kB
 L ,if kn  1
v
0 , otherwise
(6.6)
(6.7)
CONTRAST COMPRESSION:
v = clog(1+|u|)
(6.8)
CONTRAST COMPRESSION – EXAMPLE:
v = clog(1+|u|)
IMAGE SUBTRACTION:
_
Digital image processing
Chapter 6. Image enhancement
HISTOGRAM MODELING. HISTOGRAM EQUALIZATION/MODIFICATION
Hlin,U(u)
Def. Linear grey level histogram of a digital grey scale image U[M×N]:
= the function Hlin,U:{0,1,…,LMax}→{0,1,…,MN},
Hlin,U(u)=nbr. of pixels with grey level u from U.
Def. Normalized linear grey level histogram of the image U[M×N]:
= the function hlin,U:{0,1,…,LMax}→[0;1],
u
Ideally –
histogram
hlin,U(u)=Hlin,U(u)/(MN).
equalization
Def. Cumulative grey level histogram of a digital grey scale image U[M×N]:
= the function Hcum,U:{0,1,…,LMax}→{0,1,…,MN},
Hlin,V(v)
u
H cum,U (u )   H lin ,U (l ).
l 0
Def. Normalized cumulative grey level histogram of the image U[M×N]:
= the function hcum,U:{0,1,…,LMax}→[0;1],
hcum,U(u)=Hcum,U(u)/(MN).
v
u
H lin,U (l )
l 0
MN
v  f Equalization u   L 

L u
 H lin,U (l ), u  {0,1,..., LMax}.
MN l 0
Digital image processing
Chapter 6. Image enhancement
u
p
u
u
(x i )
xi
V
Uniform
quantizer
v`
pu(xi)
Fig. 6.8. Histogram equalization
a
b
Fig. 6.9 Low contrast image
a
b
Fig. 6.10 The resulting image after histogram equalization
Digital image processing
Chapter 6. Image enhancement
u
f(u)
Uniform
quantizer
v
v'
Fig. 6.11 Histogram modification
n
v = f(u) =
p (x )
u
i
(6.15)
x i=0
n
p
f(u) =
xi
x L-1

x i=0
1
n
u
1
n( )
i
u
p x
,
n = 2, 3,...
(6.15.a)
Digital image processing
Chapter 6. Image enhancement
SPATIAL OPERATIONS: most of them can be implemented by convolution
v( m,n)  

(k,l)W
a( k,l)u( m- k,n - l)
a  1,1
A   a 0,1
 a 1,1

AM
a  1,0 
a 0,0 
a 1,0 
a  1,1
a 0,1 
a 1,1 
A[ K  L]  a k , l  - Convolution mask
a  1,1
A '   a 0,1
 a 1,1
a  1,0 
a 0,0 
a 1,0 
a  1,1
a 0,1 
a 1,1 
 a 1,1
 a 0,1

a  1,1
a 1,0 
a 0,0 
a  1,0 
a 1,1 
a 0,1   A M
a  1,1
Digital image processing
Chapter 6. Image enhancement
Spatial averaging. Low-pass spatial filtering:
v(m,n)  

(6.18)
a(k,l)y(m - k,n - l)
(k,l)W
1
  y(m - k, n - l )
N ( k,l)W
(6.19)
v(m,n)=1/2[y(m,n)+1/4{y(m-1,n)+y(m+1,n)+y(m,n-1)+y(m,n+1)}]
(6.20)
v(m,n) =
l
l
0
-1
1
0 1/4 1/4
k
1 1/4 1/4
2x2 window
0
l
1
-1 1/9 1/9 1/9
k
0 1/9
1
1/9 1/9
1/9 1/9 1/9
3x3 window
-1
-1
0
1
0
1/8
0
k
0
1
1/8 1/2 1/8
0
1/8
0
5 points weighted averaging
Fig. 6.12 Convolution windows used in low-pass spatial filtering - examples
Filtering by spatial averaging – the effect on the noise power reduction:
v(m,n) = u(m,n) + (m,n)
1
v(m,n) =
 u(m - k,n - l)+ (m,n)

N w (k,l)W
(6.21)
(6.22)
Digital image processing
Chapter 6. Image enhancement
Directional low-pass spatial filtering:
v(m,n: ) =
W0
1
N
0
0
0
0
0
0
0
0
0
0
  y(m - k,n - l)
(k,l)W
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
(6.23)

l
K
Fig. 6.13 Directional spatial filtering
Median filtering:
v(m ,n)= m edian{y(m - k,n - l),(k,l) W }
(6.24)
 v(m,n) = the element in the middle of the brightness row, with increasing brightness values
a
b
Fig. 6.14 Additive noise attenuation by mean filtering
Digital image processing
Chapter 6. Image enhancement
a
b
Fig. 6.15 Gaussian noise reduction by median filtering
UNSHARP MASKING AND EDGE CRISPENING:
v(m,n) = u(m,n)+ g(m,n)
(6.25)
1
g(m,n) = u(m,n) - [u(m - 1,n)+ u(m,n - 1)+ u(m+ 1,n)+ u(m,n + 1)] (6.26)
4
Signal
Low pass
filtering
High pass
filtering
a+c
a-b
a
b
Fig. 6.16 Edge crispening algorithm
c
d
Digital image processing
Chapter 6. Image enhancement
Original image
Resulting image
Fig. 6.17 Edge crispening using a Laplacian operator
HIGH-PASS SPATIAL FILTERING
hTS (m ,n)=  (m ,n) - hTJ (m ,n)
u(m,n)
Spatial averaging vTJ(m,n)
(mean filtering)
Fig. 6.18 Low-pass filtering
(6.27)
u(m,n)
Spatial Low-Pass
Filter
+
vTS(m,n)
_+
Fig. 6.19 High-pass filtering
Digital image processing
Chapter 6. Image enhancement
BAND-PASS SPATIAL FILTERING:
hTB (m,n) = hTJ 1 (m,n) - hTJ 2 (m,n)
FTJ
hTJ1(m,n)
u(m,n)
+ + vTB(m,n)
_
(6.28)
FTJ
hTJ2(m,n)
Fig. 6.20 Band-pass image filtering
a
c
b
d
Fig. 6.21 The results of LPF (Fig. c), HPF (Fig. b),BPF (Fig. d) for a grey level image (Fig. a – original image)
Digital image processing
Chapter 6. Image enhancement
INVERSE CONTRAST RATIO MAPPING; STATISTICAL SCALING:

 =
(6.29)

v(m,n) =
(m,n)
 (m,n)
(m,n) =
(m,n) = {
v( m,n) =
1

NW
1
(6.30)

u(m - k,n - l)

[u(m- k, n - l) - (m,n) ] 2 }1/2
(6.31)
(k,l)W
N W ( k,l)W
u( m,n)
( m,n)
(6.32)
(6.33)
MAGNIFICATION AND INTERPOLATION (IMAGE ZOOMING):
• Zooming by pixel replication:
H 
1
1
1
1
(6.34)
The resulting image is obtained as:
v(m,n) = u(k,l)
with
k = Int[
m
n
], l = Int[
]
2
2
(6.35)
m,n =0, 1, 2,...
Digital image processing
Chapter 6. Image enhancement
a
b
c
Fig. 6.22 Image zooming by pixel replication by a factor of: b) 2; c) 4, on each direction
Zooming by linear interpolation:
v i (m,2n) = u(m,n),
v i (m,2n + 1) =
o  m  M - 1,
[u(m,n)+ u(m,n + 1)]
,
2
o  n  N -1
(6.36)
0  m< M -1
(6.37)
(6.38)
v(2m,n) = v i (m,n)
v(2m+ 1,n) =
[ v i (m,n)+ v i (m+ 1,n)]
, 0  m  M - 1, 0  n  2N - 1
2
1/ 4 1/ 2 1/ 4
H  1/ 2
1/ 4
1 7 
3 1


Zeros
interlacing
1
0

3

0
0 7 0
0 0 0
0 1 0

0 0 0
1
1/ 2
1/ 2
1/ 4
Rows
interpolation
1
0

3

0
4 7 3,5
0 0 0 
2 1 0,5

0 0 0
(6.39)
(6.40)
Columns
interpolation
1
2

3

1,5
4 7 3,5 
3 4
2 
2 1 0,5 

1 0,5 0,25
Fig. 6.23
Digital image processing
Chapter 6. Image enhancement
6.6 TRANSFORM DOMAIN IMAGE PROCESSING
u(m,n)
Unitary transform
Point-wise
operations
f()
v(k,l)
AUAT
Inverse transform u’(m,n)
v’(k,l)
A-1 V [AT]
Fig. 6.24 Image enhancement in the transformed domain
• Generalized linear filtering
v(k,l)= g(k,l) v(k,l)
(6.41)
where g(k,l) is called regional mask (i.e., it is 0 outside the selected region)
0
a
b
N-b N-a
FTJ
K
c
FTJ
FTB
-1
0
p
q
K
FTJ
FTB
d
r
FTS
FTB
N-d
N-c
FTB
FTJ
FTB
s
FTJ
N-1
a
b
Fig. 6.25 Regional masks for the generalized linear filtering
FTS
Digital image processing
Chapter 6. Image enhancement
E.g.: - the inverse Gaussian filter has the following regional mask:

k2  l2
 exp
,
g(k,l)= 
2
2
 g(N  k, N  l),

0  k,l  N/2
(6.42)
otherwise
- for other orthogonal transforms:
(k 2  l 2 )
g( k , l )  exp
,
2 2
0  k, l  N  1
(6.43)
Non-linear filtering
v(k,l) =|v(k,l)| e j (k,l)
v , (k,l) |v(k,l)|a e j (k,l)
(6.44)
0  a 1
(6.45)
Generalized cepstrum and homomorphic filtering
u(m,n)
T
v(k,l)
AUA
Logv(k,l)e
je (k,l)
s(k,l)
-1
T -1
c(m,n)
T -1
u’(m,n)
A S (A )
s(k,l) = [log|v(k,l)| ] e j (k,l) , |v(k,l > 0
c’(m,n)
T
ACA
s’(k,l)
exps’(k,l)e
je (k,l)
v’(k,l)
-1
A V (A )
Digital image processing
Chapter 6. Image enhancement
IMAGE PSEUDO-COLORING
R
v1(m,n)
u(m,n)
Feature
extraction
v2(m,n)
v3(m,n)
Color space
transformation
G
A-1 S (AT)-1
c(m,n)
B
Fig. 6.27 Monochrome image pseudo-coloring
COLOR IMAGE ENHANCEMENT
Monochrome image
enhancement algorithm
R
G
Input
image
Color
space
transform
Monochrome image
enhancement algorithm
Inverse
color
space
transform
B
Monochrome image
enhancement algorithm
Fig. 6.28 Color image enhancement block diagram
Output
image
rendering
Digital image processing
Chapter 6. Image enhancement
BIOMEDICAL IMAGE ENHANCEMENT - APPLICATIONS
Biomedical image types & features
Fig. 6.42
Fig. 6.44
Fig. 6.43
Fig. 6.45
Digital image processing
Chapter 6. Image enhancement
Contour extraction in biomedical images:
Table 6.1
1 1 1
H L  1
9
1
1 1 1
Operator
(6.76)
Fig. 6.46
a11 a12 a13 a21 a22 a23 a31 a32 a33
Gradient directional E
Gradient directional NE
Gradient directional SW
Filtru trece-sus 1
Filtru trece-sus 2
Laplacian
Laplacian diagonal
Laplacian orizontal
Laplacian vertical
Prewitt orizontal
Prewitt vertical
Sobel orizontal
Sobel vertical
Kirsch orizontal
Kirsch vertical
Fig. 6.47
1
1
1
0
0
-1
-1
0
0
-1
1
1
1
-3
5
1
1
1
-1
-1
-1
0
-1
0
-1
0
2
0
-3
5
1
1
-1
0
0
-1
-1
0
0
-1
-1
1
-1
5
5
1
1
1
-1
-1
-1
0
0
-1
0
1
0
2
-3
-3
-2
-2
-2
5
4
9
4
2
2
0
0
0
0
0
0
1
-1
-1
-1
-1
-1
0
0
-1
0
-1
0
-2
5
-3
-1
1
1
0
0
-1
-1
0
0
1
1
-1
1
-3
-3
-1
-1
1
-1
-1
-1
0
-1
0
1
0
-2
0
-3
-3
-1
-1
-1
0
0
-1
-1
0
0
1
-1
-1
-1
5
-3
Digital image processing
Chapter 6. Image enhancement
Histogram equalization and pseudo-coloring in biomedical images:
a
b
Fig. 6.48
Fig. 6.49
Fig. 6.50
Digital image processing
Chapter 6. Image enhancement
Fig. 6.51
Fig. 6.52
Fig. 6.53
Fig. 6.54