Image Enhancement

1
Image Enhancement

• Gray level transformation
• Linear transformation
• Non-linear transformation (e.g., Logarithmic
  transformation)
• Others (e.g., negative, gray-level slicing,
  bit-plane slicing, zig-zag transform)
• Gamma correction
• Histogram processing
• Research Case Study
• Demo

2
Gray level transformation
g(x,y)
Increase range of gray scale
Linear
n m
f(x,y)
0 a b
g(x,y)
Piece-wise linear
Depress noise
n m
f(x,y)
0 a b
3
Gray level transformation (contd)
g(x,y)
Logarithmic transform
Expand values of dark pixels To make the details
clear Compress the high level values
n
f(x,y)
0 n
g(x,y)
negative
n
f(x,y)
0 b
4
Gray level transformation (contd)
g(x,y)
Gray-scale slicing
Background compressed
n
f(x,y)
0 n
g(x,y)
Zig-zag
Large range of gray scale is displayed on the
small range device
n
f(x,y)
0 b
5
Gray level transformation (contd)
Bit-7
Bit-plane slicing
e.g., Range 0, 255 ? 0, 1 for each bit
1
Bit 7 . 1, 0
f(x,y)
0 255
Bit-7
Bit-0
6
Gray level transformation (contd)
Intensity (S r(2.5))
Gamma correction

The voltage-to-intensity response is non-linear,
so it is necessary to correct It into linear
response S r(gamma) Gamma 2.5 Gamma
correction S r(1/2.5) voltage ? ?
? intensity r(2.5)
r(0.4)
Voltage (r)
0
Intensity (S r(0.4))

Voltage (r)
0
7
Histogram processing

• P(rk) is the probability of occurrence of gray
  level rk
• P(rk) can be re-distributed for enhancing the
  image

h(rk) or P(rk)nk/n
h(sk) or P(sk)


rk
sk
0
0
Histogram equalization
8
Histogram processing (contd)
ST(r)

• Histogram equalization
• (1) s T(r) 0 ? r ? 1
• (2) Ps(s) ds Pr(r) dr
• (3) T(r) ?0r Pr(w)dw
• From (1), (2) and (3), we get
• Ps(s) 1

t sk
r
0 rk 1
P(r)
P(s)
s
r
Histogram equalization
9
Histogram processing (contd)

• Histogram equalization
• Analogue domain
• s T(r) ?0r Pr(w)dw
• (2) Discrete domain
• K0, 1,, L
• (e.g., L255 if 8bits/pixel)

10
Histogram processing (contd)

• Histogram matching
• -- We can also specify a certain histogram,
  then match it.

11
Histogram processing (contd)

• Example of histogram equalization (HE)
• -- 3bits/pixel
• -- total number of pixel n51
• gray level number of pixels number
  of pixel after HE
• 0 10
  0
• 1 8
  10
• 2 9
  8
• 3 2
  0
• 4 14
  11
• 5 1
  0
• 6 5
  15
• 7 2
  7

12
Histogram processing (contd)

• Note
• -- global histogram processing
• -- local histogram processing
• Bin (a group of successive gray levels)
• -- e.g., 1 bin 2k (bin width)
• -- If the total gray levels are 256, the
  number of bins 28 / 2k
• -- if k4 the number of bins is 16

13
Moment

• Moment
• -- nth moment

Mean value (average)
n0 ? ?0 1 n1 ? ?1 0
14
Moment (contd)

• Moment
• -- variance of r (second moment)

Standard deviation
(average contrast)
15
Enhancement by arithmetic operation

• Image subtraction
• -- e.g., image difference between the
  images before and after the contrast agents
  injection in the radiology imaging.
• N images averaging
• -- time sequence
• -- smoothing
• -- noise removal
• -- N? ? ?
• -- is noise