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)
Linear:
Increase range of gray scale n m
f(x,y)
a b
g(x,y)
Piece-wise linear:
Depress noise n m
f(x,y)
a b

3. Gray level transformation (cont’d)
g(x,y)
Logarithmic transform
Expand values of dark pixels
To make the details clear
Compress the high level values n
f(x,y) n
g(x,y)
negative: n
f(x,y) b

4. Gray level transformation (cont’d)
g(x,y)
Gray-scale slicing
Background compressed n
f(x,y) n
g(x,y)
Zig-zag:
Large range of gray scale
is displayed on the small
range device n
f(x,y) b

5. Gray level transformation (cont’d)
Bit-7
Bit-plane slicing:
e.g., Range [0, 255]  [0, 1]
for each bit 1
Bit … , 0
f(x,y)
Bit-7
Bit-0

6. Gray level transformation (cont’d)
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)
Intensity (S = r^(0.4))
Voltage (r)

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
Histogram equalization

8. Histogram processing (cont’d)
S=T(r)
Histogram equalization
(1) s = T(r)  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
rk 1
P(r)
P(s) r s
Histogram equalization

9. Histogram processing (cont’d)
Histogram equalization
Analogue domain:
s= T(r) = 0r Pr(w)dw
(2) Discrete domain:
K=0, 1,…, L
(e.g., L=255 if 8bits/pixel)

10. Histogram processing (cont’d)
Histogram matching
-- We can also specify a certain histogram, then match it.

11. Histogram processing (cont’d)
Example of histogram equalization (HE)
-- 3bits/pixel
-- total number of pixel n=51
gray level number of pixels number of pixel after HE

12. Histogram processing (cont’d)
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 k=4; the number of bins is 16

13. Moment Moment -- nth moment Mean value (average): n=0  0 =1

14. Moment (cont’d) 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