Image Enhancement Gray level transformation Linear transformation

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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