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Image Enhancement

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.

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Image Enhancement

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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) 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 (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) 0 n g(x,y) negative: n f(x,y) 0 b

  4. Gray level transformation (cont’d) 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 (cont’d) 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 (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) 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 (cont’d) S=T(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 (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 • 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 (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 n=1  1 =0

  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

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