Spatial Filtering

1. Intensity Transformation and
Spatial Filtering
24.08.2020
10:30 am

2. Histogram Processing
• Intensity levels in the range [0, L-1]
• Discrete function h(rk)=nk
• Histogram Normalization
• p(rk)=nk/MN
• Horizontal axis – intensity values rk
• Vertical axis - h(rk)=nk
• or p(rk)=nk/MN
• Four Basic image types Histogram

3. Histogram Equalization
• T(r) is monotonically increasing
function
• 0 ≤ T(r) ≤ L – 1
• Using Inverse formulation
r=T-1(s)
• T(r) is strictly monotonically
increasing function

4. Histogram Equalization
• [0,Probability Density Function (PDF)
ps(s) = pr(r)|
𝑑𝑟
𝑑𝑠
|
• Cumulative Distribution Function (CDF)
(L – 1) 0
𝑟
pr(w)𝑑𝑤
• Uniform PDF
ps(s) =
1
𝐿 −1

5. Histogram Equalization

6. Histogram Equalization
• Example
pr(r)=
2𝑟
(𝐿 −1)2 for 0 ≤r≤ L −1
0 𝑂𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒

7. Histogram Equalization

8. Histogram Equalization

9. Histogram Equalization
• Example