1. Digital Image Processing
Lecture 2
Digital Image Processing

2. Image sensors

3. Sampling and Quantization

4. Representing digital images

5. 1D sampling
Bandlimited real 1D - signal: F F

6. 2D Sampling y
f(x,y) x y x

7. Fourier transform
1D –FT:
2D – FT:

8. Separability of 2D - FT

9. Discrete Fourier transform
1D – DFT:
2D – DFT:
2D DFT is also separable!

10. What do u and v mean? y x v u
Magnitude of Fourier transform

11. 2D DFT

12. 2D DFT
Centering the DFT:

13. 2D DFT
Log of the magnitude

14. 2D Sampling
f(x,y) y x

15. Sampling

16. Question
Given that the Fourier transform of an image is non zero over a circular area of radius , what happens if
Can we do any better?

17. Hexagonal Sampling grid
Best packing density for circles

18. Fuji super CCD sensor