Digital Image Processing Lecture 2 Digital Image Processing

Image sensors

Sampling and Quantization

Representing digital images

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

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

Fourier transform 1D –FT: 2D – FT:

Separability of 2D - FT

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

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

2D DFT

2D DFT Centering the DFT:

2D DFT Log of the magnitude

2D Sampling f(x,y) y x

Sampling

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?

Hexagonal Sampling grid Best packing density for circles

Fuji super CCD sensor