Explain various image enhancement techniques in frequency domain.

OR

Short Note on Low pass and High pass filtering in frequency domain.

In frequency domain methods, the image is first converted into frequency domain. That is, the fourier transform of the image is computed first.

All the enhancement operations are performed on the Fourier transform of the image and then Inverse Fourier transform is performed to the resultant image.

$G(u,v) = H(u,v)* F(u,v)$

where G is enhanced image, H is transfer function, and F is given image.

These enhancement operations are performed in order to modify the image brightness, contrast or the distribution of the grey levels.

Filtering

Filtering can be divided into two categories namely

1. Low pass filtering
2. High pass filtering

1. Low pass filtering

• Image can be smoothed in the frequency domain by attenuating the high-frequency content of its Fourier transform. This would be a low pass filter.

• Ideal low pass filter with cutoff frequency ‘$r_{0}$ ’ is given by

  a. Buttherworth low pass filter

• Frequency response does not have a sharp transition as ideal LPF. This is more appropriate for image smoothing than the ideal LPF, since this does not introduce ringing.

• A two-dimensional butterworth low pass filter has transfer function.

  b. Gaussian low pass filter

  The form of a Gaussian low pass filter in two dimensions is given by

2. High pass filtering - An image can be smoothed in the frequency domain by attenuating the low-frequency content of its Fourier transform. This would be a high pass filter. - An ideal high pass filter with cutoff frequency $r_{0}$

a. Butterworth High pass filtering

• A two-dimensional butterworth high pass filtering has transfer function
• Frequency response does not have a sharp transition as in ideal HPF. This is more appropriate for image sharpening than the ideal HPF, since this does not introduce ringing.