Image Enhancement (Frequency Domain)

Frequency-Domain Filtering Compute the Fourier Transform of the image Multiply the result by filter transfer function Take the inverse transform Bahadir K. Gunturk

Frequency-Domain Filtering Bahadir K. Gunturk

Frequency-Domain Filtering Ideal Lowpass Filters Non-separable >> [f1,f2] = freqspace(256,'meshgrid'); >> H = zeros(256,256); d = sqrt(f1.^2 + f2.^2) < 0.5; >> H(d) = 1; >> figure; imshow(H); Separable >> [f1,f2] = freqspace(256,'meshgrid'); >> H = zeros(256,256); d = abs(f1)<0.5 & abs(f2)<0.5; >> H(d) = 1; >> figure; imshow(H); Bahadir K. Gunturk

Frequency-Domain Filtering Butterworth Lowpass Filter As order increases the frequency response approaches ideal LPF Bahadir K. Gunturk

Frequency-Domain Filtering Butterworth Lowpass Filter Approach to a sinc function. Bahadir K. Gunturk

Frequency-Domain Filtering Gaussian Lowpass Filter Bahadir K. Gunturk

Frequency-Domain Filtering Ideal LPF Butterworth LPF Gaussian LPF Bahadir K. Gunturk

Example Bahadir K. Gunturk

Highpass Filters Bahadir K. Gunturk

Example Bahadir K. Gunturk

Homomorphic Filtering Consider the illumination and reflectance components of an image Illumination Reflectance Take the ln of the image In the frequency domain Bahadir K. Gunturk

Homomorphic Filtering The illumination component of an image shows slow spatial variations. The reflectance component varies abruptly. Therefore, we can treat these components somewhat separately in the frequency domain. 1 With this filter, low-frequency components are attenuated, high-frequency components are emphasized. Bahadir K. Gunturk

Homomorphic Filtering Bahadir K. Gunturk