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 EE 7730 - Image Analysis I

Frequency-Domain Filtering Bahadir K. Gunturk EE 7730 - Image Analysis I

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 EE 7730 - Image Analysis I

Frequency-Domain Filtering Butterworth Lowpass Filter As order increases the frequency response approaches ideal LPF Bahadir K. Gunturk EE 7730 - Image Analysis I

Frequency-Domain Filtering Butterworth Lowpass Filter Bahadir K. Gunturk EE 7730 - Image Analysis I

Frequency-Domain Filtering Gaussian Lowpass Filter Bahadir K. Gunturk EE 7730 - Image Analysis I

Frequency-Domain Filtering Ideal LPF Butterworth LPF Gaussian LPF Bahadir K. Gunturk EE 7730 - Image Analysis I

Example Bahadir K. Gunturk EE 7730 - Image Analysis I

Highpass Filters Bahadir K. Gunturk EE 7730 - Image Analysis I

Example Bahadir K. Gunturk EE 7730 - Image Analysis I

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 EE 7730 - Image Analysis I

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 EE 7730 - Image Analysis I

Homomorphic Filtering Bahadir K. Gunturk EE 7730 - Image Analysis I

Summary Digital Image Fundamentals: Pixel, resolution, bit depth, ... Linear Systems: Shift invariance, causality, convolution, impulse response, ... Fourier Transform: 2D Fourier Transform of continuous and discrete signals, 2D FT properties (linearity, shifting, modulation, convolution, multiplication, energy conservation, etc.), Dirac delta function, Kronecker delta function, … 2D Sampling: Aliasing, anti-aliasing filter, downsampling, interpolation, … Discrete Fourier Transform: Periodicity, other properties, frequency-domain filtering, … Discrete Cosine Transform: Properties (real basis functions, good energy compaction), relationship with DFT, matrix representation of DCT, … Image Enhancement: Image enhancement by point processing (intensity transformation, histogram equalization, histogram specification, etc.), Image enhancement by spatial-domain filtering (lowpass filtering, highpass filtering, median filtering, high-boost filtering, gradient and laplacian operators, etc.), Image enhancement by frequency-domain filtering (lowpass/highpass filters, homomorphic filtering, etc.) Bahadir K. Gunturk EE 7730 - Image Analysis I