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Digital Image Processing ECE.09.452/ECE.09.552 Fall 2007

Digital Image Processing ECE.09.452/ECE.09.552 Fall 2007. Lecture 5 October 15, 2007. Shreekanth Mandayam ECE Department Rowan University http://engineering.rowan.edu/~shreek/fall07/dip/. Plan. Image Spectrum (Recall) 2-D Fourier Transform (DFT & FFT) Spectral Filtering

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Digital Image Processing ECE.09.452/ECE.09.552 Fall 2007

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  1. Digital Image ProcessingECE.09.452/ECE.09.552Fall 2007 Lecture 5October 15, 2007 Shreekanth Mandayam ECE Department Rowan University http://engineering.rowan.edu/~shreek/fall07/dip/

  2. Plan • Image Spectrum • (Recall) 2-D Fourier Transform (DFT & FFT) • Spectral Filtering • Digital Image Restoration • Enhancement vs. Restoration • Environmental Models • Image Degradation Model • Image Restoration Model • Point Spread Function (PSF) Models • Linear Algebraic Restoration • Unconstrained (Inverse Filter, Pseudoinverse Filter) • Constrained (Wiener Filter, Kalman Filter) • Lab 2: Spatial and Spectral Filtering

  3. Image Preprocessing Restoration Enhancement • Inverse filtering • Wiener filtering Spectral Domain Spatial Domain • Filtering • >>fft2/ifft2 • >>fftshift • Point Processing • >>imadjust • >>histeq • Spatial filtering • >>filter2

  4. S f(x,y) g(x,y) n(x,y) Degradation Model: g = f + n Noise Models • SNRg = 10log10(Pf/Pn) • Power Variance (how?) • SNRg = 10log10(sf2/ sn2)

  5. u=0 u=N/2 u=N v=N v=N/2 v=0 2-D Discrete Fourier Transform >>fft2 >>ifft2

  6. 2-D DFT Properties • Conjugate symmetry demos/demo3dft_properties/con_symm_and_trans.m • Rotation demos/demo3dft_properties/rotation.m • Separability demos/demo3dft_properties/separability.m >>fftshift

  7. Spectral Filtering: Radially Symmetric Filter u=-N/2 u=0 u=N/2 • Low-pass Filter demos/demo4freq_filtering/lowpass.m D(u,v) D0 v=N/2 v=0 v=-N/2

  8. DIP: Details

  9. Image Preprocessing Restoration Enhancement • Inverse filtering • Wiener filtering Spectral Domain Spatial Domain • Filtering • >>fft2/ifft2 • >>fftshift • Point Processing • >>imadjust • >>histeq • Spatial filtering • >>filter2

  10. “Better” visual representation Subjective No quantitative measures Remove effects of sensing environment Objective Mathematical, model dependent quantitative measures Enhancement vs. Restoration

  11. S f(x,y) g(x,y) h(x,y) n(x,y) Degradation Model: g = h*f + n Degradation Model • demos/demo5blur_invfilter/ • demos/demo5blur_invfilter/degrade.m

  12. Restoration Model Degradation Model Restoration Filter f(x,y) f(x,y) Unconstrained Constrained • Inverse Filter • Pseudo-inverse Filter • Wiener Filter • demos/demo5blur_invfilter/

  13. f(x,y) Build degradation model f(x,y) Analyze using algebraic techniques Formulate restoration algorithms Implement using Fourier transforms Approach g = h*f + n g = Hf + n W -1g = DW -1f + W -1n f = H -1g F(u,v) = G(u,v)/H(u,v) • demos/demo5blur_invfilter/

  14. Lab 2: Spatial & Spectral Filtering http://engineering.rowan.edu/~shreek/fall07/dip/lab2.html

  15. Summary

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