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

2. S. Mandayam/ DIP/ECE Dept./Rowan UniversityPlan 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. S. Mandayam/ DIP/ECE Dept./Rowan University Image Preprocessing Enhancement Restoration Spatial Domain Spectral Domain Point Processing >>imadjust >>histeq Spatial filtering >>filter2 Filtering >>fft2/ifft2 >>fftshift Inverse filtering Wiener filtering

4. S. Mandayam/ DIP/ECE Dept./Rowan University Noise Models SNR g = 10 log 10 (P f /P n ) Power Variance (how?) SNR g = 10 log 10 (  f 2 /  n 2 ) f(x,y) g(x,y) n(x,y)  Degradation Model: g = f + n

5. S. Mandayam/ DIP/ECE Dept./Rowan University 2-D Discrete Fourier Transform >>fft2 >>ifft2 u=0 u=N/2 u=N v=N v=N/2 v=0

6. S. Mandayam/ DIP/ECE Dept./Rowan University 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. S. Mandayam/ DIP/ECE Dept./Rowan University Spectral Filtering: Radially Symmetric Filter Low-pass Filter demos/demo4freq_filtering/lowpass.m u=-N/2 u=0 u=N/2 v=N/2 v=0 v=-N/2 D0D0 D(u,v)

8. S. Mandayam/ DIP/ECE Dept./Rowan University DIP: Details

9. S. Mandayam/ DIP/ECE Dept./Rowan University Image Preprocessing Enhancement Restoration Spatial Domain Spectral Domain Point Processing >>imadjust >>histeq Spatial filtering >>filter2 Filtering >>fft2/ifft2 >>fftshift Inverse filtering Wiener filtering

10. S. Mandayam/ DIP/ECE Dept./Rowan University Enhancement vs. Restoration “Better” visual representation Subjective No quantitative measures Remove effects of sensing environment Objective Mathematical, model dependent quantitative measures

11. S. Mandayam/ DIP/ECE Dept./Rowan University Degradation Model f(x,y) h(x,y) g(x,y) n(x,y)  Degradation Model: g = h*f + n demos/demo5blur_invfilter/ demos/demo5blur_invfilter/degrade.m

12. S. Mandayam/ DIP/ECE Dept./Rowan University Restoration Model f(x,y) Degradation Model f(x,y) Restoration Filter Unconstrained Constrained Inverse Filter Pseudo-inverse Filter Wiener Filter demos/demo5blur_invfilter/

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

14. S. Mandayam/ DIP/ECE Dept./Rowan University Lab 2: Spatial & Spectral Filtering http://engineering.rowan.edu/~shreek/fall07/dip/lab2.html

15. S. Mandayam/ DIP/ECE Dept./Rowan UniversitySummary