S. Mandayam/ DIP/ECE Dept./Rowan University Digital Image Processing ECE /ECE Fall 2007 Shreekanth Mandayam ECE Department Rowan University Lecture 6 October 29, 2007

S. Mandayam/ DIP/ECE Dept./Rowan UniversityPlan Digital Image Restoration Recall: 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 3: Digital Image Restoration

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

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

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

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

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/

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)

S. Mandayam/ DIP/ECE Dept./Rowan University Degradation & Restoration Examples: Gonzalez & Woods Atmospheric Turbulence Model

S. Mandayam/ DIP/ECE Dept./Rowan University Degradation & Restoration Examples: Gonzalez & Woods Example 5.11: Inverse Filtering

S. Mandayam/ DIP/ECE Dept./Rowan University Degradation & Restoration Examples: Gonzalez & Woods Example 5.12: Wiener Filtering

S. Mandayam/ DIP/ECE Dept./Rowan University Degradation & Restoration Examples: Gonzalez & Woods Example 5.10: Planar Motion Model

S. Mandayam/ DIP/ECE Dept./Rowan University Degradation & Restoration Examples: Gonzalez & Woods Example 5.13: Inverse and Wiener Filtering

S. Mandayam/ DIP/ECE Dept./Rowan University Lab 3: Digital Image Restoration

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