Digital Image Processing, 2nd ed. © 2002 R. C. Gonzalez & R. E. Woods Chapter 5 Image Restoration Chapter 5 Image Restoration Goal of Restoration : Improve an image in some predefined sense. i.e. g(x,y)=h(x,y)*f(x,y)+η(x,y) G(u,v)=H(u,v)F(u,v)+N(u,v)

Digital Image Processing, 2nd ed. © 2002 R. C. Gonzalez & R. E. Woods Chapter 5 Image Restoration Chapter 5 Image Restoration

Digital Image Processing, 2nd ed. © 2002 R. C. Gonzalez & R. E. Woods Chapter 5 Image Restoration Chapter 5 Image Restoration This test pattern is well-suited for illustrating the noise models, because it is composed of simple, constant areas that span the grey scale from black to white in only three increments. This facilitates visual analysis of the characteristics of the various noise components added to the image.

Digital Image Processing, 2nd ed. © 2002 R. C. Gonzalez & R. E. Woods Chapter 5 Image Restoration Chapter 5 Image Restoration

Digital Image Processing, 2nd ed. © 2002 R. C. Gonzalez & R. E. Woods Chapter 5 Image Restoration Chapter 5 Image Restoration

Digital Image Processing, 2nd ed. © 2002 R. C. Gonzalez & R. E. Woods Chapter 5 Image Restoration Chapter 5 Image Restoration

Digital Image Processing, 2nd ed. © 2002 R. C. Gonzalez & R. E. Woods Chapter 5 Image Restoration Chapter 5 Image Restoration

Digital Image Processing, 2nd ed. © 2002 R. C. Gonzalez & R. E. Woods Chapter 5 Image Restoration Chapter 5 Image Restoration

Digital Image Processing, 2nd ed. © 2002 R. C. Gonzalez & R. E. Woods Chapter 5 Image Restoration Chapter 5 Image Restoration

Digital Image Processing, 2nd ed. © 2002 R. C. Gonzalez & R. E. Woods Chapter 5 Image Restoration Chapter 5 Image Restoration

Digital Image Processing, 2nd ed. © 2002 R. C. Gonzalez & R. E. Woods Chapter 5 Image Restoration Chapter 5 Image Restoration

Digital Image Processing, 2nd ed. © 2002 R. C. Gonzalez & R. E. Woods Chapter 5 Image Restoration Chapter 5 Image Restoration

Digital Image Processing, 2nd ed. © 2002 R. C. Gonzalez & R. E. Woods Chapter 5 Image Restoration Chapter 5 Image Restoration

Digital Image Processing, 2nd ed. © 2002 R. C. Gonzalez & R. E. Woods Chapter 5 Image Restoration Chapter 5 Image Restoration

Digital Image Processing, 2nd ed. © 2002 R. C. Gonzalez & R. E. Woods Chapter 5 Image Restoration Chapter 5 Image Restoration

Digital Image Processing, 2nd ed. © 2002 R. C. Gonzalez & R. E. Woods Chapter 5 Image Restoration Chapter 5 Image Restoration Periodic Noise Reduction by Frequency Domain Filtering LPF & HPF  Image Enhancement 1)Bandreject Filters 1-1) Ideal : D(u,v): distance from the origin of the centered frequency rectangle W: bandwidth D 0 :radial center

Digital Image Processing, 2nd ed. © 2002 R. C. Gonzalez & R. E. Woods Chapter 5 Image Restoration Chapter 5 Image Restoration Periodic Noise Reduction by Frequency Domain Filtering 1-2) Butterworth of order n : 1-3) Gaussian :

Digital Image Processing, 2nd ed. © 2002 R. C. Gonzalez & R. E. Woods Chapter 5 Image Restoration Chapter 5 Image Restoration

Digital Image Processing, 2nd ed. © 2002 R. C. Gonzalez & R. E. Woods Chapter 5 Image Restoration Chapter 5 Image Restoration

Digital Image Processing, 2nd ed. © 2002 R. C. Gonzalez & R. E. Woods Chapter 5 Image Restoration Chapter 5 Image Restoration Periodic Noise Reduction by Frequency Domain Filtering 2)Bandreject Filters H bp (u,v)=1-H br (u,v) It helps isolate the noise pattern.

Digital Image Processing, 2nd ed. © 2002 R. C. Gonzalez & R. E. Woods Chapter 5 Image Restoration Chapter 5 Image Restoration

Digital Image Processing, 2nd ed. © 2002 R. C. Gonzalez & R. E. Woods Chapter 5 Image Restoration Chapter 5 Image Restoration Periodic Noise Reduction by Frequency Domain Filtering 3)Notch Filters 3-1) Ideal : The center of the frequency rectangle has been shifted to the point (M/2,N/2)

Digital Image Processing, 2nd ed. © 2002 R. C. Gonzalez & R. E. Woods Chapter 5 Image Restoration Chapter 5 Image Restoration Periodic Noise Reduction by Frequency Domain Filtering Notch Filters 3-2) Butterworth of order n : 3-3) Gaussian :

Digital Image Processing, 2nd ed. © 2002 R. C. Gonzalez & R. E. Woods Chapter 5 Image Restoration Chapter 5 Image Restoration

Digital Image Processing, 2nd ed. © 2002 R. C. Gonzalez & R. E. Woods Chapter 5 Image Restoration Chapter 5 Image Restoration

Digital Image Processing, 2nd ed. © 2002 R. C. Gonzalez & R. E. Woods Chapter 5 Image Restoration Chapter 5 Image Restoration Periodic Noise Reduction by Frequency Domain Filtering 4)Optimum Notch Filters To obtain w(x,y) the goal is to minimize the variance in the neighborhood of x,y in the image.

Digital Image Processing, 2nd ed. © 2002 R. C. Gonzalez & R. E. Woods Chapter 5 Image Restoration Chapter 5 Image Restoration

Digital Image Processing, 2nd ed. © 2002 R. C. Gonzalez & R. E. Woods Chapter 5 Image Restoration Chapter 5 Image Restoration

Digital Image Processing, 2nd ed. © 2002 R. C. Gonzalez & R. E. Woods Chapter 5 Image Restoration Chapter 5 Image Restoration

Digital Image Processing, 2nd ed. © 2002 R. C. Gonzalez & R. E. Woods Chapter 5 Image Restoration Chapter 5 Image Restoration

Digital Image Processing, 2nd ed. © 2002 R. C. Gonzalez & R. E. Woods Chapter 5 Image Restoration Chapter 5 Image Restoration Linear, Position-Invariant Degradations Estimation the Degradation Function 1) Estimation by Image Observation Assuming that the effect of noise is negligible.

Digital Image Processing, 2nd ed. © 2002 R. C. Gonzalez & R. E. Woods Chapter 5 Image Restoration Chapter 5 Image Restoration Linear, Position-Invariant Degradations Estimation the Degradation Function 2) Estimation by Experimentation A : impulse Fourier transform which is constant.

Digital Image Processing, 2nd ed. © 2002 R. C. Gonzalez & R. E. Woods Chapter 5 Image Restoration Chapter 5 Image Restoration

Digital Image Processing, 2nd ed. © 2002 R. C. Gonzalez & R. E. Woods Chapter 5 Image Restoration Chapter 5 Image Restoration Linear, Position-Invariant Degradations Estimation the Degradation Function 3) Estimation by modeling Turbulence model : Mathematical model :

Digital Image Processing, 2nd ed. © 2002 R. C. Gonzalez & R. E. Woods Chapter 5 Image Restoration Chapter 5 Image Restoration

Digital Image Processing, 2nd ed. © 2002 R. C. Gonzalez & R. E. Woods Chapter 5 Image Restoration Chapter 5 Image Restoration

Digital Image Processing, 2nd ed. © 2002 R. C. Gonzalez & R. E. Woods Chapter 5 Image Restoration Chapter 5 Image Restoration How to get F ^ (u,v) from degraded image G(u,v) : 1)Inverse Filtering We should know N(u,v) to use this method. We should use this method near origin because H(u,v) is near zero in other areas.

Digital Image Processing, 2nd ed. © 2002 R. C. Gonzalez & R. E. Woods Chapter 5 Image Restoration Chapter 5 Image Restoration

Digital Image Processing, 2nd ed. © 2002 R. C. Gonzalez & R. E. Woods Chapter 5 Image Restoration Chapter 5 Image Restoration How to get F ^ (u,v) from degraded image G(u,v) : 2)Wiener (Minimum mean square Error) Filtering H(u,v) : degradation function S n (u,v)=|N(u,v)| 2 power spectrum of the noise S f (u,v)=|F(u,v)| 2 power spectrum of the undergraded image

Digital Image Processing, 2nd ed. © 2002 R. C. Gonzalez & R. E. Woods Chapter 5 Image Restoration Chapter 5 Image Restoration If S f (u,v) is not known :

Digital Image Processing, 2nd ed. © 2002 R. C. Gonzalez & R. E. Woods Chapter 5 Image Restoration Chapter 5 Image Restoration

Digital Image Processing, 2nd ed. © 2002 R. C. Gonzalez & R. E. Woods Chapter 5 Image Restoration Chapter 5 Image Restoration

Digital Image Processing, 2nd ed. © 2002 R. C. Gonzalez & R. E. Woods Chapter 5 Image Restoration Chapter 5 Image Restoration How to get F ^ (u,v) from degraded image G(u,v) : 3)Constrained Least Squares Filtering

Digital Image Processing, 2nd ed. © 2002 R. C. Gonzalez & R. E. Woods Chapter 5 Image Restoration Chapter 5 Image Restoration

Digital Image Processing, 2nd ed. © 2002 R. C. Gonzalez & R. E. Woods Chapter 5 Image Restoration Chapter 5 Image Restoration

Digital Image Processing, 2nd ed. © 2002 R. C. Gonzalez & R. E. Woods Chapter 5 Image Restoration Chapter 5 Image Restoration Geometric Transformations : (rubber-sheet transformations) 1)Spatial Transformations 2)Gray-level Transformations

Digital Image Processing, 2nd ed. © 2002 R. C. Gonzalez & R. E. Woods Chapter 5 Image Restoration Chapter 5 Image Restoration

Digital Image Processing, 2nd ed. © 2002 R. C. Gonzalez & R. E. Woods Chapter 5 Image Restoration Chapter 5 Image Restoration

Digital Image Processing, 2nd ed. © 2002 R. C. Gonzalez & R. E. Woods Chapter 5 Image Restoration Chapter 5 Image Restoration

Digital Image Processing, 2nd ed. © 2002 R. C. Gonzalez & R. E. Woods Chapter 5 Image Restoration Chapter 5 Image Restoration