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lecture06 - ELEC317 Lecture 6 Digital Image Processing...

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1 ELEC317 Digital Image Processing Lecture 6 Image Restoration – Due to distortions in imaging process, data captured is different from the true image. e.g. –Relative motion between subject & camera –Band limited image due to diffraction. –Corruption by noise –Missing part of data –Let true image be u(m,n) , captured image be v(m,n) , then objective is to find an operator H such that () []() n m u n m v H , , –To measure “Goodness” of operator, we use mean squared error: [] ∑∑ == = N m N n n m v H n m u N MSE 00 2 2 , , 1 –image restoration in general consists of two stages: A. Restoration Models This is physical understanding & modeling of the relationship between received image & real image. For this purpose, we need to A.1. Model the way image is collected. A.2. Model/Measure response characteristics of detector and recorder A.3. Model/Measure statistical characteristics of noise. B. Design and implementation of restoration algorithms There are two big classes of restoration algorithms: B.1.Linear filtering method; B.2. Nonlinear methods. Image Observation Model Before useful restoration algorithm can be designed, need to understand how images are formed. A generally useful model is as follows:

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2 () []() y x y x w g y x v , , , η + = ( ) ∫∫ = ' ' ' ' ' ' , , , , dy dx y x u y x y x h y x w i [] ( ) y x y x y x w g f y x , , , , 2 1 + = Thus, the image observation modeling refers to characterization of: 1. impulse response of linear system: h(x, , y, x’,y’) normally, system is shift invariant Æ only need h(x,y) And ()() y x u y x h y x w , * , , = 2. Characterize nonlinear functions g(.) and f(.) 3. Characterize noise characteristics y x , 1 and y x , 2 . Image Formation Model The impulse response h(x,y) is related to the way image is taken. (i) Coherent Diffraction Limited Model –Here the aperture is rectangular –Image obtained is (in frequency domain) = b a rect u W 2 1 2 1 2 1 , , , ξ ( ) ( ) ( ) by c ax c ab y x u y x w sin sin * , , = (ii) Incoherent diffraction limited model Linear system h(x,y; x’,y’) Point nonlinearity g(.) w(x,y) System may not be shift invariant u(x,y) image v(x,y) (x,y) 1 (x,y) Noise 2 (x,y) Noise f(.)
3 –Here aperture is rectangle –But phase is lost () = b a tri u W 2 1 2 1 2 1 , , , ξ ( )( ) ( ) [ ] by c ax c y x u y x w 2 2 sin sin * , , = (iii) Horizontal motion –Here, while take the picture, the object move horizontally with uniform velocity. ds y s x u y x w + = 2 0 2 0 , 1 , 0 α = y x rect y x u δ 2 1 1 * , 0 0 (iv) Rectangular scanning aperture –here due to finite aperture size, we measure the average of u(x,y) only a square. ( ) ∫∫ −− = 2 2 2 2 , , β dudv v y u x u y x w = y x rect y x u , * , ( ) ( ) ( ) [] 2 1 2 1 2 1 sin sin , , βξ αξ αβ c c u W = (v) CCD interaction –Here due to interaction between the CCD cells, value at (x,y) also depends on the value of its neighbours: ( ) l y k x u y x w kl kl = ∑∑ =− = , , 1 1 1 1 ( ) = = l y k x y x u kl , * , 1 1 1 1 (vi) Atmospheric turbulence

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This note was uploaded on 04/14/2010 for the course ELEC 317 taught by Professor Nil during the Spring '02 term at HKUST.

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lecture06 - ELEC317 Lecture 6 Digital Image Processing...

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