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1、Image RestorationWe consider restoration to be a process that attempts to reconstruct or recover an image that has been degraded by using some a prior knowledge of the degradation phenomenon.Thus restoration techniques are oriented toward modeling the degradation and applying the inverse process in
2、order to recover the original image.Image Enhancement no.1第1页/共23页Degradation ModelImage Enhancement no.1第2页/共23页Linear,position invariant degradationImage Enhancement no.1第3页/共23页Degradation model for continuous functionImage Enhancement no.1AdditivityHomogenityImpulse response,Point spread functio
3、n(PSF)第4页/共23页Discrete Formulation and Algebraic approach to restorationImage Enhancement no.1Matrix forma.)Unconstrained restoration Minimizing criterion function.Obtain(inverse filtering):b.)Constrained restorationQf:criterion function can be linear composition of f第5页/共23页Inverse filteringImage E
4、nhancement no.1The inverse filtering isHow to find H(u,v)?Observation (partially a strong signal region)Experiment(point spread function,a resembling device)Model estimateWhen there is additive noise第6页/共23页Example of model estimationImage Enhancement no.1第7页/共23页Example of model estimation(blur cau
5、sed by uniform linear motion)Image Enhancement no.1第8页/共23页The problem with inverse filteringImage Enhancement no.1If H(u,v)is zero or becomes very small,the term N(u,v)/H(u,v)could dominate the restoration result.H(u,v)often drops off rapidly as a function of distance from the origin.The noise term
6、 usually falls off at a much slower rate.So carry out the restoration in a limited neighborhood about the origin in order to avoid small values.Notice:H(u,v)is very sensitive to noise!第9页/共23页ExampleImage Enhancement no.1Order 10 Butterworth filter第10页/共23页Least mean square(Wiener)filteringImage Enh
7、ancement no.1第11页/共23页ExampleImage Enhancement no.1第12页/共23页ExampleImage Enhancement no.1第13页/共23页Constrained least square filteringImage Enhancement no.1can be selected interactively or iteratively第14页/共23页ExampleImage Enhancement no.1Litter better in high and medium noise,no much difference in low
8、 noise case第15页/共23页Optimal selection ofImage Enhancement no.1第16页/共23页ExampleImage Enhancement no.1a.)initial value 10-5,adjusted to 10-6.b)wrong variance=10-2,mean=0第17页/共23页Geometric transformationsImage Enhancement no.1Also called rubber sheet transformation which modifies the spatial relation b
9、etween pixels in an image.It consists two basic operation:1.)a spatial transformation;2.)a gray-level interpolation.Four pair of tie-points,8 bilinear equations.More tie-points cover the whole region,optimization.第18页/共23页Gray-level interpolationImage Enhancement no.1Problem:noninteger values for x
10、and y.Solution:1.)nearest neighbor approach(zero-order interpolation)2.)billinear interpolation approach(four nearest neighbors)Four pair of neighbors,4 bilinear equations.第19页/共23页ExampleImage Enhancement no.1第20页/共23页ExampleImage Enhancement no.1第21页/共23页Recommended Reading Gonzalez+Woods:Chapter 5Frequency Filtering no.34第22页/共23页感谢您的观看！第23页/共23页