數(shù)字圖像處理岡薩雷斯N12PPT課件

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頁(yè)/共23頁(yè)Degradation ModelImage Enhancement no. 1),(),(),(),(vuNvuFvuHvuG),(),(),(yxyxfHyxg第2頁(yè)/共23頁(yè)Linear, position invariant degradationImage Enhancement no. 1),(),( ifinvariant position is .homogenity and additivity of propertiesboth posse

3、soperator linear A ),(),(),(),( iflinear is ).,(),( that so, 0),( Assume22112211yxgyxfHHyxfHkyxfHkyxfkyxfkHHyxfHyxgyx第3頁(yè)/共23頁(yè)Degradation model for continuous functionImage Enhancement no. 1),(),(),(),( ),(),( ),(),(),(),(),(),(),(yxHyxhddyxHfddyxfHddyxfHyxfHyxgddyxyxfyxfAdditivityHomogenityImpulse r

4、esponse,Point spread function(PSF)第4頁(yè)/共23頁(yè)Discrete Formulation and Algebraic approach to restorationImage Enhancement no. 1),(),(),( ),(1010yxnymxhnmfyxgeeeMmNn HfgMatrix forma.)Unconstrained restoration Minimizing criterion function. Obtain (inverse filtering):b.)Constrained restorationHfg,)(2fHgfJ

5、)(20)(fHgHffJTgHf1),()(222fHgfQfJgHQQHHfTTT1)(Qf: criterion function can be linear composition of f/1第5頁(yè)/共23頁(yè)Inverse filteringImage Enhancement no. 1),(),(*),(),(yxyxfyxhyxg),(),(),(),(vuNvuFvuHvuG),(),(),(),(),(),(vuHvuNvuFvuHvuGvuFThe inverse filtering isHow to find H(u,v)? Observation (partially

6、a strong signal region) Experiment (point spread function, a resembling device) Model estimateWhen there is additive noise第6頁(yè)/共23頁(yè)Example of model estimationImage Enhancement no. 16/5)(22),(vukevuH第7頁(yè)/共23頁(yè)Example of model estimation(blur caused by uniform linear motion)Image Enhancement no. 1dttyytx

7、xfyxgT) )(),(),(000)()(sin)(),(vbuajevbuavbuaTvuH第8頁(yè)/共23頁(yè)The problem with inverse filteringImage Enhancement no. 1),(),(),(),(),(),(vuHvuNvuFvuHvuGvuFIf 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

8、 distance from the origin. The noise term 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頁(yè)/共23頁(yè)ExampleImage Enhancement no. 1Order 10 Butterworth filter第10頁(yè)/共2

9、3頁(yè)Least mean square (Wiener) filteringImage Enhancement no. 1),( |)( | goal(mean)on Minimizati122RRQQfQffffEefT),(),(/ ),(| ),(| ),(|),(1),(22vuGvuSvuSvuHvuHvuHvuFf),(| ),(| ),(|),(1),(22vuGKvuHvuHvuHvuFby edapproximat is above the d),encountereoften problem a unknown( are ),(&),(When vuSvuSfnnn

10、fff1),()(222fHgfQfJ第11頁(yè)/共23頁(yè)ExampleImage Enhancement no. 1第12頁(yè)/共23頁(yè)ExampleImage Enhancement no. 1第13頁(yè)/共23頁(yè)Constrained least square filteringImage Enhancement no. 1operatorLaplacian , ),( hing)goal(smooton Minimizati2101022pf pfyxfCMxNy010141010),(yxp),(),(| ),(|),(),(2*vuGvuPvuHvuHvuFcan be selected

11、 interactively or iteratively/1),()(222fHgfQfJ第14頁(yè)/共23頁(yè)ExampleImage Enhancement no. 1Litter better in high and medium noise, no much difference in low noise case第15頁(yè)/共23頁(yè)Optimal selection ofImage Enhancement no. 1)( or ),(1 , ),(1 :Notice. adjustingafter 2 return to otherwise , if stop 3.) ;2.)compu

12、t ; of valueinitial choose 1.):Algorithm factor).accuracy an ( , that so , adjust y Iterativel . ) offunction (a , vector residual a Define222101021010222222mMNyxMNmmyxMNMxNyMxNyrrrfHgr第16頁(yè)/共23頁(yè)ExampleImage Enhancement no. 1a.) initial value 10 -5, adjusted to 10-6. b) wrong variance=10 -2, mean=0第1

13、7頁(yè)/共23頁(yè)Geometric transformationsImage Enhancement no. 1Also called rubber sheet transformation which modifies the spatial relation between 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.Mo

14、re tie-points cover the whole region, optimization.),(),(yxsyyxrx87654321cxycycxcycxycycxcx第18頁(yè)/共23頁(yè)Gray-level interpolationImage Enhancement no. 1Problem: noninteger values for x and y .Solution: 1.) nearest neighbor approach(zero-order interpolation) 2.) billinear interpolation approach (four nearest neighbors)dcxybyaxyxv) , (Four pa