1、AgendaAgendaFoundationFoundationoCh14 Imaging System,Digitalization,Display,SoftwareCh14 Imaging System,Digitalization,Display,SoftwareoCh58 Histogram,Point Operations,Algebraic Operations,Ch58 Histogram,Point Operations,Algebraic Operations,Geometric OperationsGeometric OperationsTheoryTheoryoCh912
2、 Linear System,Fourier Frequency Transform,Ch912 Linear System,Fourier Frequency Transform,Filter Design,Discrete SamplingFilter Design,Discrete SamplingoCh1315 Orthogonal Radicle Transform,Wavelet Time-Ch1315 Orthogonal Radicle Transform,Wavelet Time-frequency Transform,Optical Function Transformfr
3、equency Transform,Optical Function TransformApplicationApplicationoCh1620 Image Restoration,Compression,Pattern Ch1620 Image Restoration,Compression,Pattern RecognitionRecognitionoCh2122 Color and Multi-Spectral Image Processing,Three Ch2122 Color and Multi-Spectral Image Processing,Three Dimension
4、Image ProcessingDimension Image Processingo mathematical modelmathematical modeloThe model of image degradation and The model of image degradation and restoration as followrestoration as follow。Image degradation Image degradation is caused by system performance and is caused by system performance an
5、d noise.Restoration is achieved through noise.Restoration is achieved through rehabilitating filter(inverse filter).rehabilitating filter(inverse filter).16.2 Classical Restorationo Geometric Mean FiltersGeometric Mean FiltersoNotice that if =1,Eq reduces to a Notice that if =1,Eq reduces to a decon
6、volution filter.If =1/2 and =1,it deconvolution filter.If =1/2 and =1,it reduces to PSE filter.It is the geometric reduces to PSE filter.It is the geometric mean between ordinary deconvolution and mean between ordinary deconvolution and Wiener deconvolution.So it is also called Wiener deconvolution.
7、So it is also called geometric mean filter.It is common geometric mean filter.It is common practice,however,to refer to the more practice,however,to refer to the more general filter mentioned above as the general filter mentioned above as the geometric mean filter.geometric mean filter.12*2),(/),(),
8、(),(),(),(),(vuPvuPvuHvuHvuHvuHvuGfnoUnconstrained RestorationUnconstrained RestorationIf n=0 or if we know nothing about If n=0 or if we know nothing about the noise,we can set up the the noise,we can set up the restoration as a least squares restoration as a least squares minimization problem.mini
9、mization problem.e(f)=g-Hf e(f)=g-Hf W(f)=(g-Hf)W(f)=(g-Hf)t t(g-Hf)(g-Hf)Setting to zero the derivative of f,Setting to zero the derivative of f,yields yields f=H f=H-1-1 g goConstrained Least Squares Constrained Least Squares RestorationRestoration oIntroduce into the minimization the Introduce in
10、to the minimization the constraint that the norms of each constraint that the norms of each side of g-Hf=n be the sameside of g-Hf=n be the same，that that is,is,oNow we can set up the problem as Now we can set up the problem as the minimization of the minimization of 22nfHg222)(nfHgfQfWoWhere Q is a
11、 matrix we select to define Where Q is a matrix we select to define some linear operator on f and is a some linear operator on f and is a constant called a Lagrange multiplier.constant called a Lagrange multiplier.The ability to specify Q gives us The ability to specify Q gives us flexibility in set
12、ting the goal of the flexibility in setting the goal of the restoration.As before,we set to zero restoration.As before,we set to zero the derivative of Wthe derivative of W（f f）with respect to with respect to f:f:oWhere is a constant that must be Where is a constant that must be adjusted so that the
13、 constraint of above adjusted so that the constraint of above is satisfied.is satisfied.0)(22)(HfgHQfQffWgHQQHHfttt1)(1,16.5 SuperresolutionSuperresolutionincoherent transfer function of an incoherent transfer function of an o p t i c a l s y s t e m i s t h e o p t i c a l s y s t e m i s t h e aut
14、ocorrelation function of the autocorrelation function of the pupil function.Restoration pupil function.Restoration procedures that seek to recover procedures that seek to recover information beyond the diffraction information beyond the diffraction l i m i t a r e r e f e r r e d t o a s l i m i t a
15、 r e r e f e r r e d t o a s superresolution technique.superresolution technique.o Harris Technique Harris Technique Harris thought that it should be Harris thought that it should be possible to reconstruct that object possible to reconstruct that object in infinite detail from its in infinite detai
16、l from its diffraction-limited image.The diffraction-limited image.The technique involves applying the technique involves applying the sampling theorem,with domains sampling theorem,with domains reversed,to obtain a system of reversed,to obtain a system of linear equations that can be solved linear
17、equations that can be solved for values of the signal spectrum for values of the signal spectrum outside the diffraction-limited outside the diffraction-limited passband.passband.o Successive Energy ReductionSuccessive Energy Reduction It involves successively enforcing space-It involves successivel
18、y enforcing space-limitedness upon the image,while limitedness upon the image,while keeping the known low-frequency portion keeping the known low-frequency portion of the spectrum intact.Notice that of the spectrum intact.Notice that bandlimiting the spectrum cause g0(x)no bandlimiting the spectrum
19、cause g0(x)no longer to be space limited.The first longer to be space limited.The first step of the restoration is enforcing step of the restoration is enforcing space-limitedness upon g0(x)by setting space-limitedness upon g0(x)by setting it to zero outside the domain of the it to zero outside the
20、domain of the pulse.The second step involves pulse.The second step involves replacing.The convergence generally replacing.The convergence generally becomes rather slow after the first few becomes rather slow after the first few steps.steps.oSmall-Kernel ConvolutionSmall-Kernel ConvolutionUnless the
21、image is severely oversampled,the Unless the image is severely oversampled,the signal spectrum,and consequently the signal spectrum,and consequently the restoration MTF,will normally extend most of restoration MTF,will normally extend most of the way to the folding frequency before it dies the way t
22、o the folding frequency before it dies out.From the similarity theorem of the Fourier out.From the similarity theorem of the Fourier transform,we know that if the transfer transform,we know that if the transfer function is abroad,the impulse response will function is abroad,the impulse response will
23、 be narrow.Thus,the convolution kernel for be narrow.Thus,the convolution kernel for implementing a restoration PSF might well be implementing a restoration PSF might well be zero,or approximately so,except within a zero,or approximately so,except within a reasonably small radius about the origin.In
24、 reasonably small radius about the origin.In that case,the majority of the operations that case,the majority of the operations required for an N-by-N convolution will required for an N-by-N convolution will contribute little or nothing to the contribute little or nothing to the restoration.restorati
25、on.oTruncating the kernelTruncating the kernel A simpler approach to small-kernel A simpler approach to small-kernel convolution is merely to truncate convolution is merely to truncate the PSF array to some acceptably the PSF array to some acceptably small size.Multiplying the PSF by small size.Mult
26、iplying the PSF by a square pulse convolves the MTF a square pulse convolves the MTF with a sin(x)/x function.Unless with a sin(x)/x function.Unless the PSF is spatially bounded,this the PSF is spatially bounded,this can alter its transfer function can alter its transfer function significantly.signi
27、ficantly.oKernel DecompositionKernel DecompositionModern image-processing system often Modern image-processing system often incorporate special hardware for high-incorporate special hardware for high-speed convolution with a small kernel.speed convolution with a small kernel.This hardware becomes us
28、eful when an M-This hardware becomes useful when an M-by-M kernel is decomposed into a set of by-M kernel is decomposed into a set of smaller kernels that are then applied smaller kernels that are then applied sequentially.For example,(M-1)/2 sequentially.For example,(M-1)/2 kernels of size three by
29、 three will kernels of size three by three will implement an M-by-M convolution.While implement an M-by-M convolution.While this cannot substitute exactly for an this cannot substitute exactly for an arbitrary M-by-M kernel,the result is arbitrary M-by-M kernel,the result is often a good approximati
30、on.often a good approximation.16.2 16.2Classical Restoration16.3 Linear Algebraic Restoration16.4 restoration of less restricted degradations16.5 Superresolution16.6System Identification16.7Noise Modeling16.8 Implementation16.9 Summary16.9 SummaryAgendaAgendaFoundationoCh14 Imaging System,Digitaliza
31、tion,Display,SoftwareoCh58 Histogram,Point Operations,Algebraic Operations,Geometric OperationsTheoryoCh912 Linear System,Fourier Frequency Transform,Filter Design,Discrete SamplingoCh1315 Orthogonal Radicle Transform,Wavelet Time-frequency Transform,Optical Function TransformApplicationoCh1620 Imag
32、e Restoration,Compression,Pattern RecognitionoCh2122 Color and Multi-Spectral Image Processing,Three Dimension Image ProcessingChapter 17image compressionDeleted contentRecovery abilityApproximateka10()()log()KkkkkHE I ap ap a HaLERkw)()(log)(kkwapaL)(log)(2kkwapaLka(),1,2,.,1,kp akKKlog()kIp a 1234
33、56probability12345661()()log()2.16kkkkH ap ap a 61()()()2.3kkkkkH ap a l a()kkl a()kkp a),(),(2yxgyxfED)(DR1DD)()(1DRDR)2log(21),(),(eDyxgyxfHDD0DR(D)drentropy codingrate distortion functionThe distortion between The distortion between original image f(x,y)and original image f(x,y)and reconstruction
34、 imagereconstruction image g(x,y)is quantified by g(x,y)is quantified by the mean square error:the mean square error:2(,)(,)DEf x yg x ydoes it exist such transform does it exist such transform T,and at the same time D is T,and at the same time D is minimumminimumminimum distortion minimum distortio
35、n transform coding is the transform coding is the most efficient at given most efficient at given distortion rate by rate distortion rate by rate distortion functiondistortion function第8页（共17页）YXY=TXcoordinate rotation transformY=Xcossin44sincos44T XYBit of scalar quantization decrease at the same q
36、uantization Bit of scalar quantization decrease at the same quantization errors after coordinate rotationerrors after coordinate rotation+xXX1TTW：noise coming from bit distributionA：filter1*tTTTTISuppose data vector transform matrix ,then orthogonal transform can be expressed ,the result vector is ,
37、inverse transform is .coding mean square error is ,where is covariance matrix of X,and find when is minimum.we can get the condition of minimum by Lagrange multiplier method:,and that is where is characteristic matrix of .we can have the conclusion that:base vector T of optimal orthogonal transform
38、is the characteristic matrix of data vector X covariance matrix.The optimal orthogonal transform T is the famous Kanhuman-Loeve transformSuppose X is N1 random vector,each component X1 of X can be estimated L vector samples .Covariance matrix of X is .K-L orthogonal transform is such a linear transf
39、orm,where the row of A is characteristic matrix of ,.Transformed covariance matrix Y can be reasoned by covariance matrix of X ,where is characteristic value of .inverse transform of K-L is .One 31 random vector X has following covariance matrix:The characteristic value and characteristic vector are
40、:For a vector whose mean value is zero,the k-L transform result is If ignores the small transform base in A,it can reduce the dimension of Y:reconstruction process:standard deviation of lossy compression:(can control the error)If C is singularity,it can achieve higher compression raten Generally,it
41、is used to compare with new coding Generally,it is used to compare with new coding algorithm;algorithm;Suppose the known correlation coefficient p(0p1),Covariance matrixof the original data is:,we can calculate transform base of K-L by C.for example,p=0.91,N=8 the transform matrix is The correspondi
42、ng characteristic value,the energy and percent of anterior M diagonal elements,are as below :So we can get K-L transform has good concentration of energy,and completely reduces Correlation.第17页（共17页）beginRead signs informationInitialize FastIDCTEncoding MCUthe respective anti-quantization for several components,Zig-ZagYUV-RGBstorage RGB into cacheEOI show bitmapoverNY
