數(shù)字圖像處理英文課件：lecture5 Image Restoration

1、Image Restoration Degradation Model and General ApproachesTermsImage restoration:圖象恢復(fù)Degrade: 退化Autocorrelation:自相關(guān)Convolution:卷積Pad:填充Period:周期Linear algebra:線(xiàn)性代數(shù)TermsCirculant matrix:循環(huán)矩陣Transpose:轉(zhuǎn)置Block matrix:分塊矩陣Block circulant matrix:分塊循環(huán)矩陣Impulse: 沖激函數(shù)Dirac delta function: 狄拉克函數(shù)Impulse respo

2、nse:沖激響應(yīng)Point spread function (PSF):點(diǎn)擴(kuò)展函數(shù)Image Restoration- outlineImage enhancement vs. restorationDegradation modelNoise onlyLinear, space-invariant 位置不變性General approachesInverse filtersWiener filtersConstrained least squares filtering前者主要是一個(gè)主觀(guān)過(guò)程，后者則是一個(gè)客觀(guān)過(guò)程。后者是試圖利用退化現(xiàn)象的某種先驗(yàn)知識(shí)來(lái)重建或復(fù)原被退化圖像。Image Res

3、torationImage enhancement : process image so that the result is more suitable for a specific application, is largely a subjective process.Image restoration : recover image from distortions to its original image, is largely an objective process.Image enhancement vs. restoration 圖象增強(qiáng)：旨在改善圖象質(zhì)量。 圖象恢復(fù)：力求

4、保持圖象的本來(lái)面目，以保真原則為前提，找出圖象降質(zhì)的原因，描述其物理過(guò)程，提出數(shù)學(xué)模型。恢復(fù)的過(guò)程是沿著質(zhì)量降質(zhì)的逆過(guò)程來(lái)重現(xiàn)原始圖象。 退化：質(zhì)量降質(zhì)。 圖象退化的一種現(xiàn)象圖象模糊。Digital video camerajiObject to be imagedDirection of motion of beltConveyor beltFigure 1 Imaging of object moving at constant velocity.ji圖象恢復(fù) 圖象退化的原因： （1）攝影時(shí)照相機(jī)鏡頭的移動(dòng)； （2）放大鏡凸透變形等。 圖象退化模型：圖象模糊可以籠統(tǒng)的歸納為成象系統(tǒng)沒(méi)有理想

5、的沖激響應(yīng)。 51 A Model of the Image Degradation/Restoration Process Model the degradationObjective of restoration-to obtain an estimate of the original image. Apply the inverse process to recover the original image空間域上的卷積等同于頻域上的乘積。h是退化函數(shù)的空間描述，H是頻域描述。If H is linear, spatially invariant process, thenP142Th

6、e OTF and PSF are a Fourier transform pair, and the toolbox provide otf2psf and psf2otf functions, for converting between them. P142Noise modelsSpatial characteristics (independent or dependent)Intensity ( distribution, spectrum)Correlation with the image (additive, multiplicative) De-noising Spatia

7、l filteringFrequency domain filteringDegradation models : due to noise only MATLAB圖像噪聲腐蝕函數(shù) imnoiseThe toolbox uses function imnoise to corrupt an image with noise. The function has the basic syntax: g=imnoise(f,type,parameters)Function imnoise converts the input image to class double in the range0,1

8、 before adding noise to it. This must be taken into account when Specifying noise parameters. For example, to add Gaussian noise of Mean 64 and variance 400 to an uint8 image, we scale the mean to 64/255 and the variance to for input into imnoise.Image Restoration - 1Noise models examples Image Rest

9、oration - 1Noise models examples Image RestorationEstimation of noise parametersBy spectrum inspection: for periodic noiseBy test image: mean, variance and histogram shape, if imaging system is availableBy small patches, if only image is availableDe-noising Spatial filtering ( for additive noise)Mea

10、n filtersOrder-statistics filtersAdaptive filtersFrequency domain filtering (for periodic noise)De-noising Image Restoration De-noising Gaussian noise example Arithmetic mean filterGeometric mean filterImage Restoration Order-statistics filtersMedian filterGood for impulse noise reduction with less

11、blurringMax filterFind the brightest pointsMin filterFind the darkest pointsMidpoint filterCombines order statistics and averaging, works best for randomly distributed noise.De-noising Image RestorationDe-noising Salt & Pepper noise example Image RestorationDe-noising Salt & Pepper noise example 均值濾

12、波器算術(shù)均值濾波器幾何均值濾波器諧波均值濾波器逆諧波均值濾波器 算術(shù)均值濾波器 表示中心在(x,y)點(diǎn)，尺寸為m*n的矩形子圖像窗口的坐標(biāo)組。簡(jiǎn)單平滑了一幅圖像的局部變化，其對(duì)圖像的復(fù)原效果最差。 幾何均值濾波器幾何均值濾波相對(duì)于算術(shù)均值濾波平滑度差不多，但圖像的細(xì)節(jié)丟失更少。算術(shù)均值濾波器和幾何均值濾波器適于處理高斯或均勻分布噪聲。濾波效果對(duì)比a)原圖b)疊加了高斯噪聲的 圖像c)3*3算數(shù)均值濾波d)3*3幾何均值濾波對(duì)噪聲衰減都有作用，但幾何均值濾波比算術(shù)均值濾波減少了對(duì)圖像的模糊諧波均值濾波器諧波均值濾波器對(duì)于“鹽” 噪聲效果較好，但不適于“胡椒”噪聲。它善于處理高斯噪聲。在逆諧波均值

13、濾波器中， Q成為濾波器的階數(shù)。當(dāng)Q為正數(shù)時(shí)，濾波器消除胡椒噪聲；當(dāng)Q為負(fù)值時(shí)，濾波器消除鹽噪聲；當(dāng)Q=0,逆諧波濾波器退化為算術(shù)均值濾波器；當(dāng)Q=-1時(shí)，逆諧波均值濾波器變?yōu)橹C波均值濾波器。諧波均值濾波器適于處理脈沖噪聲，但必須知道噪聲是暗噪聲還是亮噪聲，以便于選擇合適的Q符號(hào)。 逆諧波均值濾波器濾波效果對(duì)比a)疊加了胡椒噪聲的圖像b)疊加了鹽噪聲的圖像c)對(duì)a) 3*3 Q=1.5逆諧波濾波d) 對(duì)b) 3*3 Q=-1.5逆諧波濾波 正階濾波器在使暗區(qū)模糊的損失下，使背景較為清晰。負(fù)階相反。逆諧波濾波中Q值選擇錯(cuò)誤時(shí)造成的結(jié)果濾波效果對(duì)比統(tǒng)計(jì)排序?yàn)V波器中值濾波器最大值濾波器最小值濾波器中

14、點(diǎn)濾波器修正的阿爾法均值濾波器 統(tǒng)計(jì)排序?yàn)V波器中值濾波器： 適于處理椒鹽噪聲，通過(guò)多次使用小模板，可以獲得很好的去噪效果。最大值濾波器： 這種濾波器對(duì)發(fā)現(xiàn)圖像中的最亮點(diǎn)非常有用，可以用來(lái)消除胡椒噪聲。最小值濾波器： 這種濾波器對(duì)發(fā)現(xiàn)圖像中的最暗點(diǎn)非常有用，可以用來(lái)消除鹽噪聲統(tǒng)計(jì)排序?yàn)V波器 取最大值和最小值的平均值。對(duì)高斯和均勻隨機(jī)分布的噪聲有效。中點(diǎn)濾波器 統(tǒng)計(jì)排序?yàn)V波器修正后的阿爾法均值濾波器為鄰域內(nèi)去掉d/2個(gè)最大值和d/2個(gè)最小值后剩余的mn-d個(gè)像素。由這些點(diǎn)的平均值形成的濾波器稱(chēng)為修正后的阿爾法均值濾波器。 d值可以取到0到mn-1之間的任意數(shù)。當(dāng)d=0時(shí)，濾波器退變?yōu)樗阈g(shù)均值濾波器

15、；當(dāng)d=(mn-1)/2時(shí)，濾波器就成為中值濾波器。d取其它值時(shí)，濾波器在包含多種噪聲的情況下非常適用，例如高斯噪聲和椒鹽噪聲混合的情況。由加性均勻噪聲污染的圖像 均值為0,方差為800的高斯噪聲(b) 圖(a)加上椒鹽噪聲污染的圖像 Pa=Pb=0.1得椒鹽噪聲(c) 55的算術(shù)均值濾波處理圖(b)(d) 幾何均值濾波器處理圖(b)(e) 中值濾波器處理圖(b)(f) d=5的修正后的阿爾法均值濾波器(a)(b)(c)(d)(e)(f)由于脈沖噪聲的存在,算術(shù)均值濾波器和幾何均值濾波器沒(méi)有起到良好作用.中值濾波器和阿爾法濾波器效果更好,阿爾法最好.修正后的阿爾法濾波自適應(yīng)濾波器自適應(yīng)局部噪聲

16、消除濾波器自適應(yīng)中值濾波器 自適應(yīng)濾波器自適應(yīng)濾波器是基于m*n矩形窗區(qū)域圖像的統(tǒng)計(jì)特性而變化的，其性能優(yōu)于前面所討論的任何一種濾波器；但作為提高濾波能力的代價(jià)是濾波器的復(fù)雜度增加了。隨機(jī)變量最簡(jiǎn)單的統(tǒng)計(jì)量是均值和方差，這些適當(dāng)?shù)膮?shù)是自適應(yīng)濾波器的基礎(chǔ)。均值給出了計(jì)算均值的區(qū)域中灰度平均值的度量,而方差給出了這個(gè)區(qū)域的平均對(duì)比度的度量.自適應(yīng)局部噪聲消除濾波器需要估計(jì)自適應(yīng)局部噪聲消除濾波器自適應(yīng)局部噪聲消除濾波器a)由0均值和方差為1000的加性高斯噪聲污染的圖像b) 7*7算術(shù)均值濾波處理后圖像c) 7*7幾何均值濾波處理后圖像d) 7*7自適應(yīng)噪聲消除濾波器處理后圖像濾波效果與算術(shù)、幾

17、何均值濾波器相近，但圖像更尖銳些。自適應(yīng)中值濾波器5049494925547484746對(duì)于更大概率密度的椒鹽噪聲去除需考慮：a)去除椒鹽噪聲b) 平滑其他非沖激噪聲c) 減少邊界細(xì)化或粗化等失真Zmin窗口區(qū)域灰度級(jí)的最小值Zmax窗口區(qū)域灰度級(jí)的最大值Zmed窗口區(qū)域灰度級(jí)的中值Zxy 坐標(biāo)(x,y)上的灰度級(jí)SmaxSxy允許的最大尺寸2555049494948474746自適應(yīng)中值濾波器A層次 （判斷Zmed是否為脈沖） A1=Zmed-ZminA2=Zmed-Zmax如果A10，且A20且B20，輸出Zxy否則輸出Zmed5049494925547484746255255255484

18、947474846輸出Zmed輸出ZxyZxy本身為脈沖自適應(yīng)中值濾波效果a)Pa=Pb=0.25的椒鹽噪聲污染的圖像b) 7*7中值濾波處理后圖像c) Smax=7的自適應(yīng)中值濾波處理后圖像噪聲去除水平與中值濾波效果相近，但圖像保持了點(diǎn)的尖銳性及其細(xì)節(jié)。The model of degradation5.2.1 spatial noise filtersThe method of choice for reduction of noise is spatial filtering.The linear filters function-imfilterThe nonlinear,order-

19、statistics filters functions-medfilt2 max min ordfilt252 Restoration in the Presence of Noise Only-Spatial FilteringP159: Spfilt functionP162: functionsP162: example 5.5P148: Imnoise2 functionEx505.mAdaptive local noise reduction filter5.2.2 adaptive spatial filtersAdaptive median filterLet Zmin=min

20、imum intensity value in Sxy Zmax=maximum intensity value in SxyZmed=median of the intensity value in SxyZxy=intensity value at coordinate (x,y)The adaptive median filtering algorithm works in two levels, denoted level A and level B:Level A: if Zmin Zmed Zmax goto level BElse increase the window size

21、If window size=Smax,repeat level AElse output Zmedlevel B: if Zmin Zxy T=2 0 0;0 3 0;0 0 1; tform=maketform(affine,T) tform.tdata tform.tdata.TinvIPT provides two functions for applying a spatial transformation to points: tformfwd and tforminv.The calling syntax for tformfwd is XY=tformfwd(WZ, tform

22、). Here, WZ is a P*2 matrix of points;each row of WZ contains the w and z coordinates of one point. XY is a P*2 matrix of point. WZ=1 1;3 2; XY=tformfwd(WZ,tform)XY = 2 3 6 6 WZ2=tforminv(XY,tform)WZ2 = 1 1 3 2 T1=3 0 0;0 2 0;0 0 1; tform1=maketform(affine,T1); vistformfwd(tform1,0 100,0 100); %5.13

23、(a-b) T1=3 0 0;.2 1 0;0 0 1; tform1=maketform(affine,T1); vistformfwd(tform1,0 100,0 100); %5.13(c-d) Tscale=1.5 0 0;0 2 0;0 0 1; Trotation=cos(pi/4) sin(pi/4) 0;-sin(pi/4) cos(pi/4) 0;0 0 1; Tshear=1 0 0;.2 1 0;0 0 1; T3=Tscale*Trotation*Tshear; tform3=maketform(affine,T3); vistformfwd(tform3,0 100

24、,0 100);5.3.2 applying Spatial Transformations to imagesForward mappingInverse mappingIPT function imtransform g=imtransform(f, tform, interp)Where interp is a string that specifies how input image pixels are interpolated to obtain output pixels:nearest,bilinear,bicubic(default to bilinear)Linear conformal transformation(線(xiàn)性保角、保形變換)The affine transformation matrix in this case has the form f=checkerboard(50); s=0.8; theta=pi/6; T=s*cos(theta) s*sin(t