数字图像处理知识点总结

基础1.什么是数字图像一副图像可定义为一个二维函数f（x、y），其中x和y是空间（平面）坐标，而在任何一对空间坐标（x、y）处的幅值f称为图像在该点处的强度或灰度。当x、y和灰度值f是有限的离散数值时，我们称该图像为数字图像。Thefunctionfmayrepresentintensity(formonochromeimages)orcolor(forcolorimages)orotherassociatedvalues.Digitalimage:animagethathasbeendigitizedbothinspatialcoordinatesandassociatedvalue.Consistof2sets:(1)apointsetand(2)avaluesetCanberepresentedintheformI={(x,a(x)):x属于X,a(x)属于F}Whydoweneedimagecompression?-Example:digitalcamera(4Mpixel)Rawdata–24bits,4Mpixels–12Mbytes192Mmemorycard–16pictures2.图像坐标系笛卡尔坐标不能作为像素坐标3.最小单位空间分辨率是图像中可辨别的最小细节的度量。灰度分辨率是指在灰度级中可分辨的最小变化。4.数字图像处理的概念、研究内容数字图像处理是指借助于数字计算机来处理数字图像。数字图像是由有限数量的元素组成的，每个元素都有一个特定的位置和幅值。这些元素成为图画元素、图像元素或像素。Functions:1.Acquisition2.Storage3.Processing4.Communication5.DisplayimageSamplingandQuantization采样和量化Imagesampling:digitizeanimageinthespatialdomainSpatial/imageresolution分辨率:pixelsizeornumberofpixels5.图像的领域（4，8，对角）及连通的概念Neighborhoodrelationisusedtotelladjacent（邻近，毗连）pixels.Itisusedinestablishingboundariesofobjectsandcomponentsofregionsinanimageforanalyzingregions.位于坐标（x、y）处的像素p有4个水平和垂直的相邻像素，其坐标由下式给出：（x+1，y），（x-1，y），（x，y+1），（x，y+1）这组像素成为p的4邻域，用𝑁4（p）表示。每个像素距（x，y）一个单位距离。Note:q∈N4(p)impliesp∈N4(q)4-neighborhoodrelationconsidersonlyvertical（垂直）andhorizontal（水平）neighbors.P的4个对角相邻像素的坐标如下：（x-1,y-1）,(x,y-1),(x-1,y),(x+1,y),(x,y+1),（x+1，y+1），（x+1，y-1），（x-1，y+1），（x-1，y-1）并用𝑁𝐷（p）表示。这些点与4个邻点一起称为p的8邻域，用𝑁8（p）表示8-neighborhoodrelationconsidersallneighborpixels.Diagonal-neighborhoodrelationconsidersonlydiagonal(斜的)neighborpixels.(x-1,y-1),(x+1,y-1),(x-1,y+1),(x+1,y+1)6.各不同电磁波谱的图像成像技术，波段划分？7.图像数字化过程（扫描、采样、量化）及各自含义？图像分辨率（空间、灰度）与质量的关系？（采样间距与数据量的关系、采样间距与质量的关系、量化与数据量的关系、量化与质量的关系）Imagequantization(数字化):digitizecontinuouspixelvaluesintodiscretenumbers空域增强8.图像增强的目的（不清晰的图像变得清晰或强调某些感兴趣的特征，改善图像质量，丰富信息量，加强图像判读和识别效果），分类及特点Objective:toprocessanimagesothattheresultismoresuitableforaspecificapplication.·Problemoriented·ThebestmethodforenhancingX-rayimagesmaybenotthebestmethod,evennotsuitableforenhancingpicturesofMars(火星)transmittedbyaspaceprobe(探测器)Therearetwomaincategoriesoftechniquesforimageenhancement:·Spatial（空间的）DomainMethods-whichoperatedirectlyonpixels.·FrequencyDomainMethods-whichoperateontheFourierTransformoftheimage.·Combinationalapproacheswiththesetwocategoriesarenotunusual.9.图像增强点到点运算有哪些？特点？优缺点？（对数、乘方率、分段线性、二值化、加法噪声、减法变化）•Enhancementatanypointinanimagedependsonlyonthegraylevelatthatpoint.•Contraststretching对比度扩展：darkeningthegraylevelsbelowmintheoriginalimage,brighteningthegraylevelsabovemintheoriginalimage.•Thresholding阈值化：thelimitingcaseistogenerateabinaryimage.SomeBasicGrayLevelTransformations•Negative(linear)•Log(logandinverse-logtransformations)•Powerlaw乘方律(nthpowerandn-throottransformations.Theidentitytransformationisatrivial(微不足道的)case:output=input,onlyforcompleteness完备性).•Piecewise-lineartransformationfunctions(分段线性函数)•Bitslicing位切片Definition:Thenegativeofanimagewithgraylevelsintherange[0,L-1]canbedefinedas:s=L−1−rr=L-1,s=0:White-Blackr=0,s=L-1:Black-White•Function:Reversingtheintensitylevelsofanimageinthismannerproducestheequivalent(等价物)ofaphotographicnegative(照相底片)•Applications:Enhancingwhiteorgraydetailsembeddedindarkregions,especiallywhentheblackareasaredominantinsize.“Log”Definition:Thegeneralformofthelogtransformationisdefinedass=clog(1+r)L-1=clog(1+L-1)c=Wherecisaconstant,assumethatr0“Log”Function:•Tomapanarrowrangeoflowgray-levelvaluesintheinputimageintoawiderrangeofoutputlevels.•Tomapawiderangeofhighgray-levelvaluesintheinputimageintoanarrowerrangeofoutputlevels.“Log”Applications:•Toexpandthevaluesofdarkpixelsinanimagewhilecompressingthehigher-levelvalues•TocompressdynamicrangeIngeneral,logarithmicmappingisusefulifwewishtoenhancedetailinthedarkerregionsoftheimage,attheexpenseofdetailinthebrighterregions.“InverseLog”Definition:Thegeneralformoftheinverselogtransformationisdefinedas()Wherecisaconstant“InverseLog”Function:•Tomapawiderangeoflowgray-levelvaluesintheinputimageintoanarrowerrangeofoutputlevels.•Tomapanarrowrangeofhighgray-levelvaluesintheinputimageintoawiderrangeofoutputlevels.“InverseLog”Applications:Toexpandthevaluesofbrightpixelsinanimagewhilecompressingthelower-levelvalueLogTransformationsconclusionNote:•AnycurvehavingthegeneralshapeofthelogfunctionscanaccomplishthesimilarfunctionofSpreading/Compressingofgraylevels.•Comparedwithlogtransformation,Power-Lawtransformations(discussedlater)aremoreversatile(通用的，多面手的)withdifferentparameters•However,logfunctioncancompressthedynamicrangeofimageswithlargevariationsinpixelvalues.Power-LawTransformationsDefinitions:TheBasicformofPower-LawTransformations:Wherecandγarepositiveconstants.Functions:•Thecaseofγ1:similartothecaseoflogfunction•Thecaseofγ1:similartothecaseofinverselogfunctionPiecewise-LinearTransformationFunction分段线性Advantage:•TheformofpiecewisefunctioncanbearbitrarilycomplexDisadvantage:•TheirspecificationrequiresmoreuserinputApplications•ContrastStretching(对比度拉伸):Increasethedynamicrangeofthegraylevelsinanlow-contrastimage.•Gray-LevelSlicing(灰度切割/灰度窗口变换):Highlight(使显著)aspecificrangeofgrayleve