《数字图像处理冈萨雷斯N09学习教案.pptx》由会员分享，可在线阅读，更多相关《数字图像处理冈萨雷斯N09学习教案.pptx（29页珍藏版）》请在taowenge.com淘文阁网|工程机械CAD图纸|机械工程制图|CAD装配图下载|SolidWorks_CaTia_CAD_UG_PROE_设计图分享下载上搜索。
1、会计学1数字图像处理冈萨雷斯数字图像处理冈萨雷斯N09第一页，共29页。1-d Fourier transform of a sequence1-d Fourier transform of a sequence Given a 1-d sequence f(x),x 0,1,2,3,.NFourier transformImage transform no.2 Fourier transform is periodic with 2Inverse Fourier transformThe variable u is called frequency variable.using Eulers
2、 formula:第2页/共29页第二页，共29页。1-d Fourier transform of a sequence(cont.)1-d Fourier transform of a sequence(cont.)How is the Fourier transform of a sequence sk related to the Fourier transform of the continuous signalImage transform no.3 Continuous-time Fourier transform第3页/共29页第三页，共29页。1-d Fourier tran
3、sform demo1-d Fourier transform demoImage transform no.5第4页/共29页第四页，共29页。1-d Fourier transform example1-d Fourier transform exampleImage transform no.4第5页/共29页第五页，共29页。2D base wave function2D base wave functionImage transform no.6第6页/共29页第六页，共29页。2D base wave function2D base wave functionImage trans
4、form no.7第7页/共29页第七页，共29页。2-d Fourier transform of a digital image2-d Fourier transform of a digital image Given a 2-d matrix of image samples:f(x,y),x,yZ2Fourier transformImage transform no.8 Fourier transform is 2-periodic both in u and v.Inverse Fourier transform第8页/共29页第八页，共29页。2-d Fourier trans
5、form of a digital image(cont.)2-d Fourier transform of a digital image(cont.)How is the Fourier transform of sm,n related to the Fourier transform of the continuous signalImage transform no.9 Continuous-space 2-d Fourier transform第9页/共29页第九页，共29页。Examples of 2D Fourier transformExamples of 2D Fourie
6、r transformImage transform no.10第10页/共29页第十页，共29页。Examples of 2D Fourier transformExamples of 2D Fourier transformImage transform no.11第11页/共29页第十一页，共29页。Examples of 2D Fourier transformExamples of 2D Fourier transformImage transform no.12第12页/共29页第十二页，共29页。Filtering examplesFiltering examplesImage
7、transform no.13第13页/共29页第十三页，共29页。Transfer function 5x5 lowpass filterTransfer function 5x5 lowpass filterImage transform no.14第14页/共29页第十四页，共29页。Filtering ExamplesFiltering ExamplesImage transform no.15第15页/共29页第十五页，共29页。Filtering ExamplesFiltering ExamplesImage transform no.16第16页/共29页第十六页，共29页。Fi
8、ltering ExamplesFiltering ExamplesImage transform no.17第17页/共29页第十七页，共29页。Transfer function high-pass filterTransfer function high-pass filterImage transform no.18第18页/共29页第十八页，共29页。Filtering ExamplesFiltering ExamplesImage transform no.19第19页/共29页第十九页，共29页。Properties of 2D Fourier Transform:Propert
9、ies of 2D Fourier Transform:SeparableSeparablethe discrete Fourior transform can be expressed in separate form,thus can be obtained in two steps by successive applications of 1D FFT.(So is its inverse)Image transform no.20How x or y?第20页/共29页第二十页，共29页。Properties of 2D Fourier Transform:Properties of
10、 2D Fourier Transform:TranslationTranslation the translation properties of the Fourier transform pair areImage transform no.21and,(a shift in f(x,y)does not affect the magnitude of its FT)Note an import application here,to move the origin to the center,第21页/共29页第二十一页，共29页。Properties of 2D Fourier Tr
11、ansform:Properties of 2D Fourier Transform:Periodicity and Conjugate Periodicity and Conjugate SymmetrySymmetry The discrete Fourier transform and its inverse are periodic with period N,Image transform no.22If f(x,y)is real,the Fourier transform also exhibits conjugate Symmetry:Or,more interestingly
12、,which means that the magnitude of the transform is centered on origin,calculating half of the transform can determine whole.第22页/共29页第二十二页，共29页。Properties of 2D Fourier Transform:Properties of 2D Fourier Transform:RotationRotation polar coordinatesImage transform no.23then f(x,y)and F(u,v)become f(
13、r,q )and F(w,),respectivelyThat is rotating f(x,y)by angle rotates the F(u,v)by the same angle,vice versa 第23页/共29页第二十三页，共29页。Properties of 2D Fourier TransformProperties of 2D Fourier Transform DistributivesDistributives From the definition of the Fourier transformImage transform no.24in general,第2
14、4页/共29页第二十四页，共29页。Properties of 2D Fourier Transform:Properties of 2D Fourier Transform:ScalingScalingImage transform no.25For two scalars a and b,第25页/共29页第二十五页，共29页。Properties of 2D Fourier Transform:Properties of 2D Fourier Transform:Average ValueAverage ValueImage transform no.26The average valu
15、e of 2D discrete function is defined as,From 2D Fourier transform definition,when u=0 and v=0,Therefore,第26页/共29页第二十六页，共29页。Review Questionsn nExplain image frequencyExplain image frequencyn nWhat is Separable Property of 2D Fourier Transform?What is Separable Property of 2D Fourier Transform?n nWhat is Rotation Property of 2D Fourier Transform?What is Rotation Property of 2D Fourier Transform?第27页/共29页第二十七页，共29页。Recommended ReadingRecommended Reading Gonzalez+Woods:Chapter 6 Image transform no.27第28页/共29页第二十八页，共29页。感谢您的观看感谢您的观看(gunkn)！第29页/共29页第二十九页，共29页。