数字图像处理冈萨雷斯N11.pptx
Image Enhancement in the Frequency DomainReview of Frequency Domain MethodsLowpass FilteringHighpass FilteringHomomorphic FilteringFrequency Filtering no.1 linear filtering is more intuitive in the frequency domain.small spatial masks are used more often,in practice.understanding of the frequency domain concepts is essential to the solutions of many problems not easily addressed by spatial techniques.第1页/共35页Review of Frequency Domain MethodsFrequency Filtering no.2The foundation of frequency domain techniques is the convolution theorem,G,H,F:the Fourier transforms of g,h and f,respectively.H(u,v):called the transfer function.g(x,y)exhibits some highlighted feature of f(x,y).第2页/共35页Review of Frequency Domain Methods(cont.1)Frequency Filtering no.3第3页/共35页Review of Frequency Domain Methods(cont.2)Frequency Filtering no.4第4页/共35页Review of Frequency Domain Methods(cont.3)Frequency Filtering no.5第5页/共35页Review of Frequency Domain Methods(cont.4)Frequency Filtering no.6第6页/共35页Review of Frequency Domain Methods(cont.5)Frequency Filtering no.7Frequency domain for experimentSpatial domain for implementation第7页/共35页Lowpass FilteringFrequency Filtering no.8Ideal Lowpass Filter(ILPF)Butterworth filter(BLPF)Gaussion filter(GLPF)第8页/共35页Ideal Lowpass Filter(ILPF)Frequency Filtering no.9Blurring is achieved in frequency domain by attenuating a specified range of high-frequency components.Thus,ideal filter(ILPF)isNo attenuation insider a circle,but all frequency outside the circle is attenuated.Radically symmetric.第9页/共35页Performance measurementFrequency Filtering no.10Compare the power by the same cutoff frequency loci.The total power,第10页/共35页Examples of ILPFBlurring&Ringing:Radius increase,less high-frequency removed,less blurring.However,even with 3.6%off,the blurring is still characterized by severe ringingFrequency Filtering no.11第11页/共35页Illustration of blurring and ringing properties of ILPFFrequency Filtering no.12Frequency/SpaceHow implement?第12页/共35页Butterworth filter(BLPF)The transfer function of the BLPF of order n and with cutoff frequency D0,Frequency Filtering no.13第13页/共35页Examples of ILPF and BLPF(a)Original image 12-gray-level(b)ILPF(c)Order 1BLPFFrequency Filtering no.14第14页/共35页Spatial representations of BLPFsFrequency Filtering no.15第15页/共35页Gaussian filter(GLPF)The transfer function of the GLPFBoth Gaussian,No ringing phenomenaFrequency Filtering no.16第16页/共35页Examples of BLPF and GLPFFrequency Filtering no.17?第17页/共35页Examples of GLPFFrequency Filtering no.18?第18页/共35页Examples of GLPFFrequency Filtering no.19?第19页/共35页Examples of GLPFFrequency Filtering no.20Remain the most significant feature第20页/共35页Highpass FilteringIdeal filter(IHPF)Butterworth filter(BHPF)Gaussion filter(BHPF)Frequency Filtering no.21H=1-L第21页/共35页Highpass Filtering(cont)Frequency Filtering no.22第22页/共35页Spatial representations of IHPF,BHPF,GHPFFrequency Filtering no.23第23页/共35页Results of IHPFsFrequency Filtering no.24第24页/共35页Results of BHPFsFrequency Filtering no.25第25页/共35页Results of GHPFsFrequency Filtering no.26第26页/共35页Frequency&Spatial representations of Laplacian filterFrequency Filtering no.27第27页/共35页Results of High-boost filterFrequency Filtering no.28第28页/共35页Results of High-boost filterFrequency Filtering no.29第29页/共35页Results of High-boost filterFrequency Filtering no.30第30页/共35页Homomorphing FilteringThe illumination-reflectance modelSupposeThen,Fourier transformProcess by filter function H(u,v),yieldsIn spatial domainThe desired enhanced imageFrequency Filtering no.31第31页/共35页Homomorphing Filtering(cont)Illuminationlow frequency,reflectance high frequency.Choose H(u,v)affects low and high component differently.Frequency Filtering no.32第32页/共35页Homomorphing Filtering(example)Frequency Filtering no.33The net result is simultaneous dynamic range compression and contrast enhancement.第33页/共35页Recommended Reading Gonzalez+Woods:Chapter 4 Frequency Filtering no.34第34页/共35页感谢您的观看！第35页/共35页
