数字图像处理冈萨雷斯N11PPT课件

1、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

2、 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,),(*),(),(yxfyxhyxg),(),(),(vuFvuHvuGG, H, F : the F

3、ourier transforms of g, h and f, respectively.H(u,v) : called the transfer function.),(),(),(1vuFvuHyxgg(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 n

4、o. 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

5、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

6、(ILPF) is,),( if0),( if1),(00DvuDDvuDvuH2/122)(),(vuvuDNo 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,),(1010MuNvTvu

7、PPTuvPvuP00),(100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 ILPFFr

8、equency 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,nDvuDvuH20/ ),(11),(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 1BLPF Frequ

9、ency 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 GLPF222/ ),(),(vuDevuHBoth 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

10、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) ,),( if1),( if0),(00DvuDDvuDvuHButterworth filter (BHPF) nvuDDvuH20),(/

11、11),(Gaussion filter (BHPF) 222/ ),(1),(vuDevuHFrequency 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

12、 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 filter),(),(),( : tenhancemen Image),()(),(),(22222yxfyxfyxgvuFvuyxfyxfFrequency Filtering no. 27第27页/共35页Results of High-boost filter),(),(),(2yxfyxfyxgFrequency Filteri

13、ng no. 28第28页/共35页Results of High-boost filter),() 1(),(),(1),(),(),() 1(),(),(),(),(vuHAvuHvuHvuHyxfyxfAyxfyxfyxfyxfhphblphphphblphpFrequency 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 modelSuppose),(),(

14、),(yxryxiyxf),(ln),(ln),(ln),(yxryxiyxfyxzThen, Fourier transform),(),(),(vuRvuIvuZProcess by filter function H(u,v), yields),(),(),(),(),(),(),(vuRvuHvuIvuHvuZvuHvuSIn spatial domain),( ),( ),(yxryxiyxsThe desired enhanced image),( exp),( exp),(exp),(yxryxiyxsyxgFrequency 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 Fil