數(shù)字圖像處理岡薩雷斯N11PPT課件

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頁/共35頁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頁/共35頁Review of Frequency Domain Methods(cont.1)Frequency Filtering no. 3第3頁/共35頁Review of Frequency Domain Methods(cont.2)Frequency Filtering n

4、o. 4第4頁/共35頁Review of Frequency Domain Methods(cont.3)Frequency Filtering no. 5第5頁/共35頁Review of Frequency Domain Methods(cont.4)Frequency Filtering no. 6第6頁/共35頁Review of Frequency Domain Methods(cont.5)Frequency Filtering no. 7Frequency domain for experimentSpatial domain for implementation第7頁/共35

5、頁Lowpass FilteringFrequency Filtering no. 8Ideal Lowpass Filter (ILPF)Butterworth filter (BLPF)Gaussion filter (GLPF)第8頁/共35頁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頁/共35頁P(yáng)erformance measurementFrequency Filtering no. 10Compare the power by the same cutoff frequency loci. The total power,),(1010MuNvTvu

7、PPTuvPvuP00),(100第10頁/共35頁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頁/共35頁Illustration of blurring and ringing properties of ILPFFr

8、equency Filtering no. 12Frequency/SpaceHow implement?第12頁/共35頁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頁/共35頁Examples of ILPF and BLPF(a)Original image 12-gray-level(b)ILPF(c) Order 1BLPF Frequ

9、ency Filtering no. 14第14頁/共35頁Spatial representations of BLPFsFrequency Filtering no. 15第15頁/共35頁Gaussian filter (GLPF)The transfer function of the GLPF222/ ),(),(vuDevuHBoth Gaussian, No ringing phenomenaFrequency Filtering no. 16第16頁/共35頁Examples of BLPF and GLPFFrequency Filtering no. 17?第17頁/共35

10、頁Examples of GLPFFrequency Filtering no. 18?第18頁/共35頁Examples of GLPFFrequency Filtering no. 19?第19頁/共35頁Examples of GLPFFrequency Filtering no. 20Remain the most significant feature第20頁/共35頁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頁/共35頁Highpass Filtering(cont)Frequency Filtering no. 22第22頁/共35頁Spatial representations of IHPF, BHPF, GHPFFrequency Filtering no. 23第23頁/共35頁Results of IHPFsFrequency Filtering no. 24第24頁/共35頁Results of BHPFsFrequency

12、 Filtering no. 25第25頁/共35頁Results of GHPFsFrequency Filtering no. 26第26頁/共35頁Frequency & Spatial representations of Laplacian filter),(),(),( : tenhancemen Image),()(),(),(22222yxfyxfyxgvuFvuyxfyxfFrequency Filtering no. 27第27頁/共35頁Results of High-boost filter),(),(),(2yxfyxfyxgFrequency Filteri

13、ng no. 28第28頁/共35頁Results of High-boost filter),() 1(),(),(1),(),(),() 1(),(),(),(),(vuHAvuHvuHvuHyxfyxfAyxfyxfyxfyxfhphblphphphblphpFrequency Filtering no. 29第29頁/共35頁Results of High-boost filterFrequency Filtering no. 30第30頁/共35頁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頁/共35頁Homomorphing Filtering(cont)Illuminationlow frequency, reflectance high frequency.Choose H(u,v) affects low and high component differently.Frequency Filtering no. 32第32頁/共35頁Homomorphing Fil