电子转发女学光电科学与工程学院 SCHOOL OF OPTOELECTRONIC SCIENCE AND ENGINEERING OF UESTC 1.Mean Filters ■Degradation model:: 8(x,)=f(x,)+7x,y) To remove this part Arithmetic mean filter or moving average filter fxw=1∑gs,0 mn (s,t)eSx Geometric mean filter: icxw-Πg0 mn 、(s,t)eS mn size of moving window
1. Mean Filters ◼ Arithmetic mean filter or moving average filter = xy s t S g s t mn f x y ( , ) ( , ) 1 ( , ) ˆ ◼ Geometric mean filter： mn s t Sxy f x y g s t 1 ( , ) ( , ) ( , ) ˆ = mn = size of moving window ◼ Degradation model: g x y f x y x y ( , ) ( , ) ( , ) = + To remove this part
电子科发女学光电科学与工程学院 SCHOOL OF OPTOELECTRONIC SCIENCE AND ENGINEERING OF UESTC Example-Mean Filters ab cd FIGURE 5.7 (a)X-ray image. (b)Image corrupted by additive Gaussian noise.(c)Result of filtering with an arithmetic mean filter of size 3 x 3.(d)Result of filtering with a geometric mean filter of the same size. (Original image courtesy of Mr. Joseph E. Pascente.Lixi. Inc.)
Example - Mean Filters
电子转发女学光电科学与工程学院 SCHOOL OF OPTOELECTRONIC SCIENCE AND ENGINEERING OF UESTC 1.Mean Filters Harmonic mean filter f(x,)=mn】 Works well for salt noise but fails for pepper noise Contraharmonic mean filter mn size of moving window ∑g(s,)2+ Positive O is suitable for f(x,y)= (s,t)ESx ∑g(s,t)9 eliminating pepper noise. Negative O is suitable for (s,t)ESxy eliminating salt noise. O=the filter order For O=0,the filter reduces to an arithmetic mean filter. For O=-1,the filter reduces to a harmonic mean filter
◼ Harmonic mean filter ( , ) 1 ˆ ( , ) ( , ) xy s t S f x y mn g s t = ◼ Contraharmonic mean filter + = xy xy s t S Q s t S Q g s t g s t f x y ( , ) ( , ) 1 ( , ) ( , ) ( , ) ˆ Works well for salt noise but fails for pepper noise mn = size of moving window Positive Q is suitable for eliminating pepper noise. Negative Q is suitable for eliminating salt noise. Q = the filter order For Q = 0, the filter reduces to an arithmetic mean filter. For Q = -1, the filter reduces to a harmonic mean filter. 1. Mean Filters
电子科线女学光电科学与工程学院 SCHOOL OF OPTOELECTRONIC SCIENCE AND ENGINEERING OF UESTC Example-Mean Filters cd FIGURE 5.8 (a)Image corrupted by pepper noise with a probability of 0.1.(b)Image corrupted by salt noise with the same probability. (c)Result of filtering (a)with a 3 x 3 contra- harmonic filter of order 1.5. (d)Result of filtering (b)with 0=-1.5. :
Example - Mean Filters
电子科发女学光电科学与工程学院 SCHOOL OF OPTOELECTRONIC SCIENCE AND ENGINEERING OF UESTC Example-Contraharmonic Filters ab FIGURE 5.9 Results of select- ing the wrong sign in contraharmonic filtering. (a)Result of filtering Fig.5.8(a)with a contraharmonic filter of size 3 x 3 andQ=-1.5. (b)Result of filtering 5.8(b) with O 1.5. DEMO
Example - Contraharmonic Filters DEMO