V d bin i Fourier trong matlab: Cho nh f c gi tr tng ng sau:
f(0) = 2,f(1) = 4,f(2) = 6,f(3) = 0 tm bin i Fourier ri rc ca dy:
matlab: c vo gi tr tng ng ca f: >> f = [2 4 6 0]; Thc hin bin
i Fourier: >> F = ifft(f1) Kt qu thu c nh sau: F1 = 3.2500
-0.5000 - 0.2500i -0.2500 Bin i Fourier ri rc ngc: Cho F(0) = 2i,
F(1) = 4i,F(2) = 6i,F(3) = 8i. Tnh bin i Fourier ri rc ngc. Matlab:
>> F = [2i 4i 6i 8i] F= 0 + 2.0000i >> f = fft(F) Kt qu
thu c nh sau: f= 0 +20.0000i -4.0000 - 4.0000i
-0.5000 + 0.2500i
0 + 4.0000i
0 + 6.0000i
0 + 8.0000i
0 - 4.0000i 4.0000 - 4.0000i
V d 5: c vo mt nh: >> f = imread('cameraman.tif'); Thc hin
php bin i Fourier hai chiu: >> F = fft2(f); Ph Fourier ca nh
l: >> SF = abs(F); Gc pha: >> pha = angle(F); Hin th ph
Fourier ca nh: >> g = log(1+abs(fftshift(F))); >>
imshow(g,[]) Hm ifft2 (bin i Fourier ri rc ngc hai chiu): >>
fn = ifft2(F); >> imshow(fn)
hm ifftshift a im v tr trung tm v gc bn tri trn cng ca ph:
>>ft= ifftshift(F); Gi nguyn gc pha, thay i ph ca nh:
>> G1 = 100 *exp(i*pha); >> f1 = ifft2(G1); Gi nguyn
ph, thay i gc pha ca nh: >> G2 = SF*exp(i*100); >> f2 =
ifft2(G2); Kt qu thu c nh sau: >>
imshow(f1),figure,imshow(f2)
lm sc nt nh vi mt n w nh sau: >> A = 1; >> w =
[-1,-1,-1,-1,A+8,-1,-1,-1,-1]; >> a =imread('rice.png');
>> b = filter2(w,p); >> imshow(p), figure,
imshow(a/255)
nh gc
nh lm sc nt
Vi A = 1.7, sc nt ca nh gim dn:
Ngoi ra ta c th s dng mt n unsharp lm sc nt nh. V d: >> a
= imread('tire.tif'); >> u = fspecial('unsharp',0.5);
>> au = filter2(u,a); >>
imshow(a),figure,imshow(au/255)
nh gc
After unsharp masking
ng dng khc ca b lc ngc: Lm r nh m do chuyn ng: >> >>
>> >> bc = imread('board.tif'); bg =
im2uint8(rgb2gray(bc)); b = bg(100:355,50:305); m =
fspecial('motion',7,0);
>> bm = imfilter(b,m); >> imshow(bm)
lm r nh ta cn thc hin gia php chia DFT ca nh m cho DFT ca b lc
lm m nh. Trc tin cn to ma trn tng ng vi s bin i lm m nh: >>
m2 = zeros(256,256); >>m2(1,1:7) = m; >>mf = fft2(m2);
>>bmi = ifft2(fft2(bm)./mf); >> imshow(bm),figure,
fftshow(bmi,'abs') Kt qu khng c tt do c tnh ca b lc ngc:
khc phc c tnh ca b lc ngc, ta s dng mt ngng ( trnh chia cho 0):
>> d = 0.02; >> mf = fft2(m2); >>
mf(find(abs(mf)> bmi = ifft2(fft2(bm)./mf); >>
imshow(mat2gray(abs(bmi))*2)
Lc thng thp: u tin ta c vo mt nh: >>cm =
imread('cameraman.tif'); Dch chuyn ph v trung tm ca nh v hin th n:
>>cf = fftshift(fft2(cm)); >> fftshow(cf,'log')
Tip n to mt hnh trn (khot l): >>[x,y] =
meshgrid(-128:127,-128:127); >>z = sqrt(x.^2+y.^2); ivi z
>15 th c nhn gi tr 0, ngc li c nhn gi tr 1: >>c =
(z>cfl = cf.*c; >> fftshow(cfl,'log')
Bin i Fourier ngc hin th nh ban u v hin th nh : >>cfli =
ifft2(cfl); >>figure,fftshow(cfli,'log')
Nhiu: cng nhiu Salt and pepper vo mt nh ta dng cu lnh sau:
>>t = imnoise(image,salt & pepper) S lng nhiu cng vo c mc
nh l 10%. Ta c th cung cp thm cc thng s thay i lng nhiu c cng vo
ny. c vo mt nh: >> a = imread('autumn.tif'); Thm nhiu mui v
tiu vo nh, vi 10% nhiu cng vo: >> b= imnoise(a,'salt &
pepper'); Xa nhiu mui tiu vi lc trung bnh: Thc hin trong matlab bng
lnh: >>w = fspecial(average,[m,n]) >>f = imfilter(g,w)
p dng loi b nhiu mui v tiu: chuyn nh mu sang nh gi tr xm: >>
a = rgb2gray(a); To mt n lc trung bnh 3x3: >> a1 =
fspecial('average'); Lc nh vi mt n trung bnh 3x3: >> b1 =
filter2(a1,b); >> imshow(b1,[]) To mt n trung bnh 7x7:
>> a1 = fspecial('average',[7,7]); Lc nh vi mt n trung bnh
7x7: >> b1 = filter2(a1,b); >> imshow(b1,[]) S dng lc
trung v xa nhiu mui tiu: p dng loi b nhiu mui v tiu vi mt n lc mc
nh l 3x3: >> b2 = medfilt2(a); >> imshow(b2)
Vi mt n 5x5, nhiu c loi b nhiu hn: >> b3 = medfilt2(a,[5
5]); Nhiu tun hon: >> a = imread('cameraman.tif'); To ma trn
tun hon: >> [x y] = meshgrid(1:256,1:256); >> p =
sin(x+y/1.5)+1; Cng vo nh ma trn tun hon: >> ap =
(double(a)/128+p)/4; Dch ph v trung tm ca nh: >> cpf =
fftshift(fft2(ap)) Hin th nh: >>
imshow(ap,[]),figure,imshow(log(abs(cpf)+1),[]),pixval on
nhiu tun hon
ph nh
Kh nhiu tun hon: 1. S dng lc Band Reject: S dng mt mt n hnh trn
br c bn knh bn trong hnh l z. C gi tr cc pixels bn trong hnh trn l
1 v gi tr cc pixels trn bin l 0. ng bin phi c dy ln che c cc im
nhiu. To nhiu tun hon: >> [x,y] = meshgrid(1:256,1:256);
>> s = 1+sin(x+y/1.5); c vo mt nh: >> cm =
imread('cameraman.tif'); >> cp = (double(cm)/128+s)/4; Dch ph
v trung tm ca nh: >> cpf = fftshift(fft2(cp));
>> fftshow(cpf,'log'),pixval on Chng ta s xa nhng thnh phn
tng t bin v tr ngc li kt qu. t pixval on v di chuyn xung quanh nh,
chng ta tm thy nhng hng, ct c gi tr tng t bin l (156,170) v
(102,88). >> [x,y] = meshgrid(-128:127,-128:127); >> z
= sqrt(x.^2+y.^2); Khong cch t t ti trung tm ca nh l 49.0918:
>> z(156,170) ans = 49.0918 >> z(102,88) ans = 49.0918
Chng ta to ra mt lc vi br = 1 nu (z51) v ngc li bng 0 (gia vng trn
nh v vng trn ln): >> br = (z51); Thc hin php nhn bi bin i:
>> SF = fftshift(fft2(cp)); >> tbr = SF.*br; >>
figure,fftshow(tbr,'log') Bin i Fourier ngc ta c: >> tbri
=ifft2(tbr); >> figure,fftshow(tbri,'log')
A band-reject filter2.
After inversion
S dng b lc Notch:
S dng cc ng k ngang v ng k dc che cc im nhiu sao cho giao ca cc
ng k ny c th che c cc im nhiu.
To nhiu tun hon >> [x,y] = meshgrid(1:256,1:256); >>
s = sin(x+y/1.5)+1; c vo nh cameraman: >> f =
imread('cameraman.tif'); Dch ph v trung tm ca nh: >> F =
fftshift(fft2(a)); >> sf = (double(f)/128+s)/4; >> SF =
fftshift(fft2(sf)); >>
fftshow(F,'log'),figure,fftshow(SF,'log')
F
SF
n gin l cho hng v ct ca thnh phn ph nhiu bng 0. Gi s ta ca cc
thnh phn nhiu ny ln lt l (156,170), (102,88). >> SF(156,:) =
0; >> SF(102,:) = 0; >> SF(:,88) = 0; >>
SF(:,170) = 0; >> figure,fftshow(SF,'log') Bin i Fourier ngc
ta thu c nh ban u: >> ln =ifft2(SF); >>
fftshow(ln,'log')
SF
ln
Nhiu nhiu trung tm b loi b. To nhiu hng v ct dch chuyn v v tr
nhiu s loi b c nhiu nhiu hn.
Pht hin ng bin, bin ngang, bin dc: c vo mt nh: >>ic =
imread('circuit.tif'); Pht hin ng bin ng: >>px = [-1 0 1;-1 0
1;-1 0 1]; Tnh p ng mt n px vi nh ic: >>icx = filter2(px,ic);
>>figure,imshow(icx/255)
Pht hin ng bin ngang: py= px';% chuyen vi ca px Tnh p ng mt n py
vi nh ic: icy = filter2(py,ic); figure,imshow(icy/255)
Kt hp lc ng bin ngang, bin dc: Gi px l kt qu ca lc ng bin song
song vi trc oy. Gi py l kt qu ca lc ng bin song song vi trc ox.
Gi p l kt qu tng hp, c gi tr bng:
p2 + p2 x y
>>edge_p = sqrt(icx.^2+icy.^2);
>>figure,imshow(edge_p/255) C2: s dng hm edge: G lnh help
edge
Php dn: Trong matlab g lnh: >>imdilate(image,kernel ) Vi
image l nh nh phn hoc nh mc xm cn gin, kernel l nh nhn hay phn t cu
trc. V d: >> t = imread('text.png'); To phn t cu trc sq:
>> sq = ones(3,3); Gin nh t theo phn t cu trc sq: >> td
= imdilate(t,sq);
nh gc
nh sau khi gin
php co: Trong matlab thc hin lnh: >> imerode (image,kernel
) Vi image l nh nh phn hoc nh mc xm cn co, kernel l nh nhn hay phn
t cu trc. V d: >> c = imread('text.png'); Thc hin php co theo
phn t cu trc sq:
>> ce = imerode(c,sq);
nh gc
nh co
ng dng php dn v co l: pht hin bin. V d: To nh nh phn da vo ngng
xm T: >> rice = imread('rice.png'); >> r = rice >
110; Co nh theo phn t cu trc sq: >> re = imerode(r,sq); Hin
th ng bin ca nh theo php hiu: >> r_int = r &~re;
nh gc r
bin nh r_int
